VS Project 20180209.ipynb

{
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  {
   "cell_type": "code",
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   },
   "outputs": [],
   "source": [
    "# Project Goal: Create an open source which could provide simulation data and use Anchor to validate the model\n",
    "\n",
    "# Details:\n",
    "# 1. Components\n",
    "\n",
    "# 2. Data Table:\n",
    "# For example: clothes\n",
    "# -> Product: product id, price, color, size, amount   \n",
    "# -> Inventory: shop id, product id, amount, \n",
    "# -> customer: age, membership, product id\n",
    "# -> promotion/discount: rate, product id, expiration date\n",
    "# -> session\n",
    "\n",
    "# Data Model\n",
    "# Find the initial Model for the data table (Joint distribution)\n",
    "# Consider the relationship between tables\n",
    "# Decide what distributions they would be.\n",
    "\n",
    "# 3. Be simulate \n",
    "# -> Data Table (Could be demonstrated)\n",
    "# -> graphical model\n",
    "\n",
    "# 4. Anchor "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
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     "data": {
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       "<table>\n",
       "<thead><tr><th scope=col>p.id</th><th scope=col>category</th><th scope=col>price</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1         </td><td>3          </td><td>   7.942982</td></tr>\n",
       "\t<tr><td> 2         </td><td>3          </td><td>   1.788077</td></tr>\n",
       "\t<tr><td> 3         </td><td>3          </td><td>  39.377804</td></tr>\n",
       "\t<tr><td> 4         </td><td>3          </td><td>  13.219627</td></tr>\n",
       "\t<tr><td> 5         </td><td>2          </td><td>  57.627238</td></tr>\n",
       "\t<tr><td> 6         </td><td>1          </td><td> 788.556183</td></tr>\n",
       "\t<tr><td> 7         </td><td>1          </td><td>2607.861722</td></tr>\n",
       "\t<tr><td> 8         </td><td>2          </td><td>  56.109517</td></tr>\n",
       "\t<tr><td> 9         </td><td>3          </td><td>  24.081814</td></tr>\n",
       "\t<tr><td>10         </td><td>3          </td><td>   3.747159</td></tr>\n",
       "\t<tr><td>11         </td><td>1          </td><td> 185.018350</td></tr>\n",
       "\t<tr><td>12         </td><td>1          </td><td> 237.503873</td></tr>\n",
       "\t<tr><td>13         </td><td>3          </td><td>  27.641612</td></tr>\n",
       "\t<tr><td>14         </td><td>1          </td><td> 586.288687</td></tr>\n",
       "\t<tr><td>15         </td><td>2          </td><td>  25.669882</td></tr>\n",
       "\t<tr><td>16         </td><td>2          </td><td> 134.185519</td></tr>\n",
       "\t<tr><td>17         </td><td>2          </td><td>  44.514248</td></tr>\n",
       "\t<tr><td>18         </td><td>2          </td><td>  11.270654</td></tr>\n",
       "\t<tr><td>19         </td><td>1          </td><td>  62.300608</td></tr>\n",
       "\t<tr><td>20         </td><td>3          </td><td>  37.651465</td></tr>\n",
       "\t<tr><td>21         </td><td>2          </td><td>  86.193032</td></tr>\n",
       "\t<tr><td>22         </td><td>1          </td><td>1159.333877</td></tr>\n",
       "\t<tr><td>23         </td><td>3          </td><td>  20.910624</td></tr>\n",
       "\t<tr><td>24         </td><td>3          </td><td>  29.419364</td></tr>\n",
       "\t<tr><td>25         </td><td>2          </td><td>  45.449964</td></tr>\n",
       "\t<tr><td>26         </td><td>2          </td><td>  38.585579</td></tr>\n",
       "\t<tr><td>27         </td><td>3          </td><td>  20.772515</td></tr>\n",
       "\t<tr><td>28         </td><td>2          </td><td>  65.182216</td></tr>\n",
       "\t<tr><td>29         </td><td>1          </td><td>1188.666282</td></tr>\n",
       "\t<tr><td>30         </td><td>2          </td><td>  12.392863</td></tr>\n",
       "\t<tr><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><td> 971      </td><td>2         </td><td>  10.01290</td></tr>\n",
       "\t<tr><td> 972      </td><td>3         </td><td>  17.53273</td></tr>\n",
       "\t<tr><td> 973      </td><td>3         </td><td>  38.19352</td></tr>\n",
       "\t<tr><td> 974      </td><td>3         </td><td>  33.65421</td></tr>\n",
       "\t<tr><td> 975      </td><td>2         </td><td> 108.61815</td></tr>\n",
       "\t<tr><td> 976      </td><td>2         </td><td>  65.68590</td></tr>\n",
       "\t<tr><td> 977      </td><td>2         </td><td>  69.18561</td></tr>\n",
       "\t<tr><td> 978      </td><td>2         </td><td>  54.77927</td></tr>\n",
       "\t<tr><td> 979      </td><td>2         </td><td>  75.22595</td></tr>\n",
       "\t<tr><td> 980      </td><td>3         </td><td>  38.85027</td></tr>\n",
       "\t<tr><td> 981      </td><td>1         </td><td> 902.49225</td></tr>\n",
       "\t<tr><td> 982      </td><td>2         </td><td> 116.31913</td></tr>\n",
       "\t<tr><td> 983      </td><td>3         </td><td>  55.10993</td></tr>\n",
       "\t<tr><td> 984      </td><td>3         </td><td>  57.18203</td></tr>\n",
       "\t<tr><td> 985      </td><td>2         </td><td>  88.64193</td></tr>\n",
       "\t<tr><td> 986      </td><td>2         </td><td>  57.62724</td></tr>\n",
       "\t<tr><td> 987      </td><td>1         </td><td> 546.99022</td></tr>\n",
       "\t<tr><td> 988      </td><td>3         </td><td>  33.94551</td></tr>\n",
       "\t<tr><td> 989      </td><td>2         </td><td>  56.10952</td></tr>\n",
       "\t<tr><td> 990      </td><td>1         </td><td> 355.85080</td></tr>\n",
       "\t<tr><td> 991      </td><td>2         </td><td>  47.29364</td></tr>\n",
       "\t<tr><td> 992      </td><td>1         </td><td>1035.36531</td></tr>\n",
       "\t<tr><td> 993      </td><td>1         </td><td>1099.49189</td></tr>\n",
       "\t<tr><td> 994      </td><td>2         </td><td>  73.77610</td></tr>\n",
       "\t<tr><td> 995      </td><td>1         </td><td>1159.40244</td></tr>\n",
       "\t<tr><td> 996      </td><td>3         </td><td>  31.45153</td></tr>\n",
       "\t<tr><td> 997      </td><td>2         </td><td> 134.18552</td></tr>\n",
       "\t<tr><td> 998      </td><td>1         </td><td> 121.86442</td></tr>\n",
       "\t<tr><td> 999      </td><td>2         </td><td>  11.27065</td></tr>\n",
       "\t<tr><td>1000      </td><td>1         </td><td> 860.60195</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " p.id & category & price\\\\\n",
       "\\hline\n",
       "\t  1          & 3           &    7.942982\\\\\n",
       "\t  2          & 3           &    1.788077\\\\\n",
       "\t  3          & 3           &   39.377804\\\\\n",
       "\t  4          & 3           &   13.219627\\\\\n",
       "\t  5          & 2           &   57.627238\\\\\n",
       "\t  6          & 1           &  788.556183\\\\\n",
       "\t  7          & 1           & 2607.861722\\\\\n",
       "\t  8          & 2           &   56.109517\\\\\n",
       "\t  9          & 3           &   24.081814\\\\\n",
       "\t 10          & 3           &    3.747159\\\\\n",
       "\t 11          & 1           &  185.018350\\\\\n",
       "\t 12          & 1           &  237.503873\\\\\n",
       "\t 13          & 3           &   27.641612\\\\\n",
       "\t 14          & 1           &  586.288687\\\\\n",
       "\t 15          & 2           &   25.669882\\\\\n",
       "\t 16          & 2           &  134.185519\\\\\n",
       "\t 17          & 2           &   44.514248\\\\\n",
       "\t 18          & 2           &   11.270654\\\\\n",
       "\t 19          & 1           &   62.300608\\\\\n",
       "\t 20          & 3           &   37.651465\\\\\n",
       "\t 21          & 2           &   86.193032\\\\\n",
       "\t 22          & 1           & 1159.333877\\\\\n",
       "\t 23          & 3           &   20.910624\\\\\n",
       "\t 24          & 3           &   29.419364\\\\\n",
       "\t 25          & 2           &   45.449964\\\\\n",
       "\t 26          & 2           &   38.585579\\\\\n",
       "\t 27          & 3           &   20.772515\\\\\n",
       "\t 28          & 2           &   65.182216\\\\\n",
       "\t 29          & 1           & 1188.666282\\\\\n",
       "\t 30          & 2           &   12.392863\\\\\n",
       "\t ... & ... & ...\\\\\n",
       "\t  971       & 2          &   10.01290\\\\\n",
       "\t  972       & 3          &   17.53273\\\\\n",
       "\t  973       & 3          &   38.19352\\\\\n",
       "\t  974       & 3          &   33.65421\\\\\n",
       "\t  975       & 2          &  108.61815\\\\\n",
       "\t  976       & 2          &   65.68590\\\\\n",
       "\t  977       & 2          &   69.18561\\\\\n",
       "\t  978       & 2          &   54.77927\\\\\n",
       "\t  979       & 2          &   75.22595\\\\\n",
       "\t  980       & 3          &   38.85027\\\\\n",
       "\t  981       & 1          &  902.49225\\\\\n",
       "\t  982       & 2          &  116.31913\\\\\n",
       "\t  983       & 3          &   55.10993\\\\\n",
       "\t  984       & 3          &   57.18203\\\\\n",
       "\t  985       & 2          &   88.64193\\\\\n",
       "\t  986       & 2          &   57.62724\\\\\n",
       "\t  987       & 1          &  546.99022\\\\\n",
       "\t  988       & 3          &   33.94551\\\\\n",
       "\t  989       & 2          &   56.10952\\\\\n",
       "\t  990       & 1          &  355.85080\\\\\n",
       "\t  991       & 2          &   47.29364\\\\\n",
       "\t  992       & 1          & 1035.36531\\\\\n",
       "\t  993       & 1          & 1099.49189\\\\\n",
       "\t  994       & 2          &   73.77610\\\\\n",
       "\t  995       & 1          & 1159.40244\\\\\n",
       "\t  996       & 3          &   31.45153\\\\\n",
       "\t  997       & 2          &  134.18552\\\\\n",
       "\t  998       & 1          &  121.86442\\\\\n",
       "\t  999       & 2          &   11.27065\\\\\n",
       "\t 1000       & 1          &  860.60195\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "p.id | category | price | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "|  1          | 3           |    7.942982 | \n",
       "|  2          | 3           |    1.788077 | \n",
       "|  3          | 3           |   39.377804 | \n",
       "|  4          | 3           |   13.219627 | \n",
       "|  5          | 2           |   57.627238 | \n",
       "|  6          | 1           |  788.556183 | \n",
       "|  7          | 1           | 2607.861722 | \n",
       "|  8          | 2           |   56.109517 | \n",
       "|  9          | 3           |   24.081814 | \n",
       "| 10          | 3           |    3.747159 | \n",
       "| 11          | 1           |  185.018350 | \n",
       "| 12          | 1           |  237.503873 | \n",
       "| 13          | 3           |   27.641612 | \n",
       "| 14          | 1           |  586.288687 | \n",
       "| 15          | 2           |   25.669882 | \n",
       "| 16          | 2           |  134.185519 | \n",
       "| 17          | 2           |   44.514248 | \n",
       "| 18          | 2           |   11.270654 | \n",
       "| 19          | 1           |   62.300608 | \n",
       "| 20          | 3           |   37.651465 | \n",
       "| 21          | 2           |   86.193032 | \n",
       "| 22          | 1           | 1159.333877 | \n",
       "| 23          | 3           |   20.910624 | \n",
       "| 24          | 3           |   29.419364 | \n",
       "| 25          | 2           |   45.449964 | \n",
       "| 26          | 2           |   38.585579 | \n",
       "| 27          | 3           |   20.772515 | \n",
       "| 28          | 2           |   65.182216 | \n",
       "| 29          | 1           | 1188.666282 | \n",
       "| 30          | 2           |   12.392863 | \n",
       "| ... | ... | ... | \n",
       "|  971       | 2          |   10.01290 | \n",
       "|  972       | 3          |   17.53273 | \n",
       "|  973       | 3          |   38.19352 | \n",
       "|  974       | 3          |   33.65421 | \n",
       "|  975       | 2          |  108.61815 | \n",
       "|  976       | 2          |   65.68590 | \n",
       "|  977       | 2          |   69.18561 | \n",
       "|  978       | 2          |   54.77927 | \n",
       "|  979       | 2          |   75.22595 | \n",
       "|  980       | 3          |   38.85027 | \n",
       "|  981       | 1          |  902.49225 | \n",
       "|  982       | 2          |  116.31913 | \n",
       "|  983       | 3          |   55.10993 | \n",
       "|  984       | 3          |   57.18203 | \n",
       "|  985       | 2          |   88.64193 | \n",
       "|  986       | 2          |   57.62724 | \n",
       "|  987       | 1          |  546.99022 | \n",
       "|  988       | 3          |   33.94551 | \n",
       "|  989       | 2          |   56.10952 | \n",
       "|  990       | 1          |  355.85080 | \n",
       "|  991       | 2          |   47.29364 | \n",
       "|  992       | 1          | 1035.36531 | \n",
       "|  993       | 1          | 1099.49189 | \n",
       "|  994       | 2          |   73.77610 | \n",
       "|  995       | 1          | 1159.40244 | \n",
       "|  996       | 3          |   31.45153 | \n",
       "|  997       | 2          |  134.18552 | \n",
       "|  998       | 1          |  121.86442 | \n",
       "|  999       | 2          |   11.27065 | \n",
       "| 1000       | 1          |  860.60195 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     p.id category price      \n",
       "1     1   3           7.942982\n",
       "2     2   3           1.788077\n",
       "3     3   3          39.377804\n",
       "4     4   3          13.219627\n",
       "5     5   2          57.627238\n",
       "6     6   1         788.556183\n",
       "7     7   1        2607.861722\n",
       "8     8   2          56.109517\n",
       "9     9   3          24.081814\n",
       "10   10   3           3.747159\n",
       "11   11   1         185.018350\n",
       "12   12   1         237.503873\n",
       "13   13   3          27.641612\n",
       "14   14   1         586.288687\n",
       "15   15   2          25.669882\n",
       "16   16   2         134.185519\n",
       "17   17   2          44.514248\n",
       "18   18   2          11.270654\n",
       "19   19   1          62.300608\n",
       "20   20   3          37.651465\n",
       "21   21   2          86.193032\n",
       "22   22   1        1159.333877\n",
       "23   23   3          20.910624\n",
       "24   24   3          29.419364\n",
       "25   25   2          45.449964\n",
       "26   26   2          38.585579\n",
       "27   27   3          20.772515\n",
       "28   28   2          65.182216\n",
       "29   29   1        1188.666282\n",
       "30   30   2          12.392863\n",
       "...  ...  ...      ...        \n",
       "971   971 2          10.01290 \n",
       "972   972 3          17.53273 \n",
       "973   973 3          38.19352 \n",
       "974   974 3          33.65421 \n",
       "975   975 2         108.61815 \n",
       "976   976 2          65.68590 \n",
       "977   977 2          69.18561 \n",
       "978   978 2          54.77927 \n",
       "979   979 2          75.22595 \n",
       "980   980 3          38.85027 \n",
       "981   981 1         902.49225 \n",
       "982   982 2         116.31913 \n",
       "983   983 3          55.10993 \n",
       "984   984 3          57.18203 \n",
       "985   985 2          88.64193 \n",
       "986   986 2          57.62724 \n",
       "987   987 1         546.99022 \n",
       "988   988 3          33.94551 \n",
       "989   989 2          56.10952 \n",
       "990   990 1         355.85080 \n",
       "991   991 2          47.29364 \n",
       "992   992 1        1035.36531 \n",
       "993   993 1        1099.49189 \n",
       "994   994 2          73.77610 \n",
       "995   995 1        1159.40244 \n",
       "996   996 3          31.45153 \n",
       "997   997 2         134.18552 \n",
       "998   998 1         121.86442 \n",
       "999   999 2          11.27065 \n",
       "1000 1000 1         860.60195 "
      ]
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   "source": [
    "# Bullet through approach\n",
    "\n",
    "# Build n products table with one feature(category): clothes, shoes, computers\n",
    "# Assume the average price of clothes would be 100, the average price of shoes would be 200, and the average price of computer would be 4000\n",
    "\n",
    "Product.Table <- function(n_product, alpha = 2, beta = 5, clothes_price_scaling_factor= 100, shoes_price_scaling_factor = 200, computer_price_scaling_factor = 4000){\n",
    "  \n",
    "  set.seed(12345)\n",
    "  \n",
    "  category <- sample(1:3,n_product,replace=TRUE) # 3 = clothes, 2 = shoes, 1 = computer\n",
    "  p.id <- 1:n_product\n",
    "  # Assume the price will follow a beta distribution with alpha = 2, beta = 5\n",
    "  clothes.price <- clothes_price_scaling_factor * rbeta(table(category)[[3]], shape1 = alpha , shape2 = beta)\n",
    "  shoes.price <- shoes_price_scaling_factor * rbeta(table(category)[[2]], shape1 = alpha, shape2 = beta)\n",
    "  computer.price <- computer_price_scaling_factor * rbeta(table(category)[[1]], shape1 = alpha, shape2 = beta)\n",
    "  \n",
    "  # Build the data frame with the product_id column and the price column\n",
    "  price <- ifelse(category == 3, clothes.price, ifelse(category == 2, shoes.price, computer.price))\n",
    "  product <- as.data.frame(cbind(p.id, category, price))\n",
    "  product$category <- as.factor(product$category)    \n",
    "  \n",
    "  # Return the whole product table\n",
    "  return(product)\n",
    "}\n",
    "\n",
    "# Build 1000 products table with three categories: clothes, shoes, computers\n",
    "Product.Table(n = 1000)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>c.id</th><th scope=col>gender</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td>1 </td></tr>\n",
       "\t<tr><td> 2</td><td>1 </td></tr>\n",
       "\t<tr><td> 3</td><td>1 </td></tr>\n",
       "\t<tr><td> 4</td><td>1 </td></tr>\n",
       "\t<tr><td> 5</td><td>0 </td></tr>\n",
       "\t<tr><td> 6</td><td>0 </td></tr>\n",
       "\t<tr><td> 7</td><td>0 </td></tr>\n",
       "\t<tr><td> 8</td><td>1 </td></tr>\n",
       "\t<tr><td> 9</td><td>1 </td></tr>\n",
       "\t<tr><td>10</td><td>1 </td></tr>\n",
       "\t<tr><td>11</td><td>0 </td></tr>\n",
       "\t<tr><td>12</td><td>0 </td></tr>\n",
       "\t<tr><td>13</td><td>1 </td></tr>\n",
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       "\t<tr><td>20</td><td>1 </td></tr>\n",
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       "\t<tr><td>23</td><td>1 </td></tr>\n",
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       "\t<tr><td>29</td><td>0 </td></tr>\n",
       "\t<tr><td>30</td><td>0 </td></tr>\n",
       "\t<tr><td>...</td><td>...</td></tr>\n",
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       "\t<tr><td> 976</td><td>1   </td></tr>\n",
       "\t<tr><td> 977</td><td>1   </td></tr>\n",
       "\t<tr><td> 978</td><td>0   </td></tr>\n",
       "\t<tr><td> 979</td><td>1   </td></tr>\n",
       "\t<tr><td> 980</td><td>1   </td></tr>\n",
       "\t<tr><td> 981</td><td>0   </td></tr>\n",
       "\t<tr><td> 982</td><td>0   </td></tr>\n",
       "\t<tr><td> 983</td><td>1   </td></tr>\n",
       "\t<tr><td> 984</td><td>1   </td></tr>\n",
       "\t<tr><td> 985</td><td>0   </td></tr>\n",
       "\t<tr><td> 986</td><td>0   </td></tr>\n",
       "\t<tr><td> 987</td><td>0   </td></tr>\n",
       "\t<tr><td> 988</td><td>1   </td></tr>\n",
       "\t<tr><td> 989</td><td>0   </td></tr>\n",
       "\t<tr><td> 990</td><td>0   </td></tr>\n",
       "\t<tr><td> 991</td><td>1   </td></tr>\n",
       "\t<tr><td> 992</td><td>0   </td></tr>\n",
       "\t<tr><td> 993</td><td>0   </td></tr>\n",
       "\t<tr><td> 994</td><td>1   </td></tr>\n",
       "\t<tr><td> 995</td><td>0   </td></tr>\n",
       "\t<tr><td> 996</td><td>1   </td></tr>\n",
       "\t<tr><td> 997</td><td>0   </td></tr>\n",
       "\t<tr><td> 998</td><td>0   </td></tr>\n",
       "\t<tr><td> 999</td><td>0   </td></tr>\n",
       "\t<tr><td>1000</td><td>0   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " c.id & gender\\\\\n",
       "\\hline\n",
       "\t  1 & 1 \\\\\n",
       "\t  2 & 1 \\\\\n",
       "\t  3 & 1 \\\\\n",
       "\t  4 & 1 \\\\\n",
       "\t  5 & 0 \\\\\n",
       "\t  6 & 0 \\\\\n",
       "\t  7 & 0 \\\\\n",
       "\t  8 & 1 \\\\\n",
       "\t  9 & 1 \\\\\n",
       "\t 10 & 1 \\\\\n",
       "\t 11 & 0 \\\\\n",
       "\t 12 & 0 \\\\\n",
       "\t 13 & 1 \\\\\n",
       "\t 14 & 0 \\\\\n",
       "\t 15 & 0 \\\\\n",
       "\t 16 & 0 \\\\\n",
       "\t 17 & 0 \\\\\n",
       "\t 18 & 0 \\\\\n",
       "\t 19 & 0 \\\\\n",
       "\t 20 & 1 \\\\\n",
       "\t 21 & 0 \\\\\n",
       "\t 22 & 0 \\\\\n",
       "\t 23 & 1 \\\\\n",
       "\t 24 & 1 \\\\\n",
       "\t 25 & 1 \\\\\n",
       "\t 26 & 0 \\\\\n",
       "\t 27 & 1 \\\\\n",
       "\t 28 & 1 \\\\\n",
       "\t 29 & 0 \\\\\n",
       "\t 30 & 0 \\\\\n",
       "\t ... & ...\\\\\n",
       "\t  971 & 1   \\\\\n",
       "\t  972 & 1   \\\\\n",
       "\t  973 & 1   \\\\\n",
       "\t  974 & 1   \\\\\n",
       "\t  975 & 1   \\\\\n",
       "\t  976 & 1   \\\\\n",
       "\t  977 & 1   \\\\\n",
       "\t  978 & 0   \\\\\n",
       "\t  979 & 1   \\\\\n",
       "\t  980 & 1   \\\\\n",
       "\t  981 & 0   \\\\\n",
       "\t  982 & 0   \\\\\n",
       "\t  983 & 1   \\\\\n",
       "\t  984 & 1   \\\\\n",
       "\t  985 & 0   \\\\\n",
       "\t  986 & 0   \\\\\n",
       "\t  987 & 0   \\\\\n",
       "\t  988 & 1   \\\\\n",
       "\t  989 & 0   \\\\\n",
       "\t  990 & 0   \\\\\n",
       "\t  991 & 1   \\\\\n",
       "\t  992 & 0   \\\\\n",
       "\t  993 & 0   \\\\\n",
       "\t  994 & 1   \\\\\n",
       "\t  995 & 0   \\\\\n",
       "\t  996 & 1   \\\\\n",
       "\t  997 & 0   \\\\\n",
       "\t  998 & 0   \\\\\n",
       "\t  999 & 0   \\\\\n",
       "\t 1000 & 0   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "c.id | gender | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "|  1 | 1  | \n",
       "|  2 | 1  | \n",
       "|  3 | 1  | \n",
       "|  4 | 1  | \n",
       "|  5 | 0  | \n",
       "|  6 | 0  | \n",
       "|  7 | 0  | \n",
       "|  8 | 1  | \n",
       "|  9 | 1  | \n",
       "| 10 | 1  | \n",
       "| 11 | 0  | \n",
       "| 12 | 0  | \n",
       "| 13 | 1  | \n",
       "| 14 | 0  | \n",
       "| 15 | 0  | \n",
       "| 16 | 0  | \n",
       "| 17 | 0  | \n",
       "| 18 | 0  | \n",
       "| 19 | 0  | \n",
       "| 20 | 1  | \n",
       "| 21 | 0  | \n",
       "| 22 | 0  | \n",
       "| 23 | 1  | \n",
       "| 24 | 1  | \n",
       "| 25 | 1  | \n",
       "| 26 | 0  | \n",
       "| 27 | 1  | \n",
       "| 28 | 1  | \n",
       "| 29 | 0  | \n",
       "| 30 | 0  | \n",
       "| ... | ... | \n",
       "|  971 | 1    | \n",
       "|  972 | 1    | \n",
       "|  973 | 1    | \n",
       "|  974 | 1    | \n",
       "|  975 | 1    | \n",
       "|  976 | 1    | \n",
       "|  977 | 1    | \n",
       "|  978 | 0    | \n",
       "|  979 | 1    | \n",
       "|  980 | 1    | \n",
       "|  981 | 0    | \n",
       "|  982 | 0    | \n",
       "|  983 | 1    | \n",
       "|  984 | 1    | \n",
       "|  985 | 0    | \n",
       "|  986 | 0    | \n",
       "|  987 | 0    | \n",
       "|  988 | 1    | \n",
       "|  989 | 0    | \n",
       "|  990 | 0    | \n",
       "|  991 | 1    | \n",
       "|  992 | 0    | \n",
       "|  993 | 0    | \n",
       "|  994 | 1    | \n",
       "|  995 | 0    | \n",
       "|  996 | 1    | \n",
       "|  997 | 0    | \n",
       "|  998 | 0    | \n",
       "|  999 | 0    | \n",
       "| 1000 | 0    | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     c.id gender\n",
       "1     1   1     \n",
       "2     2   1     \n",
       "3     3   1     \n",
       "4     4   1     \n",
       "5     5   0     \n",
       "6     6   0     \n",
       "7     7   0     \n",
       "8     8   1     \n",
       "9     9   1     \n",
       "10   10   1     \n",
       "11   11   0     \n",
       "12   12   0     \n",
       "13   13   1     \n",
       "14   14   0     \n",
       "15   15   0     \n",
       "16   16   0     \n",
       "17   17   0     \n",
       "18   18   0     \n",
       "19   19   0     \n",
       "20   20   1     \n",
       "21   21   0     \n",
       "22   22   0     \n",
       "23   23   1     \n",
       "24   24   1     \n",
       "25   25   1     \n",
       "26   26   0     \n",
       "27   27   1     \n",
       "28   28   1     \n",
       "29   29   0     \n",
       "30   30   0     \n",
       "...  ...  ...   \n",
       "971   971 1     \n",
       "972   972 1     \n",
       "973   973 1     \n",
       "974   974 1     \n",
       "975   975 1     \n",
       "976   976 1     \n",
       "977   977 1     \n",
       "978   978 0     \n",
       "979   979 1     \n",
       "980   980 1     \n",
       "981   981 0     \n",
       "982   982 0     \n",
       "983   983 1     \n",
       "984   984 1     \n",
       "985   985 0     \n",
       "986   986 0     \n",
       "987   987 0     \n",
       "988   988 1     \n",
       "989   989 0     \n",
       "990   990 0     \n",
       "991   991 1     \n",
       "992   992 0     \n",
       "993   993 0     \n",
       "994   994 1     \n",
       "995   995 0     \n",
       "996   996 1     \n",
       "997   997 0     \n",
       "998   998 0     \n",
       "999   999 0     \n",
       "1000 1000 0     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Build n customers table with one features: gender(male and female)\n",
    "\n",
    "Customer.Table <- function(n_customer, p.gender = 0.5){\n",
    "  \n",
    "  set.seed(12345)\n",
    "  # Assume gender would follow the binomial distribution with the probability = 0.5\n",
    "  gender <- rbinom(n_customer, 1, p.gender) # 1 means male and 0 means female\n",
    "  c.id <- 1:n_customer\n",
    "  \n",
    "  # Build the data frame with customer_id and gender\n",
    "  customer <- as.data.frame(cbind(c.id, gender))\n",
    "  customer$gender <- as.factor(customer$gender)\n",
    "  \n",
    "  # Return the whole customer table\n",
    "  return(customer)\n",
    "  \n",
    "}\n",
    "\n",
    "# Build 1000 customers table with one features: gender(male and female)\n",
    "Customer.Table(1000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>customer.id</th><th scope=col>number of product</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>...</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th></tr></thead>\n",
       "<tbody>\n",
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       "\t<tr><td>968</td><td>16 </td><td>788</td><td>1  </td><td>920</td><td>1  </td><td>497</td><td>1  </td><td>832</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>645</td><td>14 </td><td>178</td><td>1  </td><td> 52</td><td>1  </td><td> 11</td><td>1  </td><td>150</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>368</td><td>81 </td><td>470</td><td>1  </td><td>521</td><td>1  </td><td>242</td><td>1  </td><td>603</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>196</td><td>26 </td><td>470</td><td>1  </td><td>404</td><td>1  </td><td>531</td><td>1  </td><td>208</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>893</td><td>17 </td><td>514</td><td>1  </td><td>705</td><td>1  </td><td>290</td><td>1  </td><td>766</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>757</td><td>46 </td><td> 48</td><td>1  </td><td>450</td><td>1  </td><td>792</td><td>1  </td><td>238</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>665</td><td> 7 </td><td>571</td><td>1  </td><td>276</td><td>1  </td><td>544</td><td>1  </td><td>520</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>246</td><td>72 </td><td>679</td><td>1  </td><td>583</td><td>1  </td><td> 85</td><td>1  </td><td>377</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td> 13</td><td>54 </td><td> 57</td><td>1  </td><td>921</td><td>1  </td><td>604</td><td>1  </td><td>127</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>387</td><td>21 </td><td>443</td><td>1  </td><td>998</td><td>1  </td><td>  3</td><td>1  </td><td>604</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>873</td><td>40 </td><td>507</td><td>1  </td><td>340</td><td>1  </td><td>205</td><td>1  </td><td>929</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>221</td><td>12 </td><td>255</td><td>1  </td><td>383</td><td>1  </td><td>564</td><td>1  </td><td>724</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>642</td><td> 8 </td><td>862</td><td>1  </td><td>347</td><td>1  </td><td> 43</td><td>1  </td><td>506</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>726</td><td>84 </td><td>970</td><td>1  </td><td>280</td><td>1  </td><td>649</td><td>1  </td><td>846</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>799</td><td>17 </td><td>256</td><td>1  </td><td>807</td><td>1  </td><td>835</td><td>1  </td><td>815</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>387</td><td>98 </td><td>687</td><td>1  </td><td>738</td><td>1  </td><td>351</td><td>0  </td><td>513</td><td>1  </td><td>...</td><td>771</td><td> 1 </td><td>997</td><td> 1 </td><td>595</td><td> 1 </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>464</td><td>14 </td><td>328</td><td>1  </td><td> 74</td><td>1  </td><td>731</td><td>1  </td><td>218</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>444</td><td>90 </td><td>268</td><td>1  </td><td>633</td><td>1  </td><td>642</td><td>1  </td><td>479</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td> 29</td><td>20 </td><td>563</td><td>1  </td><td>773</td><td>1  </td><td>643</td><td>1  </td><td>375</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>773</td><td>13 </td><td>379</td><td>1  </td><td>670</td><td>1  </td><td>533</td><td>1  </td><td>318</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>467</td><td>23 </td><td>362</td><td>1  </td><td>181</td><td>1  </td><td>819</td><td>1  </td><td>630</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>738</td><td>28 </td><td>387</td><td>1  </td><td> 90</td><td>1  </td><td>611</td><td>1  </td><td>705</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>823</td><td>40 </td><td>317</td><td>1  </td><td>836</td><td>1  </td><td>716</td><td>1  </td><td>789</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>361</td><td> 7 </td><td>498</td><td>1  </td><td>258</td><td>1  </td><td>664</td><td>1  </td><td> 42</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>909</td><td>53 </td><td>444</td><td>1  </td><td>972</td><td>1  </td><td>447</td><td>1  </td><td> 93</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>422</td><td>96 </td><td>544</td><td>1  </td><td>611</td><td>1  </td><td>836</td><td>1  </td><td>912</td><td>1  </td><td>...</td><td>256</td><td> 1 </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>142</td><td>83 </td><td>682</td><td>1  </td><td>180</td><td>1  </td><td>953</td><td>1  </td><td>554</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>194</td><td>36 </td><td>798</td><td>1  </td><td>228</td><td>1  </td><td>129</td><td>1  </td><td>865</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>893</td><td>27 </td><td>947</td><td>1  </td><td>250</td><td>1  </td><td>652</td><td>1  </td><td>598</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>   </td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><td>674</td><td>23 </td><td>131</td><td>1  </td><td>782</td><td>1  </td><td> 62</td><td>1  </td><td> 12</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>795</td><td>73 </td><td>696</td><td>1  </td><td>476</td><td>1  </td><td>787</td><td>1  </td><td>593</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>577</td><td>77 </td><td>872</td><td>1  </td><td>984</td><td>1  </td><td> 56</td><td>1  </td><td>281</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>192</td><td>38 </td><td>722</td><td>1  </td><td>487</td><td>1  </td><td>220</td><td>1  </td><td>648</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>655</td><td>77 </td><td>577</td><td>1  </td><td>467</td><td>1  </td><td>446</td><td>1  </td><td>449</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>244</td><td>20 </td><td>860</td><td>1  </td><td> 32</td><td>1  </td><td>434</td><td>1  </td><td>357</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>695</td><td>12 </td><td>180</td><td>1  </td><td> 55</td><td>1  </td><td>723</td><td>1  </td><td>664</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>407</td><td>22 </td><td>903</td><td>1  </td><td>327</td><td>1  </td><td>540</td><td>1  </td><td>641</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>279</td><td>16 </td><td>634</td><td>1  </td><td>476</td><td>1  </td><td>235</td><td>1  </td><td>138</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>443</td><td>44 </td><td>565</td><td>1  </td><td>810</td><td>1  </td><td>551</td><td>1  </td><td>507</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td> 17</td><td>35 </td><td> 49</td><td>1  </td><td>937</td><td>1  </td><td>334</td><td>1  </td><td>750</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>455</td><td>40 </td><td>270</td><td>1  </td><td>315</td><td>1  </td><td>963</td><td>1  </td><td> 17</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>598</td><td>58 </td><td>109</td><td>1  </td><td>364</td><td>1  </td><td>873</td><td>1  </td><td>283</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>357</td><td>23 </td><td> 21</td><td>1  </td><td>143</td><td>1  </td><td> 90</td><td>1  </td><td>124</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>556</td><td>35 </td><td>776</td><td>1  </td><td>331</td><td>1  </td><td>905</td><td>1  </td><td>841</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>479</td><td>54 </td><td>995</td><td>1  </td><td>904</td><td>1  </td><td>211</td><td>1  </td><td>752</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>692</td><td>50 </td><td>533</td><td>1  </td><td>115</td><td>1  </td><td>710</td><td>1  </td><td>517</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>626</td><td> 7 </td><td>504</td><td>1  </td><td> 18</td><td>1  </td><td>642</td><td>1  </td><td>420</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>798</td><td>19 </td><td> 70</td><td>1  </td><td>536</td><td>1  </td><td>272</td><td>1  </td><td>159</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>594</td><td>87 </td><td>141</td><td>1  </td><td>659</td><td>1  </td><td>650</td><td>1  </td><td>874</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>511</td><td>54 </td><td>426</td><td>1  </td><td>139</td><td>1  </td><td>121</td><td>1  </td><td>925</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>146</td><td>99 </td><td>981</td><td>1  </td><td>967</td><td>1  </td><td> 57</td><td>1  </td><td>212</td><td>1  </td><td>...</td><td>300</td><td> 1 </td><td>292</td><td> 1 </td><td>262</td><td> 1 </td><td>971</td><td> 1 </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>533</td><td>11 </td><td>874</td><td>1  </td><td>853</td><td>1  </td><td>868</td><td>1  </td><td>569</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>910</td><td>35 </td><td>926</td><td>1  </td><td>648</td><td>1  </td><td>400</td><td>1  </td><td>525</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>289</td><td> 5 </td><td>712</td><td>1  </td><td>463</td><td>1  </td><td>290</td><td>1  </td><td> 94</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>534</td><td>50 </td><td> 37</td><td>1  </td><td>902</td><td>1  </td><td>287</td><td>1  </td><td> 73</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>882</td><td> 9 </td><td>115</td><td>1  </td><td>664</td><td>1  </td><td>286</td><td>1  </td><td>974</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>802</td><td>19 </td><td>931</td><td>1  </td><td>448</td><td>1  </td><td>145</td><td>1  </td><td>423</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>920</td><td>25 </td><td>150</td><td>1  </td><td>218</td><td>1  </td><td>737</td><td>1  </td><td>153</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>780</td><td>14 </td><td>174</td><td>1  </td><td>800</td><td>1  </td><td>912</td><td>1  </td><td>285</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       " customer.id & number of product & product.id & buy & product.id & buy & product.id & buy & product.id & buy & ... & product.id & buy & product.id & buy & product.id & buy & product.id & buy & product.id & buy\\\\\n",
       "\\hline\n",
       "\t 583 & 16  & 588 & 1   & 775 & 1   & 152 & 1   & 235 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 968 & 16  & 788 & 1   & 920 & 1   & 497 & 1   & 832 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 645 & 14  & 178 & 1   &  52 & 1   &  11 & 1   & 150 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 368 & 81  & 470 & 1   & 521 & 1   & 242 & 1   & 603 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 196 & 26  & 470 & 1   & 404 & 1   & 531 & 1   & 208 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 893 & 17  & 514 & 1   & 705 & 1   & 290 & 1   & 766 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 757 & 46  &  48 & 1   & 450 & 1   & 792 & 1   & 238 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 665 &  7  & 571 & 1   & 276 & 1   & 544 & 1   & 520 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 246 & 72  & 679 & 1   & 583 & 1   &  85 & 1   & 377 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t  13 & 54  &  57 & 1   & 921 & 1   & 604 & 1   & 127 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 387 & 21  & 443 & 1   & 998 & 1   &   3 & 1   & 604 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 873 & 40  & 507 & 1   & 340 & 1   & 205 & 1   & 929 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 221 & 12  & 255 & 1   & 383 & 1   & 564 & 1   & 724 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 642 &  8  & 862 & 1   & 347 & 1   &  43 & 1   & 506 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 726 & 84  & 970 & 1   & 280 & 1   & 649 & 1   & 846 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 799 & 17  & 256 & 1   & 807 & 1   & 835 & 1   & 815 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 387 & 98  & 687 & 1   & 738 & 1   & 351 & 0   & 513 & 1   & ... & 771 &  1  & 997 &  1  & 595 &  1  & NA  & NA  & NA  & NA \\\\\n",
       "\t 464 & 14  & 328 & 1   &  74 & 1   & 731 & 1   & 218 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 444 & 90  & 268 & 1   & 633 & 1   & 642 & 1   & 479 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t  29 & 20  & 563 & 1   & 773 & 1   & 643 & 1   & 375 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 773 & 13  & 379 & 1   & 670 & 1   & 533 & 1   & 318 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 467 & 23  & 362 & 1   & 181 & 1   & 819 & 1   & 630 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 738 & 28  & 387 & 1   &  90 & 1   & 611 & 1   & 705 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 823 & 40  & 317 & 1   & 836 & 1   & 716 & 1   & 789 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 361 &  7  & 498 & 1   & 258 & 1   & 664 & 1   &  42 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 909 & 53  & 444 & 1   & 972 & 1   & 447 & 1   &  93 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 422 & 96  & 544 & 1   & 611 & 1   & 836 & 1   & 912 & 1   & ... & 256 &  1  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 142 & 83  & 682 & 1   & 180 & 1   & 953 & 1   & 554 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 194 & 36  & 798 & 1   & 228 & 1   & 129 & 1   & 865 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 893 & 27  & 947 & 1   & 250 & 1   & 652 & 1   & 598 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t ... & ... & ... & ... & ... & ... & ... & ... & ... & ... &     & ... & ... & ... & ... & ... & ... & ... & ... & ... & ...\\\\\n",
       "\t 674 & 23  & 131 & 1   & 782 & 1   &  62 & 1   &  12 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 795 & 73  & 696 & 1   & 476 & 1   & 787 & 1   & 593 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 577 & 77  & 872 & 1   & 984 & 1   &  56 & 1   & 281 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 192 & 38  & 722 & 1   & 487 & 1   & 220 & 1   & 648 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 655 & 77  & 577 & 1   & 467 & 1   & 446 & 1   & 449 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 244 & 20  & 860 & 1   &  32 & 1   & 434 & 1   & 357 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 695 & 12  & 180 & 1   &  55 & 1   & 723 & 1   & 664 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 407 & 22  & 903 & 1   & 327 & 1   & 540 & 1   & 641 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 279 & 16  & 634 & 1   & 476 & 1   & 235 & 1   & 138 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 443 & 44  & 565 & 1   & 810 & 1   & 551 & 1   & 507 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t  17 & 35  &  49 & 1   & 937 & 1   & 334 & 1   & 750 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 455 & 40  & 270 & 1   & 315 & 1   & 963 & 1   &  17 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 598 & 58  & 109 & 1   & 364 & 1   & 873 & 1   & 283 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 357 & 23  &  21 & 1   & 143 & 1   &  90 & 1   & 124 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 556 & 35  & 776 & 1   & 331 & 1   & 905 & 1   & 841 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 479 & 54  & 995 & 1   & 904 & 1   & 211 & 1   & 752 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 692 & 50  & 533 & 1   & 115 & 1   & 710 & 1   & 517 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 626 &  7  & 504 & 1   &  18 & 1   & 642 & 1   & 420 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 798 & 19  &  70 & 1   & 536 & 1   & 272 & 1   & 159 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 594 & 87  & 141 & 1   & 659 & 1   & 650 & 1   & 874 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 511 & 54  & 426 & 1   & 139 & 1   & 121 & 1   & 925 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 146 & 99  & 981 & 1   & 967 & 1   &  57 & 1   & 212 & 1   & ... & 300 &  1  & 292 &  1  & 262 &  1  & 971 &  1  & NA  & NA \\\\\n",
       "\t 533 & 11  & 874 & 1   & 853 & 1   & 868 & 1   & 569 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 910 & 35  & 926 & 1   & 648 & 1   & 400 & 1   & 525 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 289 &  5  & 712 & 1   & 463 & 1   & 290 & 1   &  94 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 534 & 50  &  37 & 1   & 902 & 1   & 287 & 1   &  73 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 882 &  9  & 115 & 1   & 664 & 1   & 286 & 1   & 974 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 802 & 19  & 931 & 1   & 448 & 1   & 145 & 1   & 423 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 920 & 25  & 150 & 1   & 218 & 1   & 737 & 1   & 153 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 780 & 14  & 174 & 1   & 800 & 1   & 912 & 1   & 285 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "customer.id | number of product | product.id | buy | product.id | buy | product.id | buy | product.id | buy | ... | product.id | buy | product.id | buy | product.id | buy | product.id | buy | product.id | buy | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 583 | 16  | 588 | 1   | 775 | 1   | 152 | 1   | 235 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 968 | 16  | 788 | 1   | 920 | 1   | 497 | 1   | 832 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 645 | 14  | 178 | 1   |  52 | 1   |  11 | 1   | 150 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 368 | 81  | 470 | 1   | 521 | 1   | 242 | 1   | 603 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 196 | 26  | 470 | 1   | 404 | 1   | 531 | 1   | 208 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 893 | 17  | 514 | 1   | 705 | 1   | 290 | 1   | 766 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 757 | 46  |  48 | 1   | 450 | 1   | 792 | 1   | 238 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 665 |  7  | 571 | 1   | 276 | 1   | 544 | 1   | 520 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 246 | 72  | 679 | 1   | 583 | 1   |  85 | 1   | 377 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "|  13 | 54  |  57 | 1   | 921 | 1   | 604 | 1   | 127 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 387 | 21  | 443 | 1   | 998 | 1   |   3 | 1   | 604 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 873 | 40  | 507 | 1   | 340 | 1   | 205 | 1   | 929 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 221 | 12  | 255 | 1   | 383 | 1   | 564 | 1   | 724 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 642 |  8  | 862 | 1   | 347 | 1   |  43 | 1   | 506 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 726 | 84  | 970 | 1   | 280 | 1   | 649 | 1   | 846 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 799 | 17  | 256 | 1   | 807 | 1   | 835 | 1   | 815 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 387 | 98  | 687 | 1   | 738 | 1   | 351 | 0   | 513 | 1   | ... | 771 |  1  | 997 |  1  | 595 |  1  | NA  | NA  | NA  | NA  | \n",
       "| 464 | 14  | 328 | 1   |  74 | 1   | 731 | 1   | 218 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 444 | 90  | 268 | 1   | 633 | 1   | 642 | 1   | 479 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "|  29 | 20  | 563 | 1   | 773 | 1   | 643 | 1   | 375 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 773 | 13  | 379 | 1   | 670 | 1   | 533 | 1   | 318 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 467 | 23  | 362 | 1   | 181 | 1   | 819 | 1   | 630 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 738 | 28  | 387 | 1   |  90 | 1   | 611 | 1   | 705 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 823 | 40  | 317 | 1   | 836 | 1   | 716 | 1   | 789 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 361 |  7  | 498 | 1   | 258 | 1   | 664 | 1   |  42 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 909 | 53  | 444 | 1   | 972 | 1   | 447 | 1   |  93 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 422 | 96  | 544 | 1   | 611 | 1   | 836 | 1   | 912 | 1   | ... | 256 |  1  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 142 | 83  | 682 | 1   | 180 | 1   | 953 | 1   | 554 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 194 | 36  | 798 | 1   | 228 | 1   | 129 | 1   | 865 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 893 | 27  | 947 | 1   | 250 | 1   | 652 | 1   | 598 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |     | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | \n",
       "| 674 | 23  | 131 | 1   | 782 | 1   |  62 | 1   |  12 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 795 | 73  | 696 | 1   | 476 | 1   | 787 | 1   | 593 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 577 | 77  | 872 | 1   | 984 | 1   |  56 | 1   | 281 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 192 | 38  | 722 | 1   | 487 | 1   | 220 | 1   | 648 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 655 | 77  | 577 | 1   | 467 | 1   | 446 | 1   | 449 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 244 | 20  | 860 | 1   |  32 | 1   | 434 | 1   | 357 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 695 | 12  | 180 | 1   |  55 | 1   | 723 | 1   | 664 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 407 | 22  | 903 | 1   | 327 | 1   | 540 | 1   | 641 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 279 | 16  | 634 | 1   | 476 | 1   | 235 | 1   | 138 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 443 | 44  | 565 | 1   | 810 | 1   | 551 | 1   | 507 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "|  17 | 35  |  49 | 1   | 937 | 1   | 334 | 1   | 750 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 455 | 40  | 270 | 1   | 315 | 1   | 963 | 1   |  17 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 598 | 58  | 109 | 1   | 364 | 1   | 873 | 1   | 283 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 357 | 23  |  21 | 1   | 143 | 1   |  90 | 1   | 124 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 556 | 35  | 776 | 1   | 331 | 1   | 905 | 1   | 841 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 479 | 54  | 995 | 1   | 904 | 1   | 211 | 1   | 752 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 692 | 50  | 533 | 1   | 115 | 1   | 710 | 1   | 517 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 626 |  7  | 504 | 1   |  18 | 1   | 642 | 1   | 420 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 798 | 19  |  70 | 1   | 536 | 1   | 272 | 1   | 159 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 594 | 87  | 141 | 1   | 659 | 1   | 650 | 1   | 874 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 511 | 54  | 426 | 1   | 139 | 1   | 121 | 1   | 925 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 146 | 99  | 981 | 1   | 967 | 1   |  57 | 1   | 212 | 1   | ... | 300 |  1  | 292 |  1  | 262 |  1  | 971 |  1  | NA  | NA  | \n",
       "| 533 | 11  | 874 | 1   | 853 | 1   | 868 | 1   | 569 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 910 | 35  | 926 | 1   | 648 | 1   | 400 | 1   | 525 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 289 |  5  | 712 | 1   | 463 | 1   | 290 | 1   |  94 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 534 | 50  |  37 | 1   | 902 | 1   | 287 | 1   |  73 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 882 |  9  | 115 | 1   | 664 | 1   | 286 | 1   | 974 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 802 | 19  | 931 | 1   | 448 | 1   | 145 | 1   | 423 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 920 | 25  | 150 | 1   | 218 | 1   | 737 | 1   | 153 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 780 | 14  | 174 | 1   | 800 | 1   | 912 | 1   | 285 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      customer.id number of product product.id buy product.id buy product.id\n",
       " [1,] 583         16                588        1   775        1   152       \n",
       " [2,] 968         16                788        1   920        1   497       \n",
       " [3,] 645         14                178        1    52        1    11       \n",
       " [4,] 368         81                470        1   521        1   242       \n",
       " [5,] 196         26                470        1   404        1   531       \n",
       " [6,] 893         17                514        1   705        1   290       \n",
       " [7,] 757         46                 48        1   450        1   792       \n",
       " [8,] 665          7                571        1   276        1   544       \n",
       " [9,] 246         72                679        1   583        1    85       \n",
       "[10,]  13         54                 57        1   921        1   604       \n",
       "[11,] 387         21                443        1   998        1     3       \n",
       "[12,] 873         40                507        1   340        1   205       \n",
       "[13,] 221         12                255        1   383        1   564       \n",
       "[14,] 642          8                862        1   347        1    43       \n",
       "[15,] 726         84                970        1   280        1   649       \n",
       "[16,] 799         17                256        1   807        1   835       \n",
       "[17,] 387         98                687        1   738        1   351       \n",
       "[18,] 464         14                328        1    74        1   731       \n",
       "[19,] 444         90                268        1   633        1   642       \n",
       "[20,]  29         20                563        1   773        1   643       \n",
       "[21,] 773         13                379        1   670        1   533       \n",
       "[22,] 467         23                362        1   181        1   819       \n",
       "[23,] 738         28                387        1    90        1   611       \n",
       "[24,] 823         40                317        1   836        1   716       \n",
       "[25,] 361          7                498        1   258        1   664       \n",
       "[26,] 909         53                444        1   972        1   447       \n",
       "[27,] 422         96                544        1   611        1   836       \n",
       "[28,] 142         83                682        1   180        1   953       \n",
       "[29,] 194         36                798        1   228        1   129       \n",
       "[30,] 893         27                947        1   250        1   652       \n",
       "[31,] ...         ...               ...        ... ...        ... ...       \n",
       "[32,] 674         23                131        1   782        1    62       \n",
       "[33,] 795         73                696        1   476        1   787       \n",
       "[34,] 577         77                872        1   984        1    56       \n",
       "[35,] 192         38                722        1   487        1   220       \n",
       "[36,] 655         77                577        1   467        1   446       \n",
       "[37,] 244         20                860        1    32        1   434       \n",
       "[38,] 695         12                180        1    55        1   723       \n",
       "[39,] 407         22                903        1   327        1   540       \n",
       "[40,] 279         16                634        1   476        1   235       \n",
       "[41,] 443         44                565        1   810        1   551       \n",
       "[42,]  17         35                 49        1   937        1   334       \n",
       "[43,] 455         40                270        1   315        1   963       \n",
       "[44,] 598         58                109        1   364        1   873       \n",
       "[45,] 357         23                 21        1   143        1    90       \n",
       "[46,] 556         35                776        1   331        1   905       \n",
       "[47,] 479         54                995        1   904        1   211       \n",
       "[48,] 692         50                533        1   115        1   710       \n",
       "[49,] 626          7                504        1    18        1   642       \n",
       "[50,] 798         19                 70        1   536        1   272       \n",
       "[51,] 594         87                141        1   659        1   650       \n",
       "[52,] 511         54                426        1   139        1   121       \n",
       "[53,] 146         99                981        1   967        1    57       \n",
       "[54,] 533         11                874        1   853        1   868       \n",
       "[55,] 910         35                926        1   648        1   400       \n",
       "[56,] 289          5                712        1   463        1   290       \n",
       "[57,] 534         50                 37        1   902        1   287       \n",
       "[58,] 882          9                115        1   664        1   286       \n",
       "[59,] 802         19                931        1   448        1   145       \n",
       "[60,] 920         25                150        1   218        1   737       \n",
       "[61,] 780         14                174        1   800        1   912       \n",
       "      buy product.id buy ... product.id buy product.id buy product.id buy\n",
       " [1,] 1   235        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [2,] 1   832        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [3,] 1   150        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [4,] 1   603        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [5,] 1   208        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [6,] 1   766        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [7,] 1   238        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [8,] 1   520        1   ...  NA        NA   NA        NA   NA        NA \n",
       " [9,] 1   377        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[10,] 1   127        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[11,] 1   604        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[12,] 1   929        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[13,] 1   724        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[14,] 1   506        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[15,] 1   846        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[16,] 1   815        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[17,] 0   513        1   ... 771         1  997         1  595         1 \n",
       "[18,] 1   218        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[19,] 1   479        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[20,] 1   375        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[21,] 1   318        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[22,] 1   630        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[23,] 1   705        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[24,] 1   789        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[25,] 1    42        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[26,] 1    93        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[27,] 1   912        1   ... 256         1   NA        NA   NA        NA \n",
       "[28,] 1   554        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[29,] 1   865        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[30,] 1   598        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[31,] ... ...        ...     ...        ... ...        ... ...        ...\n",
       "[32,] 1    12        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[33,] 1   593        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[34,] 1   281        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[35,] 1   648        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[36,] 1   449        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[37,] 1   357        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[38,] 1   664        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[39,] 1   641        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[40,] 1   138        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[41,] 1   507        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[42,] 1   750        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[43,] 1    17        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[44,] 1   283        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[45,] 1   124        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[46,] 1   841        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[47,] 1   752        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[48,] 1   517        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[49,] 1   420        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[50,] 1   159        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[51,] 1   874        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[52,] 1   925        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[53,] 1   212        1   ... 300         1  292         1  262         1 \n",
       "[54,] 1   569        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[55,] 1   525        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[56,] 1    94        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[57,] 1    73        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[58,] 1   974        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[59,] 1   423        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[60,] 1   153        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[61,] 1   285        1   ...  NA        NA   NA        NA   NA        NA \n",
       "      product.id buy product.id buy\n",
       " [1,] NA         NA  NA         NA \n",
       " [2,] NA         NA  NA         NA \n",
       " [3,] NA         NA  NA         NA \n",
       " [4,] NA         NA  NA         NA \n",
       " [5,] NA         NA  NA         NA \n",
       " [6,] NA         NA  NA         NA \n",
       " [7,] NA         NA  NA         NA \n",
       " [8,] NA         NA  NA         NA \n",
       " [9,] NA         NA  NA         NA \n",
       "[10,] NA         NA  NA         NA \n",
       "[11,] NA         NA  NA         NA \n",
       "[12,] NA         NA  NA         NA \n",
       "[13,] NA         NA  NA         NA \n",
       "[14,] NA         NA  NA         NA \n",
       "[15,] NA         NA  NA         NA \n",
       "[16,] NA         NA  NA         NA \n",
       "[17,] NA         NA  NA         NA \n",
       "[18,] NA         NA  NA         NA \n",
       "[19,] NA         NA  NA         NA \n",
       "[20,] NA         NA  NA         NA \n",
       "[21,] NA         NA  NA         NA \n",
       "[22,] NA         NA  NA         NA \n",
       "[23,] NA         NA  NA         NA \n",
       "[24,] NA         NA  NA         NA \n",
       "[25,] NA         NA  NA         NA \n",
       "[26,] NA         NA  NA         NA \n",
       "[27,] NA         NA  NA         NA \n",
       "[28,] NA         NA  NA         NA \n",
       "[29,] NA         NA  NA         NA \n",
       "[30,] NA         NA  NA         NA \n",
       "[31,] ...        ... ...        ...\n",
       "[32,]  NA        NA  NA         NA \n",
       "[33,]  NA        NA  NA         NA \n",
       "[34,]  NA        NA  NA         NA \n",
       "[35,]  NA        NA  NA         NA \n",
       "[36,]  NA        NA  NA         NA \n",
       "[37,]  NA        NA  NA         NA \n",
       "[38,]  NA        NA  NA         NA \n",
       "[39,]  NA        NA  NA         NA \n",
       "[40,]  NA        NA  NA         NA \n",
       "[41,]  NA        NA  NA         NA \n",
       "[42,]  NA        NA  NA         NA \n",
       "[43,]  NA        NA  NA         NA \n",
       "[44,]  NA        NA  NA         NA \n",
       "[45,]  NA        NA  NA         NA \n",
       "[46,]  NA        NA  NA         NA \n",
       "[47,]  NA        NA  NA         NA \n",
       "[48,]  NA        NA  NA         NA \n",
       "[49,]  NA        NA  NA         NA \n",
       "[50,]  NA        NA  NA         NA \n",
       "[51,]  NA        NA  NA         NA \n",
       "[52,]  NA        NA  NA         NA \n",
       "[53,] 971         1  NA         NA \n",
       "[54,]  NA        NA  NA         NA \n",
       "[55,]  NA        NA  NA         NA \n",
       "[56,]  NA        NA  NA         NA \n",
       "[57,]  NA        NA  NA         NA \n",
       "[58,]  NA        NA  NA         NA \n",
       "[59,]  NA        NA  NA         NA \n",
       "[60,]  NA        NA  NA         NA \n",
       "[61,]  NA        NA  NA         NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3. Simulate the sessions data\n",
    "\n",
    "# Build the table with n sessions recording the following columns: customer id, number of products, and purchasing history (each product id and buy the product or not)\n",
    "\n",
    "# The feature: Number of products which each customer would see would follow the uniform distribution with minimum product = 1 and the maximum product = 100)\n",
    "# Assumptions: 1. The products each customer view are independent.\n",
    "#              2. We sample customers with replacement and sample products with replacement.    \n",
    "\n",
    "# Record the n customers' shopping history. \n",
    "# This table would use the previous two table: the customer table and the product table. \n",
    "\n",
    "Sessions.Table <- function(n_sessions, n_customer, n_product){\n",
    "  \n",
    "  # Call the previous functions to gain the two table.\n",
    "  customer <- Customer.Table(n_customer = n_customer)\n",
    "  product <- Product.Table(n_product = n_product)\n",
    "  \n",
    "  # Build the matrix to store the sessions\n",
    "  # Assume the maximum products each customer view is 100.\n",
    "  sessions <- matrix(NA, nrow = n_sessions, ncol = 202)\n",
    "  colnames(sessions) <- c(\"customer.id\", \"number of product\", rep(c(\"product.id\", \"buy\"), times = 100))\n",
    "  \n",
    "  for (i in 1:n_sessions){\n",
    "    \n",
    "    # Select one customer\n",
    "    c.index <- sample(1:n_customer,1,replace=T) \n",
    "    # Check the customer's id\n",
    "    sessions[i, 1] <- customer[c.index, 1] \n",
    "    #sessions2[i, 1] <- customer[c.index, 1]\n",
    "    # Check the customer is male or not \n",
    "    male <- ifelse(customer[c.index, 2] == 1, 1, 0) \n",
    "    \n",
    "    # Decide number of products which the customer views\n",
    "    views <- sample(1:100,1,replace=T) \n",
    "    sessions[i, 2] <- views\n",
    "    #sessions2[i, 2] <- views\n",
    "    \n",
    "    for (j in 1:views){\n",
    "      \n",
    "      # Select one product\n",
    "      p.index <- sample(1:n_product,1,replace=T) \n",
    "      sessions[i, 2*j+1] <- product[p.index, 1] \n",
    "      #sessions2[i, 2*j+1] <- product[p.index, 1] \n",
    "      \n",
    "      # Check the product's category and price\n",
    "      if (product[p.index,2] == 1){ \n",
    "        category1 <- 1\n",
    "        category2 <- 0\n",
    "        category3 <- 0\n",
    "        price <- product[p.index, 3]\n",
    "      } else if (product[p.index,2] == 2){\n",
    "        category1 <- 0\n",
    "        category2 <- 1\n",
    "        category3 <- 0\n",
    "        price <- product[p.index, 3]\n",
    "      } else {\n",
    "        category1 <- 0\n",
    "        category2 <- 0\n",
    "        category3 <- 1\n",
    "        price <- product[p.index, 3]\n",
    "      } \n",
    "      \n",
    "      # We use logistic function to calculate the probability of buying the product\n",
    "      # log(p/1-p) = alpha0 + alpha11*male*category1 + alpha12*male*category2 + alpha13*male*category3 +\n",
    "      #              [alpha21*price+ alpha31*price^2]*category1 + [alpha22*price+ alpha32*price^2]*category2\n",
    "      #              + [alpha23*price+ alpha33*price^2]*category3\n",
    "      \n",
    "      # For all the parameters setting, the below are our assumptions.\n",
    "      # 1. Assume the customer has 10% probiblity to buy something. alpha0 = log(0.1/1-0.1)\n",
    "      \n",
    "      alpha0 = log(0.1/0.9)\n",
    "      \n",
    "      # 2. Assume the probability of male buing computer is larger than the probability of male buying clothes or shoes.\n",
    "      #    alpha11 = 1, alpha12 = -1, alpha13 = -1 \n",
    "      \n",
    "      alpha11 = 1\n",
    "      alpha12 = -1\n",
    "      alpha13 = -1\n",
    "      \n",
    "      \n",
    "      # 3. Assume the relationship between price and category would follow the Polynomial function. f(x) = ax^2 + bx \n",
    "      \n",
    "      #    For computer. The price = 4000, there still be 1 amount sold. The price = 8000, nothing is sold.\n",
    "      \n",
    "      a1 <- matrix(c(64000000, 16000000, 8000, 4000), nrow = 2)\n",
    "      b1 <- c(0,1)\n",
    "      alpha21 <- solve(a1, b1)[1]\n",
    "      alpha31 <- solve(a1, b1)[2]\n",
    "      \n",
    "      #    For shoes. The price = 200, there still be 10 amount sold. The price = 400, nothing is sold.\n",
    "      \n",
    "      a2 <- matrix(c(160000, 40000, 400, 200), nrow = 2)\n",
    "      b2 <- c(0, 10)\n",
    "      alpha22 <- solve(a2, b2)[1]\n",
    "      alpha32 <- solve(a2, b2)[2]\n",
    "      \n",
    "      #    For clothes. The price = 100, there still be 10 amount sold. The price = 200, nothing is sold.\n",
    "      \n",
    "      a3 <- matrix(c(40000, 10000, 200, 100), nrow = 2)\n",
    "      b3 <- c(0, 10)    \n",
    "      alpha23 <- solve(a3, b3)[1]\n",
    "      alpha33 <- solve(a3, b3)[2]\n",
    "      \n",
    "      # Use the logist function  \n",
    "      bx <- alpha0 + alpha11*male*category1 + alpha12*male*category2 + alpha13*male*category3 + (alpha21*price+ alpha31*price^2)*category1 + (alpha22*price+ alpha32*price^2)*category2 + (alpha23*price+ alpha33*price^2)*category3\n",
    "      # The probability of buying product\n",
    "      p <- 1/(1+exp(-bx)) \n",
    "      \n",
    "      # Decide the customer will buy or not   \n",
    "      sessions[i, 2*j+2] <- ifelse(p > 0.5, 1, 0) \n",
    "      \n",
    "      \n",
    "    }\n",
    "  }\n",
    "  \n",
    "  return(sessions)\n",
    "}\n",
    "\n",
    "# Build 1000 sessions by sampling 1000 customers with replacement which sampling 1000 products replacement\n",
    "Sessions.Table(n_sessions = 1000, n_product = 1000, n_customer = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>customer.id</th><th scope=col>number of product</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>...</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th><th scope=col>product.id</th><th scope=col>buy</th></tr></thead>\n",
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       "\t<tr><td>645</td><td>14 </td><td>178</td><td>0  </td><td> 52</td><td>0  </td><td> 11</td><td>0  </td><td>150</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>368</td><td>81 </td><td>470</td><td>1  </td><td>521</td><td>0  </td><td>242</td><td>0  </td><td>603</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>196</td><td>26 </td><td>470</td><td>1  </td><td>404</td><td>0  </td><td>531</td><td>1  </td><td>208</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>893</td><td>17 </td><td>514</td><td>0  </td><td>705</td><td>1  </td><td>290</td><td>0  </td><td>766</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>757</td><td>46 </td><td> 48</td><td>0  </td><td>450</td><td>0  </td><td>792</td><td>0  </td><td>238</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>665</td><td> 7 </td><td>571</td><td>0  </td><td>276</td><td>0  </td><td>544</td><td>0  </td><td>520</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>246</td><td>72 </td><td>679</td><td>0  </td><td>583</td><td>1  </td><td> 85</td><td>0  </td><td>377</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td> 13</td><td>54 </td><td> 57</td><td>0  </td><td>921</td><td>0  </td><td>604</td><td>0  </td><td>127</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>387</td><td>21 </td><td>443</td><td>0  </td><td>998</td><td>0  </td><td>  3</td><td>0  </td><td>604</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>873</td><td>40 </td><td>507</td><td>0  </td><td>340</td><td>0  </td><td>205</td><td>0  </td><td>929</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>221</td><td>12 </td><td>255</td><td>0  </td><td>383</td><td>0  </td><td>564</td><td>0  </td><td>724</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>642</td><td> 8 </td><td>862</td><td>1  </td><td>347</td><td>0  </td><td> 43</td><td>0  </td><td>506</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>726</td><td>84 </td><td>970</td><td>0  </td><td>280</td><td>0  </td><td>649</td><td>1  </td><td>846</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>799</td><td>17 </td><td>256</td><td>0  </td><td>807</td><td>0  </td><td>835</td><td>0  </td><td>815</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>387</td><td>98 </td><td>687</td><td>0  </td><td>738</td><td>0  </td><td>351</td><td>0  </td><td>513</td><td>1  </td><td>...</td><td>771</td><td> 0 </td><td>997</td><td> 1 </td><td>595</td><td> 1 </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>464</td><td>14 </td><td>328</td><td>0  </td><td> 74</td><td>0  </td><td>731</td><td>0  </td><td>218</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>444</td><td>90 </td><td>268</td><td>0  </td><td>633</td><td>1  </td><td>642</td><td>0  </td><td>479</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td> 29</td><td>20 </td><td>563</td><td>0  </td><td>773</td><td>0  </td><td>643</td><td>0  </td><td>375</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>773</td><td>13 </td><td>379</td><td>0  </td><td>670</td><td>1  </td><td>533</td><td>0  </td><td>318</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>467</td><td>23 </td><td>362</td><td>0  </td><td>181</td><td>0  </td><td>819</td><td>1  </td><td>630</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>738</td><td>28 </td><td>387</td><td>1  </td><td> 90</td><td>0  </td><td>611</td><td>0  </td><td>705</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>823</td><td>40 </td><td>317</td><td>0  </td><td>836</td><td>0  </td><td>716</td><td>0  </td><td>789</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>361</td><td> 7 </td><td>498</td><td>0  </td><td>258</td><td>0  </td><td>664</td><td>0  </td><td> 42</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>909</td><td>53 </td><td>444</td><td>0  </td><td>972</td><td>0  </td><td>447</td><td>0  </td><td> 93</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>422</td><td>96 </td><td>544</td><td>0  </td><td>611</td><td>0  </td><td>836</td><td>0  </td><td>912</td><td>0  </td><td>...</td><td>256</td><td> 0 </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>142</td><td>83 </td><td>682</td><td>0  </td><td>180</td><td>0  </td><td>953</td><td>0  </td><td>554</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>194</td><td>36 </td><td>798</td><td>0  </td><td>228</td><td>0  </td><td>129</td><td>0  </td><td>865</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>893</td><td>27 </td><td>947</td><td>0  </td><td>250</td><td>0  </td><td>652</td><td>1  </td><td>598</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>   </td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><td>674</td><td>23 </td><td>131</td><td>0  </td><td>782</td><td>1  </td><td> 62</td><td>0  </td><td> 12</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>795</td><td>73 </td><td>696</td><td>0  </td><td>476</td><td>1  </td><td>787</td><td>0  </td><td>593</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>577</td><td>77 </td><td>872</td><td>1  </td><td>984</td><td>0  </td><td> 56</td><td>0  </td><td>281</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>192</td><td>38 </td><td>722</td><td>0  </td><td>487</td><td>1  </td><td>220</td><td>0  </td><td>648</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>655</td><td>77 </td><td>577</td><td>0  </td><td>467</td><td>0  </td><td>446</td><td>0  </td><td>449</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>244</td><td>20 </td><td>860</td><td>0  </td><td> 32</td><td>0  </td><td>434</td><td>1  </td><td>357</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>695</td><td>12 </td><td>180</td><td>0  </td><td> 55</td><td>0  </td><td>723</td><td>0  </td><td>664</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>407</td><td>22 </td><td>903</td><td>0  </td><td>327</td><td>0  </td><td>540</td><td>0  </td><td>641</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>279</td><td>16 </td><td>634</td><td>0  </td><td>476</td><td>1  </td><td>235</td><td>0  </td><td>138</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>443</td><td>44 </td><td>565</td><td>0  </td><td>810</td><td>0  </td><td>551</td><td>0  </td><td>507</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td> 17</td><td>35 </td><td> 49</td><td>1  </td><td>937</td><td>0  </td><td>334</td><td>0  </td><td>750</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>455</td><td>40 </td><td>270</td><td>0  </td><td>315</td><td>0  </td><td>963</td><td>0  </td><td> 17</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>598</td><td>58 </td><td>109</td><td>1  </td><td>364</td><td>0  </td><td>873</td><td>0  </td><td>283</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>357</td><td>23 </td><td> 21</td><td>0  </td><td>143</td><td>1  </td><td> 90</td><td>0  </td><td>124</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>556</td><td>35 </td><td>776</td><td>0  </td><td>331</td><td>0  </td><td>905</td><td>0  </td><td>841</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>479</td><td>54 </td><td>995</td><td>0  </td><td>904</td><td>1  </td><td>211</td><td>1  </td><td>752</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>692</td><td>50 </td><td>533</td><td>0  </td><td>115</td><td>0  </td><td>710</td><td>0  </td><td>517</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>626</td><td> 7 </td><td>504</td><td>0  </td><td> 18</td><td>0  </td><td>642</td><td>0  </td><td>420</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>798</td><td>19 </td><td> 70</td><td>0  </td><td>536</td><td>0  </td><td>272</td><td>1  </td><td>159</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>594</td><td>87 </td><td>141</td><td>0  </td><td>659</td><td>0  </td><td>650</td><td>0  </td><td>874</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>511</td><td>54 </td><td>426</td><td>0  </td><td>139</td><td>1  </td><td>121</td><td>0  </td><td>925</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>146</td><td>99 </td><td>981</td><td>0  </td><td>967</td><td>0  </td><td> 57</td><td>0  </td><td>212</td><td>0  </td><td>...</td><td>300</td><td> 0 </td><td>292</td><td> 0 </td><td>262</td><td> 0 </td><td>971</td><td> 0 </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>533</td><td>11 </td><td>874</td><td>0  </td><td>853</td><td>0  </td><td>868</td><td>0  </td><td>569</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>910</td><td>35 </td><td>926</td><td>0  </td><td>648</td><td>0  </td><td>400</td><td>0  </td><td>525</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>289</td><td> 5 </td><td>712</td><td>0  </td><td>463</td><td>0  </td><td>290</td><td>0  </td><td> 94</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>534</td><td>50 </td><td> 37</td><td>0  </td><td>902</td><td>0  </td><td>287</td><td>1  </td><td> 73</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>882</td><td> 9 </td><td>115</td><td>0  </td><td>664</td><td>0  </td><td>286</td><td>0  </td><td>974</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>802</td><td>19 </td><td>931</td><td>0  </td><td>448</td><td>0  </td><td>145</td><td>0  </td><td>423</td><td>1  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>920</td><td>25 </td><td>150</td><td>0  </td><td>218</td><td>0  </td><td>737</td><td>0  </td><td>153</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "\t<tr><td>780</td><td>14 </td><td>174</td><td>0  </td><td>800</td><td>0  </td><td>912</td><td>0  </td><td>285</td><td>0  </td><td>...</td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td> NA</td><td>NA </td><td>NA </td><td>NA </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       " customer.id & number of product & product.id & buy & product.id & buy & product.id & buy & product.id & buy & ... & product.id & buy & product.id & buy & product.id & buy & product.id & buy & product.id & buy\\\\\n",
       "\\hline\n",
       "\t 583 & 16  & 588 & 0   & 775 & 0   & 152 & 0   & 235 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 968 & 16  & 788 & 1   & 920 & 0   & 497 & 0   & 832 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 645 & 14  & 178 & 0   &  52 & 0   &  11 & 0   & 150 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 368 & 81  & 470 & 1   & 521 & 0   & 242 & 0   & 603 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 196 & 26  & 470 & 1   & 404 & 0   & 531 & 1   & 208 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 893 & 17  & 514 & 0   & 705 & 1   & 290 & 0   & 766 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 757 & 46  &  48 & 0   & 450 & 0   & 792 & 0   & 238 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 665 &  7  & 571 & 0   & 276 & 0   & 544 & 0   & 520 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 246 & 72  & 679 & 0   & 583 & 1   &  85 & 0   & 377 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t  13 & 54  &  57 & 0   & 921 & 0   & 604 & 0   & 127 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 387 & 21  & 443 & 0   & 998 & 0   &   3 & 0   & 604 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 873 & 40  & 507 & 0   & 340 & 0   & 205 & 0   & 929 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 221 & 12  & 255 & 0   & 383 & 0   & 564 & 0   & 724 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 642 &  8  & 862 & 1   & 347 & 0   &  43 & 0   & 506 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 726 & 84  & 970 & 0   & 280 & 0   & 649 & 1   & 846 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 799 & 17  & 256 & 0   & 807 & 0   & 835 & 0   & 815 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 387 & 98  & 687 & 0   & 738 & 0   & 351 & 0   & 513 & 1   & ... & 771 &  0  & 997 &  1  & 595 &  1  & NA  & NA  & NA  & NA \\\\\n",
       "\t 464 & 14  & 328 & 0   &  74 & 0   & 731 & 0   & 218 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 444 & 90  & 268 & 0   & 633 & 1   & 642 & 0   & 479 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t  29 & 20  & 563 & 0   & 773 & 0   & 643 & 0   & 375 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 773 & 13  & 379 & 0   & 670 & 1   & 533 & 0   & 318 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 467 & 23  & 362 & 0   & 181 & 0   & 819 & 1   & 630 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 738 & 28  & 387 & 1   &  90 & 0   & 611 & 0   & 705 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 823 & 40  & 317 & 0   & 836 & 0   & 716 & 0   & 789 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 361 &  7  & 498 & 0   & 258 & 0   & 664 & 0   &  42 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 909 & 53  & 444 & 0   & 972 & 0   & 447 & 0   &  93 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 422 & 96  & 544 & 0   & 611 & 0   & 836 & 0   & 912 & 0   & ... & 256 &  0  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 142 & 83  & 682 & 0   & 180 & 0   & 953 & 0   & 554 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 194 & 36  & 798 & 0   & 228 & 0   & 129 & 0   & 865 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t 893 & 27  & 947 & 0   & 250 & 0   & 652 & 1   & 598 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA  & NA  & NA \\\\\n",
       "\t ... & ... & ... & ... & ... & ... & ... & ... & ... & ... &     & ... & ... & ... & ... & ... & ... & ... & ... & ... & ...\\\\\n",
       "\t 674 & 23  & 131 & 0   & 782 & 1   &  62 & 0   &  12 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 795 & 73  & 696 & 0   & 476 & 1   & 787 & 0   & 593 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 577 & 77  & 872 & 1   & 984 & 0   &  56 & 0   & 281 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 192 & 38  & 722 & 0   & 487 & 1   & 220 & 0   & 648 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 655 & 77  & 577 & 0   & 467 & 0   & 446 & 0   & 449 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 244 & 20  & 860 & 0   &  32 & 0   & 434 & 1   & 357 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 695 & 12  & 180 & 0   &  55 & 0   & 723 & 0   & 664 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 407 & 22  & 903 & 0   & 327 & 0   & 540 & 0   & 641 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 279 & 16  & 634 & 0   & 476 & 1   & 235 & 0   & 138 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 443 & 44  & 565 & 0   & 810 & 0   & 551 & 0   & 507 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t  17 & 35  &  49 & 1   & 937 & 0   & 334 & 0   & 750 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 455 & 40  & 270 & 0   & 315 & 0   & 963 & 0   &  17 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 598 & 58  & 109 & 1   & 364 & 0   & 873 & 0   & 283 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 357 & 23  &  21 & 0   & 143 & 1   &  90 & 0   & 124 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 556 & 35  & 776 & 0   & 331 & 0   & 905 & 0   & 841 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 479 & 54  & 995 & 0   & 904 & 1   & 211 & 1   & 752 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 692 & 50  & 533 & 0   & 115 & 0   & 710 & 0   & 517 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 626 &  7  & 504 & 0   &  18 & 0   & 642 & 0   & 420 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 798 & 19  &  70 & 0   & 536 & 0   & 272 & 1   & 159 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 594 & 87  & 141 & 0   & 659 & 0   & 650 & 0   & 874 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 511 & 54  & 426 & 0   & 139 & 1   & 121 & 0   & 925 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 146 & 99  & 981 & 0   & 967 & 0   &  57 & 0   & 212 & 0   & ... & 300 &  0  & 292 &  0  & 262 &  0  & 971 &  0  & NA  & NA \\\\\n",
       "\t 533 & 11  & 874 & 0   & 853 & 0   & 868 & 0   & 569 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 910 & 35  & 926 & 0   & 648 & 0   & 400 & 0   & 525 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 289 &  5  & 712 & 0   & 463 & 0   & 290 & 0   &  94 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 534 & 50  &  37 & 0   & 902 & 0   & 287 & 1   &  73 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 882 &  9  & 115 & 0   & 664 & 0   & 286 & 0   & 974 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 802 & 19  & 931 & 0   & 448 & 0   & 145 & 0   & 423 & 1   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 920 & 25  & 150 & 0   & 218 & 0   & 737 & 0   & 153 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\t 780 & 14  & 174 & 0   & 800 & 0   & 912 & 0   & 285 & 0   & ... &  NA & NA  &  NA & NA  &  NA & NA  &  NA & NA  & NA  & NA \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "customer.id | number of product | product.id | buy | product.id | buy | product.id | buy | product.id | buy | ... | product.id | buy | product.id | buy | product.id | buy | product.id | buy | product.id | buy | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 583 | 16  | 588 | 0   | 775 | 0   | 152 | 0   | 235 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 968 | 16  | 788 | 1   | 920 | 0   | 497 | 0   | 832 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 645 | 14  | 178 | 0   |  52 | 0   |  11 | 0   | 150 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 368 | 81  | 470 | 1   | 521 | 0   | 242 | 0   | 603 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 196 | 26  | 470 | 1   | 404 | 0   | 531 | 1   | 208 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 893 | 17  | 514 | 0   | 705 | 1   | 290 | 0   | 766 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 757 | 46  |  48 | 0   | 450 | 0   | 792 | 0   | 238 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 665 |  7  | 571 | 0   | 276 | 0   | 544 | 0   | 520 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 246 | 72  | 679 | 0   | 583 | 1   |  85 | 0   | 377 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "|  13 | 54  |  57 | 0   | 921 | 0   | 604 | 0   | 127 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 387 | 21  | 443 | 0   | 998 | 0   |   3 | 0   | 604 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 873 | 40  | 507 | 0   | 340 | 0   | 205 | 0   | 929 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 221 | 12  | 255 | 0   | 383 | 0   | 564 | 0   | 724 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 642 |  8  | 862 | 1   | 347 | 0   |  43 | 0   | 506 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 726 | 84  | 970 | 0   | 280 | 0   | 649 | 1   | 846 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 799 | 17  | 256 | 0   | 807 | 0   | 835 | 0   | 815 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 387 | 98  | 687 | 0   | 738 | 0   | 351 | 0   | 513 | 1   | ... | 771 |  0  | 997 |  1  | 595 |  1  | NA  | NA  | NA  | NA  | \n",
       "| 464 | 14  | 328 | 0   |  74 | 0   | 731 | 0   | 218 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 444 | 90  | 268 | 0   | 633 | 1   | 642 | 0   | 479 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "|  29 | 20  | 563 | 0   | 773 | 0   | 643 | 0   | 375 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 773 | 13  | 379 | 0   | 670 | 1   | 533 | 0   | 318 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 467 | 23  | 362 | 0   | 181 | 0   | 819 | 1   | 630 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 738 | 28  | 387 | 1   |  90 | 0   | 611 | 0   | 705 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 823 | 40  | 317 | 0   | 836 | 0   | 716 | 0   | 789 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 361 |  7  | 498 | 0   | 258 | 0   | 664 | 0   |  42 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 909 | 53  | 444 | 0   | 972 | 0   | 447 | 0   |  93 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 422 | 96  | 544 | 0   | 611 | 0   | 836 | 0   | 912 | 0   | ... | 256 |  0  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 142 | 83  | 682 | 0   | 180 | 0   | 953 | 0   | 554 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 194 | 36  | 798 | 0   | 228 | 0   | 129 | 0   | 865 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| 893 | 27  | 947 | 0   | 250 | 0   | 652 | 1   | 598 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | NA  | NA  | \n",
       "| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |     | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | \n",
       "| 674 | 23  | 131 | 0   | 782 | 1   |  62 | 0   |  12 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 795 | 73  | 696 | 0   | 476 | 1   | 787 | 0   | 593 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 577 | 77  | 872 | 1   | 984 | 0   |  56 | 0   | 281 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 192 | 38  | 722 | 0   | 487 | 1   | 220 | 0   | 648 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 655 | 77  | 577 | 0   | 467 | 0   | 446 | 0   | 449 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 244 | 20  | 860 | 0   |  32 | 0   | 434 | 1   | 357 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 695 | 12  | 180 | 0   |  55 | 0   | 723 | 0   | 664 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 407 | 22  | 903 | 0   | 327 | 0   | 540 | 0   | 641 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 279 | 16  | 634 | 0   | 476 | 1   | 235 | 0   | 138 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 443 | 44  | 565 | 0   | 810 | 0   | 551 | 0   | 507 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "|  17 | 35  |  49 | 1   | 937 | 0   | 334 | 0   | 750 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 455 | 40  | 270 | 0   | 315 | 0   | 963 | 0   |  17 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 598 | 58  | 109 | 1   | 364 | 0   | 873 | 0   | 283 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 357 | 23  |  21 | 0   | 143 | 1   |  90 | 0   | 124 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 556 | 35  | 776 | 0   | 331 | 0   | 905 | 0   | 841 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 479 | 54  | 995 | 0   | 904 | 1   | 211 | 1   | 752 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 692 | 50  | 533 | 0   | 115 | 0   | 710 | 0   | 517 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 626 |  7  | 504 | 0   |  18 | 0   | 642 | 0   | 420 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 798 | 19  |  70 | 0   | 536 | 0   | 272 | 1   | 159 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 594 | 87  | 141 | 0   | 659 | 0   | 650 | 0   | 874 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 511 | 54  | 426 | 0   | 139 | 1   | 121 | 0   | 925 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 146 | 99  | 981 | 0   | 967 | 0   |  57 | 0   | 212 | 0   | ... | 300 |  0  | 292 |  0  | 262 |  0  | 971 |  0  | NA  | NA  | \n",
       "| 533 | 11  | 874 | 0   | 853 | 0   | 868 | 0   | 569 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 910 | 35  | 926 | 0   | 648 | 0   | 400 | 0   | 525 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 289 |  5  | 712 | 0   | 463 | 0   | 290 | 0   |  94 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 534 | 50  |  37 | 0   | 902 | 0   | 287 | 1   |  73 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 882 |  9  | 115 | 0   | 664 | 0   | 286 | 0   | 974 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 802 | 19  | 931 | 0   | 448 | 0   | 145 | 0   | 423 | 1   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 920 | 25  | 150 | 0   | 218 | 0   | 737 | 0   | 153 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "| 780 | 14  | 174 | 0   | 800 | 0   | 912 | 0   | 285 | 0   | ... |  NA | NA  |  NA | NA  |  NA | NA  |  NA | NA  | NA  | NA  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      customer.id number of product product.id buy product.id buy product.id\n",
       " [1,] 583         16                588        0   775        0   152       \n",
       " [2,] 968         16                788        1   920        0   497       \n",
       " [3,] 645         14                178        0    52        0    11       \n",
       " [4,] 368         81                470        1   521        0   242       \n",
       " [5,] 196         26                470        1   404        0   531       \n",
       " [6,] 893         17                514        0   705        1   290       \n",
       " [7,] 757         46                 48        0   450        0   792       \n",
       " [8,] 665          7                571        0   276        0   544       \n",
       " [9,] 246         72                679        0   583        1    85       \n",
       "[10,]  13         54                 57        0   921        0   604       \n",
       "[11,] 387         21                443        0   998        0     3       \n",
       "[12,] 873         40                507        0   340        0   205       \n",
       "[13,] 221         12                255        0   383        0   564       \n",
       "[14,] 642          8                862        1   347        0    43       \n",
       "[15,] 726         84                970        0   280        0   649       \n",
       "[16,] 799         17                256        0   807        0   835       \n",
       "[17,] 387         98                687        0   738        0   351       \n",
       "[18,] 464         14                328        0    74        0   731       \n",
       "[19,] 444         90                268        0   633        1   642       \n",
       "[20,]  29         20                563        0   773        0   643       \n",
       "[21,] 773         13                379        0   670        1   533       \n",
       "[22,] 467         23                362        0   181        0   819       \n",
       "[23,] 738         28                387        1    90        0   611       \n",
       "[24,] 823         40                317        0   836        0   716       \n",
       "[25,] 361          7                498        0   258        0   664       \n",
       "[26,] 909         53                444        0   972        0   447       \n",
       "[27,] 422         96                544        0   611        0   836       \n",
       "[28,] 142         83                682        0   180        0   953       \n",
       "[29,] 194         36                798        0   228        0   129       \n",
       "[30,] 893         27                947        0   250        0   652       \n",
       "[31,] ...         ...               ...        ... ...        ... ...       \n",
       "[32,] 674         23                131        0   782        1    62       \n",
       "[33,] 795         73                696        0   476        1   787       \n",
       "[34,] 577         77                872        1   984        0    56       \n",
       "[35,] 192         38                722        0   487        1   220       \n",
       "[36,] 655         77                577        0   467        0   446       \n",
       "[37,] 244         20                860        0    32        0   434       \n",
       "[38,] 695         12                180        0    55        0   723       \n",
       "[39,] 407         22                903        0   327        0   540       \n",
       "[40,] 279         16                634        0   476        1   235       \n",
       "[41,] 443         44                565        0   810        0   551       \n",
       "[42,]  17         35                 49        1   937        0   334       \n",
       "[43,] 455         40                270        0   315        0   963       \n",
       "[44,] 598         58                109        1   364        0   873       \n",
       "[45,] 357         23                 21        0   143        1    90       \n",
       "[46,] 556         35                776        0   331        0   905       \n",
       "[47,] 479         54                995        0   904        1   211       \n",
       "[48,] 692         50                533        0   115        0   710       \n",
       "[49,] 626          7                504        0    18        0   642       \n",
       "[50,] 798         19                 70        0   536        0   272       \n",
       "[51,] 594         87                141        0   659        0   650       \n",
       "[52,] 511         54                426        0   139        1   121       \n",
       "[53,] 146         99                981        0   967        0    57       \n",
       "[54,] 533         11                874        0   853        0   868       \n",
       "[55,] 910         35                926        0   648        0   400       \n",
       "[56,] 289          5                712        0   463        0   290       \n",
       "[57,] 534         50                 37        0   902        0   287       \n",
       "[58,] 882          9                115        0   664        0   286       \n",
       "[59,] 802         19                931        0   448        0   145       \n",
       "[60,] 920         25                150        0   218        0   737       \n",
       "[61,] 780         14                174        0   800        0   912       \n",
       "      buy product.id buy ... product.id buy product.id buy product.id buy\n",
       " [1,] 0   235        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [2,] 0   832        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [3,] 0   150        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [4,] 0   603        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [5,] 1   208        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [6,] 0   766        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [7,] 0   238        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [8,] 0   520        0   ...  NA        NA   NA        NA   NA        NA \n",
       " [9,] 0   377        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[10,] 0   127        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[11,] 0   604        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[12,] 0   929        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[13,] 0   724        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[14,] 0   506        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[15,] 1   846        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[16,] 0   815        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[17,] 0   513        1   ... 771         0  997         1  595         1 \n",
       "[18,] 0   218        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[19,] 0   479        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[20,] 0   375        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[21,] 0   318        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[22,] 1   630        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[23,] 0   705        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[24,] 0   789        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[25,] 0    42        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[26,] 0    93        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[27,] 0   912        0   ... 256         0   NA        NA   NA        NA \n",
       "[28,] 0   554        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[29,] 0   865        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[30,] 1   598        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[31,] ... ...        ...     ...        ... ...        ... ...        ...\n",
       "[32,] 0    12        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[33,] 0   593        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[34,] 0   281        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[35,] 0   648        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[36,] 0   449        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[37,] 1   357        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[38,] 0   664        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[39,] 0   641        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[40,] 0   138        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[41,] 0   507        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[42,] 0   750        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[43,] 0    17        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[44,] 0   283        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[45,] 0   124        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[46,] 0   841        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[47,] 1   752        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[48,] 0   517        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[49,] 0   420        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[50,] 1   159        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[51,] 0   874        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[52,] 0   925        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[53,] 0   212        0   ... 300         0  292         0  262         0 \n",
       "[54,] 0   569        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[55,] 0   525        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[56,] 0    94        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[57,] 1    73        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[58,] 0   974        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[59,] 0   423        1   ...  NA        NA   NA        NA   NA        NA \n",
       "[60,] 0   153        0   ...  NA        NA   NA        NA   NA        NA \n",
       "[61,] 0   285        0   ...  NA        NA   NA        NA   NA        NA \n",
       "      product.id buy product.id buy\n",
       " [1,] NA         NA  NA         NA \n",
       " [2,] NA         NA  NA         NA \n",
       " [3,] NA         NA  NA         NA \n",
       " [4,] NA         NA  NA         NA \n",
       " [5,] NA         NA  NA         NA \n",
       " [6,] NA         NA  NA         NA \n",
       " [7,] NA         NA  NA         NA \n",
       " [8,] NA         NA  NA         NA \n",
       " [9,] NA         NA  NA         NA \n",
       "[10,] NA         NA  NA         NA \n",
       "[11,] NA         NA  NA         NA \n",
       "[12,] NA         NA  NA         NA \n",
       "[13,] NA         NA  NA         NA \n",
       "[14,] NA         NA  NA         NA \n",
       "[15,] NA         NA  NA         NA \n",
       "[16,] NA         NA  NA         NA \n",
       "[17,] NA         NA  NA         NA \n",
       "[18,] NA         NA  NA         NA \n",
       "[19,] NA         NA  NA         NA \n",
       "[20,] NA         NA  NA         NA \n",
       "[21,] NA         NA  NA         NA \n",
       "[22,] NA         NA  NA         NA \n",
       "[23,] NA         NA  NA         NA \n",
       "[24,] NA         NA  NA         NA \n",
       "[25,] NA         NA  NA         NA \n",
       "[26,] NA         NA  NA         NA \n",
       "[27,] NA         NA  NA         NA \n",
       "[28,] NA         NA  NA         NA \n",
       "[29,] NA         NA  NA         NA \n",
       "[30,] NA         NA  NA         NA \n",
       "[31,] ...        ... ...        ...\n",
       "[32,]  NA        NA  NA         NA \n",
       "[33,]  NA        NA  NA         NA \n",
       "[34,]  NA        NA  NA         NA \n",
       "[35,]  NA        NA  NA         NA \n",
       "[36,]  NA        NA  NA         NA \n",
       "[37,]  NA        NA  NA         NA \n",
       "[38,]  NA        NA  NA         NA \n",
       "[39,]  NA        NA  NA         NA \n",
       "[40,]  NA        NA  NA         NA \n",
       "[41,]  NA        NA  NA         NA \n",
       "[42,]  NA        NA  NA         NA \n",
       "[43,]  NA        NA  NA         NA \n",
       "[44,]  NA        NA  NA         NA \n",
       "[45,]  NA        NA  NA         NA \n",
       "[46,]  NA        NA  NA         NA \n",
       "[47,]  NA        NA  NA         NA \n",
       "[48,]  NA        NA  NA         NA \n",
       "[49,]  NA        NA  NA         NA \n",
       "[50,]  NA        NA  NA         NA \n",
       "[51,]  NA        NA  NA         NA \n",
       "[52,]  NA        NA  NA         NA \n",
       "[53,] 971         0  NA         NA \n",
       "[54,]  NA        NA  NA         NA \n",
       "[55,]  NA        NA  NA         NA \n",
       "[56,]  NA        NA  NA         NA \n",
       "[57,]  NA        NA  NA         NA \n",
       "[58,]  NA        NA  NA         NA \n",
       "[59,]  NA        NA  NA         NA \n",
       "[60,]  NA        NA  NA         NA \n",
       "[61,]  NA        NA  NA         NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Since the original formula would give high probability to buy products, \n",
    "# we give f0 and beta0 to adjust the formula to make the probabilities of buying would be close to 10%.\n",
    "\n",
    "Sessions.Table.Adjust <- function(n_sessions, n_customer, n_product){\n",
    "  \n",
    "  # Call the previous functions to gain the two table.\n",
    "  customer <- Customer.Table(n_customer = n_customer)\n",
    "  product <- Product.Table(n_product = n_product)\n",
    "  \n",
    "  # Build the matrix to store the sessions\n",
    "  # Assume the maximum products each customer view is 100.\n",
    "  sessions <- matrix(NA, nrow = n_sessions, ncol = 202)\n",
    "  colnames(sessions) <- c(\"customer.id\", \"number of product\", rep(c(\"product.id\", \"buy\"), times = 100))\n",
    "  \n",
    "  for (i in 1:n_sessions){\n",
    "    \n",
    "    # Select one customer\n",
    "    c.index <- sample(1:n_customer,1,replace=T) \n",
    "    # Check the customer's id\n",
    "    sessions[i, 1] <- customer[c.index, 1] \n",
    "    # Check the customer is male or not \n",
    "    male <- ifelse(customer[c.index, 2] == 1, 1, 0) \n",
    "    \n",
    "    # Decide number of products which the customer views\n",
    "    views <- sample(1:100,1,replace=T) \n",
    "    sessions[i, 2] <- views\n",
    "    \n",
    "    for (j in 1:views){\n",
    "      \n",
    "      # Select one product\n",
    "      p.index <- sample(1:n_product,1,replace=T) \n",
    "      sessions[i, 2*j+1] <- product[p.index, 1] \n",
    "      \n",
    "      # Check the product's category and price\n",
    "      if (product[p.index,2] == 1){ \n",
    "        category1 <- 1\n",
    "        category2 <- 0\n",
    "        category3 <- 0\n",
    "        price <- product[p.index, 3]\n",
    "      } else if (product[p.index,2] == 2){\n",
    "        category1 <- 0\n",
    "        category2 <- 1\n",
    "        category3 <- 0\n",
    "        price <- product[p.index, 3]\n",
    "      } else {\n",
    "        category1 <- 0\n",
    "        category2 <- 0\n",
    "        category3 <- 1\n",
    "        price <- product[p.index, 3]\n",
    "      } \n",
    "      \n",
    "      # We use logistic function to calculate the probability of buying the product\n",
    "      # log(p/1-p) = alpha0 + alpha11*male*category1 + alpha12*male*category2 + alpha13*male*category3 +\n",
    "      #              [alpha21*price+ alpha31*price^2]*category1 + [alpha22*price+ alpha32*price^2]*category2\n",
    "      #              + [alpha23*price+ alpha33*price^2]*category3\n",
    "      \n",
    "      # For all the parameters setting, the below are our assumptions.\n",
    "      # 1. Assume the customer has 10% probiblity to buy something. alpha0 = log(0.1/1-0.1)\n",
    "      \n",
    "      alpha0 = log(0.1/0.9)\n",
    "      \n",
    "      # 2. Assume the probability of male buing computer is larger than the probability of male buying clothes or shoes.\n",
    "      #    alpha11 = 1, alpha12 = -1, alpha13 = -1 \n",
    "      \n",
    "      alpha11 = 1\n",
    "      alpha12 = -1\n",
    "      alpha13 = -1\n",
    "      \n",
    "      \n",
    "      # 3. Assume the relationship between price and category would follow the Polynomial function. f(x) = ax^2 + bx \n",
    "      \n",
    "      #    For computer. The price = 4000, there still be 1 amount sold. The price = 8000, nothing is sold.\n",
    "      \n",
    "      a1 <- matrix(c(64000000, 16000000, 8000, 4000), nrow = 2)\n",
    "      b1 <- c(0,1)\n",
    "      alpha21 <- solve(a1, b1)[1]\n",
    "      alpha31 <- solve(a1, b1)[2]\n",
    "      \n",
    "      #    For shoes. The price = 200, there still be 10 amount sold. The price = 400, nothing is sold.\n",
    "      \n",
    "      a2 <- matrix(c(160000, 40000, 400, 200), nrow = 2)\n",
    "      b2 <- c(0, 10)\n",
    "      alpha22 <- solve(a2, b2)[1]\n",
    "      alpha32 <- solve(a2, b2)[2]\n",
    "      \n",
    "      #    For clothes. The price = 100, there still be 10 amount sold. The price = 200, nothing is sold.\n",
    "      \n",
    "      a3 <- matrix(c(40000, 10000, 200, 100), nrow = 2)\n",
    "      b3 <- c(0, 10)    \n",
    "      alpha23 <- solve(a3, b3)[1]\n",
    "      alpha33 <- solve(a3, b3)[2]\n",
    "      \n",
    "      bx <- alpha0 + alpha11*male*category1 + alpha12*male*category2 + alpha13*male*category3 + (alpha21*price+ alpha31*price^2)*category1 + (alpha22*price+ alpha32*price^2)*category2 + (alpha23*price+ alpha33*price^2)*category3\n",
    "      \n",
    "      # Give hyper-parameter (f-f0)/beta0 to adjuct the probability since the original probabilities are too high.\n",
    "      # We want to keep the probability close to 10%\n",
    "      p_beta <- 1/(1+exp(-(bx-800)/0.1))\n",
    "      \n",
    "      sessions[i, 2*j+2] <- ifelse(p_beta > 0.5, 1, 0) # Decide the customer will buy or not\n",
    "      \n",
    "    }\n",
    "  }\n",
    "  \n",
    "  return(sessions)\n",
    "}\n",
    "\n",
    "# Build the table with 1000 sessions which we already adjust the probabilities.\n",
    "Sessions.Table.Adjust(n_sessions = 1000, n_customer = 1000, n_product = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QqCBAmCBAgQJEAgmSDxzyhgGUECBJIJ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\nAgQJECBIgMA/z01ACizuj/QAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"The probability without the hyper-parameter\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>customer_id</th><th scope=col>view</th><th scope=col>buy</th><th scope=col>buy_adjust</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>2546</td><td> 39 </td><td> 39 </td><td> 9  </td></tr>\n",
       "\t<tr><td>3454</td><td>  3 </td><td>  3 </td><td> 1  </td></tr>\n",
       "\t<tr><td> 260</td><td> 56 </td><td> 55 </td><td>10  </td></tr>\n",
       "\t<tr><td>3441</td><td> 76 </td><td> 75 </td><td>19  </td></tr>\n",
       "\t<tr><td>3129</td><td> 55 </td><td> 54 </td><td> 9  </td></tr>\n",
       "\t<tr><td>8407</td><td> 74 </td><td> 74 </td><td>17  </td></tr>\n",
       "\t<tr><td>9444</td><td> 73 </td><td> 70 </td><td>16  </td></tr>\n",
       "\t<tr><td>3590</td><td> 99 </td><td> 97 </td><td>16  </td></tr>\n",
       "\t<tr><td> 281</td><td> 21 </td><td> 21 </td><td> 4  </td></tr>\n",
       "\t<tr><td> 776</td><td> 96 </td><td> 93 </td><td>16  </td></tr>\n",
       "\t<tr><td> 597</td><td> 34 </td><td> 34 </td><td> 5  </td></tr>\n",
       "\t<tr><td> 524</td><td> 99 </td><td> 97 </td><td>23  </td></tr>\n",
       "\t<tr><td>1205</td><td>  8 </td><td>  8 </td><td> 1  </td></tr>\n",
       "\t<tr><td>2581</td><td> 57 </td><td> 55 </td><td>14  </td></tr>\n",
       "\t<tr><td>4539</td><td> 77 </td><td> 74 </td><td> 9  </td></tr>\n",
       "\t<tr><td>2514</td><td> 16 </td><td> 16 </td><td> 1  </td></tr>\n",
       "\t<tr><td>2163</td><td> 40 </td><td> 40 </td><td> 6  </td></tr>\n",
       "\t<tr><td>4228</td><td> 65 </td><td> 64 </td><td> 9  </td></tr>\n",
       "\t<tr><td>1198</td><td> 64 </td><td> 63 </td><td> 8  </td></tr>\n",
       "\t<tr><td>4746</td><td>  6 </td><td>  6 </td><td> 0  </td></tr>\n",
       "\t<tr><td>9017</td><td> 99 </td><td> 95 </td><td>23  </td></tr>\n",
       "\t<tr><td>2440</td><td> 61 </td><td> 60 </td><td>16  </td></tr>\n",
       "\t<tr><td>4239</td><td> 75 </td><td> 74 </td><td>17  </td></tr>\n",
       "\t<tr><td>3150</td><td> 51 </td><td> 50 </td><td>10  </td></tr>\n",
       "\t<tr><td>8465</td><td> 40 </td><td> 39 </td><td> 6  </td></tr>\n",
       "\t<tr><td>8762</td><td>  7 </td><td>  7 </td><td> 1  </td></tr>\n",
       "\t<tr><td>9918</td><td> 81 </td><td> 81 </td><td>13  </td></tr>\n",
       "\t<tr><td>9660</td><td>  7 </td><td>  7 </td><td> 2  </td></tr>\n",
       "\t<tr><td>4095</td><td>100 </td><td>100 </td><td>20  </td></tr>\n",
       "\t<tr><td> 156</td><td> 42 </td><td> 42 </td><td>10  </td></tr>\n",
       "\t<tr><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><td>9017</td><td>86  </td><td>80  </td><td>17  </td></tr>\n",
       "\t<tr><td>4987</td><td>54  </td><td>52  </td><td> 6  </td></tr>\n",
       "\t<tr><td>4653</td><td>97  </td><td>95  </td><td>20  </td></tr>\n",
       "\t<tr><td>6949</td><td>53  </td><td>50  </td><td> 9  </td></tr>\n",
       "\t<tr><td>2186</td><td>69  </td><td>66  </td><td>15  </td></tr>\n",
       "\t<tr><td>1950</td><td>74  </td><td>74  </td><td>16  </td></tr>\n",
       "\t<tr><td>4968</td><td>41  </td><td>40  </td><td> 9  </td></tr>\n",
       "\t<tr><td>1849</td><td>39  </td><td>38  </td><td>10  </td></tr>\n",
       "\t<tr><td>5701</td><td> 6  </td><td> 6  </td><td> 0  </td></tr>\n",
       "\t<tr><td>6929</td><td>87  </td><td>85  </td><td>17  </td></tr>\n",
       "\t<tr><td>6880</td><td>47  </td><td>46  </td><td> 4  </td></tr>\n",
       "\t<tr><td> 101</td><td>37  </td><td>36  </td><td> 6  </td></tr>\n",
       "\t<tr><td>5011</td><td>96  </td><td>94  </td><td>20  </td></tr>\n",
       "\t<tr><td>2001</td><td>85  </td><td>83  </td><td>13  </td></tr>\n",
       "\t<tr><td>1464</td><td> 8  </td><td> 7  </td><td> 1  </td></tr>\n",
       "\t<tr><td>5706</td><td> 5  </td><td> 5  </td><td> 2  </td></tr>\n",
       "\t<tr><td> 947</td><td>62  </td><td>61  </td><td>11  </td></tr>\n",
       "\t<tr><td>8817</td><td>69  </td><td>69  </td><td>12  </td></tr>\n",
       "\t<tr><td>6327</td><td>79  </td><td>77  </td><td>17  </td></tr>\n",
       "\t<tr><td>6005</td><td>88  </td><td>84  </td><td>20  </td></tr>\n",
       "\t<tr><td>7886</td><td>78  </td><td>77  </td><td>13  </td></tr>\n",
       "\t<tr><td>4520</td><td> 2  </td><td> 2  </td><td> 1  </td></tr>\n",
       "\t<tr><td>3172</td><td>59  </td><td>57  </td><td>11  </td></tr>\n",
       "\t<tr><td>4719</td><td>42  </td><td>41  </td><td>11  </td></tr>\n",
       "\t<tr><td>1828</td><td>22  </td><td>21  </td><td> 4  </td></tr>\n",
       "\t<tr><td>9225</td><td>62  </td><td>61  </td><td>14  </td></tr>\n",
       "\t<tr><td>2448</td><td> 6  </td><td> 6  </td><td> 1  </td></tr>\n",
       "\t<tr><td>6544</td><td> 5  </td><td> 5  </td><td> 0  </td></tr>\n",
       "\t<tr><td> 341</td><td>71  </td><td>69  </td><td>14  </td></tr>\n",
       "\t<tr><td>4891</td><td>28  </td><td>26  </td><td> 3  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " customer\\_id & view & buy & buy\\_adjust\\\\\n",
       "\\hline\n",
       "\t 2546 &  39  &  39  &  9  \\\\\n",
       "\t 3454 &   3  &   3  &  1  \\\\\n",
       "\t  260 &  56  &  55  & 10  \\\\\n",
       "\t 3441 &  76  &  75  & 19  \\\\\n",
       "\t 3129 &  55  &  54  &  9  \\\\\n",
       "\t 8407 &  74  &  74  & 17  \\\\\n",
       "\t 9444 &  73  &  70  & 16  \\\\\n",
       "\t 3590 &  99  &  97  & 16  \\\\\n",
       "\t  281 &  21  &  21  &  4  \\\\\n",
       "\t  776 &  96  &  93  & 16  \\\\\n",
       "\t  597 &  34  &  34  &  5  \\\\\n",
       "\t  524 &  99  &  97  & 23  \\\\\n",
       "\t 1205 &   8  &   8  &  1  \\\\\n",
       "\t 2581 &  57  &  55  & 14  \\\\\n",
       "\t 4539 &  77  &  74  &  9  \\\\\n",
       "\t 2514 &  16  &  16  &  1  \\\\\n",
       "\t 2163 &  40  &  40  &  6  \\\\\n",
       "\t 4228 &  65  &  64  &  9  \\\\\n",
       "\t 1198 &  64  &  63  &  8  \\\\\n",
       "\t 4746 &   6  &   6  &  0  \\\\\n",
       "\t 9017 &  99  &  95  & 23  \\\\\n",
       "\t 2440 &  61  &  60  & 16  \\\\\n",
       "\t 4239 &  75  &  74  & 17  \\\\\n",
       "\t 3150 &  51  &  50  & 10  \\\\\n",
       "\t 8465 &  40  &  39  &  6  \\\\\n",
       "\t 8762 &   7  &   7  &  1  \\\\\n",
       "\t 9918 &  81  &  81  & 13  \\\\\n",
       "\t 9660 &   7  &   7  &  2  \\\\\n",
       "\t 4095 & 100  & 100  & 20  \\\\\n",
       "\t  156 &  42  &  42  & 10  \\\\\n",
       "\t ... & ... & ... & ...\\\\\n",
       "\t 9017 & 86   & 80   & 17  \\\\\n",
       "\t 4987 & 54   & 52   &  6  \\\\\n",
       "\t 4653 & 97   & 95   & 20  \\\\\n",
       "\t 6949 & 53   & 50   &  9  \\\\\n",
       "\t 2186 & 69   & 66   & 15  \\\\\n",
       "\t 1950 & 74   & 74   & 16  \\\\\n",
       "\t 4968 & 41   & 40   &  9  \\\\\n",
       "\t 1849 & 39   & 38   & 10  \\\\\n",
       "\t 5701 &  6   &  6   &  0  \\\\\n",
       "\t 6929 & 87   & 85   & 17  \\\\\n",
       "\t 6880 & 47   & 46   &  4  \\\\\n",
       "\t  101 & 37   & 36   &  6  \\\\\n",
       "\t 5011 & 96   & 94   & 20  \\\\\n",
       "\t 2001 & 85   & 83   & 13  \\\\\n",
       "\t 1464 &  8   &  7   &  1  \\\\\n",
       "\t 5706 &  5   &  5   &  2  \\\\\n",
       "\t  947 & 62   & 61   & 11  \\\\\n",
       "\t 8817 & 69   & 69   & 12  \\\\\n",
       "\t 6327 & 79   & 77   & 17  \\\\\n",
       "\t 6005 & 88   & 84   & 20  \\\\\n",
       "\t 7886 & 78   & 77   & 13  \\\\\n",
       "\t 4520 &  2   &  2   &  1  \\\\\n",
       "\t 3172 & 59   & 57   & 11  \\\\\n",
       "\t 4719 & 42   & 41   & 11  \\\\\n",
       "\t 1828 & 22   & 21   &  4  \\\\\n",
       "\t 9225 & 62   & 61   & 14  \\\\\n",
       "\t 2448 &  6   &  6   &  1  \\\\\n",
       "\t 6544 &  5   &  5   &  0  \\\\\n",
       "\t  341 & 71   & 69   & 14  \\\\\n",
       "\t 4891 & 28   & 26   &  3  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "customer_id | view | buy | buy_adjust | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 2546 |  39  |  39  |  9   | \n",
       "| 3454 |   3  |   3  |  1   | \n",
       "|  260 |  56  |  55  | 10   | \n",
       "| 3441 |  76  |  75  | 19   | \n",
       "| 3129 |  55  |  54  |  9   | \n",
       "| 8407 |  74  |  74  | 17   | \n",
       "| 9444 |  73  |  70  | 16   | \n",
       "| 3590 |  99  |  97  | 16   | \n",
       "|  281 |  21  |  21  |  4   | \n",
       "|  776 |  96  |  93  | 16   | \n",
       "|  597 |  34  |  34  |  5   | \n",
       "|  524 |  99  |  97  | 23   | \n",
       "| 1205 |   8  |   8  |  1   | \n",
       "| 2581 |  57  |  55  | 14   | \n",
       "| 4539 |  77  |  74  |  9   | \n",
       "| 2514 |  16  |  16  |  1   | \n",
       "| 2163 |  40  |  40  |  6   | \n",
       "| 4228 |  65  |  64  |  9   | \n",
       "| 1198 |  64  |  63  |  8   | \n",
       "| 4746 |   6  |   6  |  0   | \n",
       "| 9017 |  99  |  95  | 23   | \n",
       "| 2440 |  61  |  60  | 16   | \n",
       "| 4239 |  75  |  74  | 17   | \n",
       "| 3150 |  51  |  50  | 10   | \n",
       "| 8465 |  40  |  39  |  6   | \n",
       "| 8762 |   7  |   7  |  1   | \n",
       "| 9918 |  81  |  81  | 13   | \n",
       "| 9660 |   7  |   7  |  2   | \n",
       "| 4095 | 100  | 100  | 20   | \n",
       "|  156 |  42  |  42  | 10   | \n",
       "| ... | ... | ... | ... | \n",
       "| 9017 | 86   | 80   | 17   | \n",
       "| 4987 | 54   | 52   |  6   | \n",
       "| 4653 | 97   | 95   | 20   | \n",
       "| 6949 | 53   | 50   |  9   | \n",
       "| 2186 | 69   | 66   | 15   | \n",
       "| 1950 | 74   | 74   | 16   | \n",
       "| 4968 | 41   | 40   |  9   | \n",
       "| 1849 | 39   | 38   | 10   | \n",
       "| 5701 |  6   |  6   |  0   | \n",
       "| 6929 | 87   | 85   | 17   | \n",
       "| 6880 | 47   | 46   |  4   | \n",
       "|  101 | 37   | 36   |  6   | \n",
       "| 5011 | 96   | 94   | 20   | \n",
       "| 2001 | 85   | 83   | 13   | \n",
       "| 1464 |  8   |  7   |  1   | \n",
       "| 5706 |  5   |  5   |  2   | \n",
       "|  947 | 62   | 61   | 11   | \n",
       "| 8817 | 69   | 69   | 12   | \n",
       "| 6327 | 79   | 77   | 17   | \n",
       "| 6005 | 88   | 84   | 20   | \n",
       "| 7886 | 78   | 77   | 13   | \n",
       "| 4520 |  2   |  2   |  1   | \n",
       "| 3172 | 59   | 57   | 11   | \n",
       "| 4719 | 42   | 41   | 11   | \n",
       "| 1828 | 22   | 21   |  4   | \n",
       "| 9225 | 62   | 61   | 14   | \n",
       "| 2448 |  6   |  6   |  1   | \n",
       "| 6544 |  5   |  5   |  0   | \n",
       "|  341 | 71   | 69   | 14   | \n",
       "| 4891 | 28   | 26   |  3   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "    customer_id view buy buy_adjust\n",
       "1   2546         39   39  9        \n",
       "2   3454          3    3  1        \n",
       "3    260         56   55 10        \n",
       "4   3441         76   75 19        \n",
       "5   3129         55   54  9        \n",
       "6   8407         74   74 17        \n",
       "7   9444         73   70 16        \n",
       "8   3590         99   97 16        \n",
       "9    281         21   21  4        \n",
       "10   776         96   93 16        \n",
       "11   597         34   34  5        \n",
       "12   524         99   97 23        \n",
       "13  1205          8    8  1        \n",
       "14  2581         57   55 14        \n",
       "15  4539         77   74  9        \n",
       "16  2514         16   16  1        \n",
       "17  2163         40   40  6        \n",
       "18  4228         65   64  9        \n",
       "19  1198         64   63  8        \n",
       "20  4746          6    6  0        \n",
       "21  9017         99   95 23        \n",
       "22  2440         61   60 16        \n",
       "23  4239         75   74 17        \n",
       "24  3150         51   50 10        \n",
       "25  8465         40   39  6        \n",
       "26  8762          7    7  1        \n",
       "27  9918         81   81 13        \n",
       "28  9660          7    7  2        \n",
       "29  4095        100  100 20        \n",
       "30   156         42   42 10        \n",
       "... ...         ...  ... ...       \n",
       "271 9017        86   80  17        \n",
       "272 4987        54   52   6        \n",
       "273 4653        97   95  20        \n",
       "274 6949        53   50   9        \n",
       "275 2186        69   66  15        \n",
       "276 1950        74   74  16        \n",
       "277 4968        41   40   9        \n",
       "278 1849        39   38  10        \n",
       "279 5701         6    6   0        \n",
       "280 6929        87   85  17        \n",
       "281 6880        47   46   4        \n",
       "282  101        37   36   6        \n",
       "283 5011        96   94  20        \n",
       "284 2001        85   83  13        \n",
       "285 1464         8    7   1        \n",
       "286 5706         5    5   2        \n",
       "287  947        62   61  11        \n",
       "288 8817        69   69  12        \n",
       "289 6327        79   77  17        \n",
       "290 6005        88   84  20        \n",
       "291 7886        78   77  13        \n",
       "292 4520         2    2   1        \n",
       "293 3172        59   57  11        \n",
       "294 4719        42   41  11        \n",
       "295 1828        22   21   4        \n",
       "296 9225        62   61  14        \n",
       "297 2448         6    6   1        \n",
       "298 6544         5    5   0        \n",
       "299  341        71   69  14        \n",
       "300 4891        28   26   3        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QXTPplt7emiHx157YI3Duns/OV28e789grDZd/kbyZ3MFj0xe0aebjbrbDsWpZa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\nrkJggg==",
      "text/plain": [
       "Plot with title \"The probability with the hyper-parameter\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Summary of number of products each customer view and buy with histograms of the probability of buying\n",
    "\n",
    "Summary.Probability <- function(n_sessions, n_customer, n_product){\n",
    "  \n",
    "  sessions <- Sessions.Table(n_sessions = n_sessions, n_customer = n_customer, n_product = n_product)\n",
    "  sessions2 <- Sessions.Table.Adjust(n_sessions = n_sessions, n_customer = n_customer, n_product = n_product)\n",
    "  \n",
    "  # Build the data frame to contain the two sessions' summary data\n",
    "  TableOfSummary <- matrix(NA, nrow = n_sessions, ncol = 4)\n",
    "  colnames(TableOfSummary) <- c(\"customer_id\", \"view\", \"buy\",\"buy_adjust\")\n",
    "  \n",
    "  # To sum up all products each customer bought in each session\n",
    "  \n",
    "  for (i in 1:n_sessions) {\n",
    "    TableOfSummary[i, 3] <- sum(sessions[i, seq(4, 202, 2)], na.rm = TRUE)\n",
    "    TableOfSummary[i, 4] <- sum(sessions2[i, seq(4, 202, 2)], na.rm = TRUE)\n",
    "  }\n",
    "  \n",
    "  # Store the customer_id and number of product each customer view\n",
    "  TableOfSummary[1:n_sessions, 1:2] <- sessions[1:n_sessions,1:2]\n",
    "  TableOfSummary <- as.data.frame(TableOfSummary)\n",
    "  \n",
    "  # Plot the histogram of the probabilities with and without hyper-parameters\n",
    "  \n",
    "  hist(TableOfSummary[,3]/TableOfSummary[,2], main = \"The probability without the hyper-parameter\", xlab = \"The Probability of Buying\")\n",
    "  hist(TableOfSummary[,4]/TableOfSummary[,2], main = \"The probability with the hyper-parameter\", xlab = \"The Probability of Buying\")\n",
    "  \n",
    "  return(TableOfSummary)\n",
    "}\n",
    "\n",
    "# Bulid the summary table of the two different sessions and show the histogram\n",
    "Summary.Probability(n_sessions = 300, n_product = 500, n_customer = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Customer</th><th scope=col>Product</th><th scope=col>Gender</th><th scope=col>Viewed</th><th scope=col>Bought</th><th scope=col>Session</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1597</th><td>2   </td><td>  42</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1598</th><td>2   </td><td> 352</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1599</th><td>2   </td><td> 586</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1600</th><td>2   </td><td> 596</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1601</th><td>2   </td><td> 639</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1602</th><td>2   </td><td> 800</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1603</th><td>2   </td><td>1008</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1604</th><td>2   </td><td>1261</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1605</th><td>2   </td><td>1895</td><td>M   </td><td>1   </td><td>1   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1606</th><td>2   </td><td>2551</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1607</th><td>2   </td><td>2553</td><td>M   </td><td>1   </td><td>1   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1608</th><td>2   </td><td>2624</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1609</th><td>2   </td><td>2707</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1610</th><td>2   </td><td>2755</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1611</th><td>2   </td><td>2891</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1612</th><td>2   </td><td>3048</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1613</th><td>2   </td><td>3058</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1614</th><td>2   </td><td>3475</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1615</th><td>2   </td><td>3507</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1616</th><td>2   </td><td>3738</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1617</th><td>2   </td><td>3844</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1618</th><td>2   </td><td>3888</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1619</th><td>2   </td><td>3976</td><td>M   </td><td>1   </td><td>0   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>1620</th><td>2   </td><td>4538</td><td>M   </td><td>1   </td><td>1   </td><td> 39 </td></tr>\n",
       "\t<tr><th scope=row>6635</th><td>6   </td><td> 140</td><td>F   </td><td>1   </td><td>0   </td><td>133 </td></tr>\n",
       "\t<tr><th scope=row>6636</th><td>6   </td><td> 145</td><td>F   </td><td>1   </td><td>0   </td><td>133 </td></tr>\n",
       "\t<tr><th scope=row>6637</th><td>6   </td><td> 253</td><td>F   </td><td>1   </td><td>1   </td><td>133 </td></tr>\n",
       "\t<tr><th scope=row>6638</th><td>6   </td><td> 421</td><td>F   </td><td>1   </td><td>0   </td><td>133 </td></tr>\n",
       "\t<tr><th scope=row>6639</th><td>6   </td><td> 492</td><td>F   </td><td>1   </td><td>0   </td><td>133 </td></tr>\n",
       "\t<tr><th scope=row>6640</th><td>6   </td><td> 554</td><td>F   </td><td>1   </td><td>0   </td><td>133 </td></tr>\n",
       "\t<tr><th scope=row>...</th><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><th scope=row>49361</th><td>998 </td><td>3900</td><td>F   </td><td>1   </td><td>0   </td><td>989 </td></tr>\n",
       "\t<tr><th scope=row>49362</th><td>998 </td><td>3986</td><td>F   </td><td>1   </td><td>0   </td><td>989 </td></tr>\n",
       "\t<tr><th scope=row>49363</th><td>998 </td><td>4071</td><td>F   </td><td>1   </td><td>0   </td><td>989 </td></tr>\n",
       "\t<tr><th scope=row>49364</th><td>998 </td><td>4229</td><td>F   </td><td>1   </td><td>1   </td><td>989 </td></tr>\n",
       "\t<tr><th scope=row>49365</th><td>998 </td><td>4486</td><td>F   </td><td>1   </td><td>0   </td><td>989 </td></tr>\n",
       "\t<tr><th scope=row>31036</th><td>999 </td><td>   4</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31037</th><td>999 </td><td>  67</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31038</th><td>999 </td><td>  93</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31039</th><td>999 </td><td> 973</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31040</th><td>999 </td><td>1082</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31041</th><td>999 </td><td>1294</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31042</th><td>999 </td><td>1514</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31043</th><td>999 </td><td>1720</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31044</th><td>999 </td><td>1784</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31045</th><td>999 </td><td>2162</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31046</th><td>999 </td><td>2204</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31047</th><td>999 </td><td>2521</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31048</th><td>999 </td><td>2589</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31049</th><td>999 </td><td>2819</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31050</th><td>999 </td><td>2846</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31051</th><td>999 </td><td>2891</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31052</th><td>999 </td><td>3050</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31053</th><td>999 </td><td>3176</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31054</th><td>999 </td><td>3560</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31055</th><td>999 </td><td>3590</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31056</th><td>999 </td><td>4134</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31057</th><td>999 </td><td>4153</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31058</th><td>999 </td><td>4235</td><td>F   </td><td>1   </td><td>1   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31059</th><td>999 </td><td>4316</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "\t<tr><th scope=row>31060</th><td>999 </td><td>4784</td><td>F   </td><td>1   </td><td>0   </td><td>617 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       "  & Customer & Product & Gender & Viewed & Bought & Session\\\\\n",
       "\\hline\n",
       "\t1597 & 2    &   42 & M    & 1    & 0    &  39 \\\\\n",
       "\t1598 & 2    &  352 & M    & 1    & 0    &  39 \\\\\n",
       "\t1599 & 2    &  586 & M    & 1    & 0    &  39 \\\\\n",
       "\t1600 & 2    &  596 & M    & 1    & 0    &  39 \\\\\n",
       "\t1601 & 2    &  639 & M    & 1    & 0    &  39 \\\\\n",
       "\t1602 & 2    &  800 & M    & 1    & 0    &  39 \\\\\n",
       "\t1603 & 2    & 1008 & M    & 1    & 0    &  39 \\\\\n",
       "\t1604 & 2    & 1261 & M    & 1    & 0    &  39 \\\\\n",
       "\t1605 & 2    & 1895 & M    & 1    & 1    &  39 \\\\\n",
       "\t1606 & 2    & 2551 & M    & 1    & 0    &  39 \\\\\n",
       "\t1607 & 2    & 2553 & M    & 1    & 1    &  39 \\\\\n",
       "\t1608 & 2    & 2624 & M    & 1    & 0    &  39 \\\\\n",
       "\t1609 & 2    & 2707 & M    & 1    & 0    &  39 \\\\\n",
       "\t1610 & 2    & 2755 & M    & 1    & 0    &  39 \\\\\n",
       "\t1611 & 2    & 2891 & M    & 1    & 0    &  39 \\\\\n",
       "\t1612 & 2    & 3048 & M    & 1    & 0    &  39 \\\\\n",
       "\t1613 & 2    & 3058 & M    & 1    & 0    &  39 \\\\\n",
       "\t1614 & 2    & 3475 & M    & 1    & 0    &  39 \\\\\n",
       "\t1615 & 2    & 3507 & M    & 1    & 0    &  39 \\\\\n",
       "\t1616 & 2    & 3738 & M    & 1    & 0    &  39 \\\\\n",
       "\t1617 & 2    & 3844 & M    & 1    & 0    &  39 \\\\\n",
       "\t1618 & 2    & 3888 & M    & 1    & 0    &  39 \\\\\n",
       "\t1619 & 2    & 3976 & M    & 1    & 0    &  39 \\\\\n",
       "\t1620 & 2    & 4538 & M    & 1    & 1    &  39 \\\\\n",
       "\t6635 & 6    &  140 & F    & 1    & 0    & 133 \\\\\n",
       "\t6636 & 6    &  145 & F    & 1    & 0    & 133 \\\\\n",
       "\t6637 & 6    &  253 & F    & 1    & 1    & 133 \\\\\n",
       "\t6638 & 6    &  421 & F    & 1    & 0    & 133 \\\\\n",
       "\t6639 & 6    &  492 & F    & 1    & 0    & 133 \\\\\n",
       "\t6640 & 6    &  554 & F    & 1    & 0    & 133 \\\\\n",
       "\t... & ... & ... & ... & ... & ... & ...\\\\\n",
       "\t49361 & 998  & 3900 & F    & 1    & 0    & 989 \\\\\n",
       "\t49362 & 998  & 3986 & F    & 1    & 0    & 989 \\\\\n",
       "\t49363 & 998  & 4071 & F    & 1    & 0    & 989 \\\\\n",
       "\t49364 & 998  & 4229 & F    & 1    & 1    & 989 \\\\\n",
       "\t49365 & 998  & 4486 & F    & 1    & 0    & 989 \\\\\n",
       "\t31036 & 999  &    4 & F    & 1    & 0    & 617 \\\\\n",
       "\t31037 & 999  &   67 & F    & 1    & 0    & 617 \\\\\n",
       "\t31038 & 999  &   93 & F    & 1    & 1    & 617 \\\\\n",
       "\t31039 & 999  &  973 & F    & 1    & 0    & 617 \\\\\n",
       "\t31040 & 999  & 1082 & F    & 1    & 0    & 617 \\\\\n",
       "\t31041 & 999  & 1294 & F    & 1    & 1    & 617 \\\\\n",
       "\t31042 & 999  & 1514 & F    & 1    & 1    & 617 \\\\\n",
       "\t31043 & 999  & 1720 & F    & 1    & 1    & 617 \\\\\n",
       "\t31044 & 999  & 1784 & F    & 1    & 0    & 617 \\\\\n",
       "\t31045 & 999  & 2162 & F    & 1    & 0    & 617 \\\\\n",
       "\t31046 & 999  & 2204 & F    & 1    & 0    & 617 \\\\\n",
       "\t31047 & 999  & 2521 & F    & 1    & 0    & 617 \\\\\n",
       "\t31048 & 999  & 2589 & F    & 1    & 1    & 617 \\\\\n",
       "\t31049 & 999  & 2819 & F    & 1    & 0    & 617 \\\\\n",
       "\t31050 & 999  & 2846 & F    & 1    & 1    & 617 \\\\\n",
       "\t31051 & 999  & 2891 & F    & 1    & 0    & 617 \\\\\n",
       "\t31052 & 999  & 3050 & F    & 1    & 0    & 617 \\\\\n",
       "\t31053 & 999  & 3176 & F    & 1    & 0    & 617 \\\\\n",
       "\t31054 & 999  & 3560 & F    & 1    & 1    & 617 \\\\\n",
       "\t31055 & 999  & 3590 & F    & 1    & 0    & 617 \\\\\n",
       "\t31056 & 999  & 4134 & F    & 1    & 0    & 617 \\\\\n",
       "\t31057 & 999  & 4153 & F    & 1    & 0    & 617 \\\\\n",
       "\t31058 & 999  & 4235 & F    & 1    & 1    & 617 \\\\\n",
       "\t31059 & 999  & 4316 & F    & 1    & 0    & 617 \\\\\n",
       "\t31060 & 999  & 4784 & F    & 1    & 0    & 617 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Customer | Product | Gender | Viewed | Bought | Session | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1597 | 2    |   42 | M    | 1    | 0    |  39  | \n",
       "| 1598 | 2    |  352 | M    | 1    | 0    |  39  | \n",
       "| 1599 | 2    |  586 | M    | 1    | 0    |  39  | \n",
       "| 1600 | 2    |  596 | M    | 1    | 0    |  39  | \n",
       "| 1601 | 2    |  639 | M    | 1    | 0    |  39  | \n",
       "| 1602 | 2    |  800 | M    | 1    | 0    |  39  | \n",
       "| 1603 | 2    | 1008 | M    | 1    | 0    |  39  | \n",
       "| 1604 | 2    | 1261 | M    | 1    | 0    |  39  | \n",
       "| 1605 | 2    | 1895 | M    | 1    | 1    |  39  | \n",
       "| 1606 | 2    | 2551 | M    | 1    | 0    |  39  | \n",
       "| 1607 | 2    | 2553 | M    | 1    | 1    |  39  | \n",
       "| 1608 | 2    | 2624 | M    | 1    | 0    |  39  | \n",
       "| 1609 | 2    | 2707 | M    | 1    | 0    |  39  | \n",
       "| 1610 | 2    | 2755 | M    | 1    | 0    |  39  | \n",
       "| 1611 | 2    | 2891 | M    | 1    | 0    |  39  | \n",
       "| 1612 | 2    | 3048 | M    | 1    | 0    |  39  | \n",
       "| 1613 | 2    | 3058 | M    | 1    | 0    |  39  | \n",
       "| 1614 | 2    | 3475 | M    | 1    | 0    |  39  | \n",
       "| 1615 | 2    | 3507 | M    | 1    | 0    |  39  | \n",
       "| 1616 | 2    | 3738 | M    | 1    | 0    |  39  | \n",
       "| 1617 | 2    | 3844 | M    | 1    | 0    |  39  | \n",
       "| 1618 | 2    | 3888 | M    | 1    | 0    |  39  | \n",
       "| 1619 | 2    | 3976 | M    | 1    | 0    |  39  | \n",
       "| 1620 | 2    | 4538 | M    | 1    | 1    |  39  | \n",
       "| 6635 | 6    |  140 | F    | 1    | 0    | 133  | \n",
       "| 6636 | 6    |  145 | F    | 1    | 0    | 133  | \n",
       "| 6637 | 6    |  253 | F    | 1    | 1    | 133  | \n",
       "| 6638 | 6    |  421 | F    | 1    | 0    | 133  | \n",
       "| 6639 | 6    |  492 | F    | 1    | 0    | 133  | \n",
       "| 6640 | 6    |  554 | F    | 1    | 0    | 133  | \n",
       "| ... | ... | ... | ... | ... | ... | ... | \n",
       "| 49361 | 998  | 3900 | F    | 1    | 0    | 989  | \n",
       "| 49362 | 998  | 3986 | F    | 1    | 0    | 989  | \n",
       "| 49363 | 998  | 4071 | F    | 1    | 0    | 989  | \n",
       "| 49364 | 998  | 4229 | F    | 1    | 1    | 989  | \n",
       "| 49365 | 998  | 4486 | F    | 1    | 0    | 989  | \n",
       "| 31036 | 999  |    4 | F    | 1    | 0    | 617  | \n",
       "| 31037 | 999  |   67 | F    | 1    | 0    | 617  | \n",
       "| 31038 | 999  |   93 | F    | 1    | 1    | 617  | \n",
       "| 31039 | 999  |  973 | F    | 1    | 0    | 617  | \n",
       "| 31040 | 999  | 1082 | F    | 1    | 0    | 617  | \n",
       "| 31041 | 999  | 1294 | F    | 1    | 1    | 617  | \n",
       "| 31042 | 999  | 1514 | F    | 1    | 1    | 617  | \n",
       "| 31043 | 999  | 1720 | F    | 1    | 1    | 617  | \n",
       "| 31044 | 999  | 1784 | F    | 1    | 0    | 617  | \n",
       "| 31045 | 999  | 2162 | F    | 1    | 0    | 617  | \n",
       "| 31046 | 999  | 2204 | F    | 1    | 0    | 617  | \n",
       "| 31047 | 999  | 2521 | F    | 1    | 0    | 617  | \n",
       "| 31048 | 999  | 2589 | F    | 1    | 1    | 617  | \n",
       "| 31049 | 999  | 2819 | F    | 1    | 0    | 617  | \n",
       "| 31050 | 999  | 2846 | F    | 1    | 1    | 617  | \n",
       "| 31051 | 999  | 2891 | F    | 1    | 0    | 617  | \n",
       "| 31052 | 999  | 3050 | F    | 1    | 0    | 617  | \n",
       "| 31053 | 999  | 3176 | F    | 1    | 0    | 617  | \n",
       "| 31054 | 999  | 3560 | F    | 1    | 1    | 617  | \n",
       "| 31055 | 999  | 3590 | F    | 1    | 0    | 617  | \n",
       "| 31056 | 999  | 4134 | F    | 1    | 0    | 617  | \n",
       "| 31057 | 999  | 4153 | F    | 1    | 0    | 617  | \n",
       "| 31058 | 999  | 4235 | F    | 1    | 1    | 617  | \n",
       "| 31059 | 999  | 4316 | F    | 1    | 0    | 617  | \n",
       "| 31060 | 999  | 4784 | F    | 1    | 0    | 617  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      Customer Product Gender Viewed Bought Session\n",
       "1597  2          42    M      1      0       39    \n",
       "1598  2         352    M      1      0       39    \n",
       "1599  2         586    M      1      0       39    \n",
       "1600  2         596    M      1      0       39    \n",
       "1601  2         639    M      1      0       39    \n",
       "1602  2         800    M      1      0       39    \n",
       "1603  2        1008    M      1      0       39    \n",
       "1604  2        1261    M      1      0       39    \n",
       "1605  2        1895    M      1      1       39    \n",
       "1606  2        2551    M      1      0       39    \n",
       "1607  2        2553    M      1      1       39    \n",
       "1608  2        2624    M      1      0       39    \n",
       "1609  2        2707    M      1      0       39    \n",
       "1610  2        2755    M      1      0       39    \n",
       "1611  2        2891    M      1      0       39    \n",
       "1612  2        3048    M      1      0       39    \n",
       "1613  2        3058    M      1      0       39    \n",
       "1614  2        3475    M      1      0       39    \n",
       "1615  2        3507    M      1      0       39    \n",
       "1616  2        3738    M      1      0       39    \n",
       "1617  2        3844    M      1      0       39    \n",
       "1618  2        3888    M      1      0       39    \n",
       "1619  2        3976    M      1      0       39    \n",
       "1620  2        4538    M      1      1       39    \n",
       "6635  6         140    F      1      0      133    \n",
       "6636  6         145    F      1      0      133    \n",
       "6637  6         253    F      1      1      133    \n",
       "6638  6         421    F      1      0      133    \n",
       "6639  6         492    F      1      0      133    \n",
       "6640  6         554    F      1      0      133    \n",
       "...   ...      ...     ...    ...    ...    ...    \n",
       "49361 998      3900    F      1      0      989    \n",
       "49362 998      3986    F      1      0      989    \n",
       "49363 998      4071    F      1      0      989    \n",
       "49364 998      4229    F      1      1      989    \n",
       "49365 998      4486    F      1      0      989    \n",
       "31036 999         4    F      1      0      617    \n",
       "31037 999        67    F      1      0      617    \n",
       "31038 999        93    F      1      1      617    \n",
       "31039 999       973    F      1      0      617    \n",
       "31040 999      1082    F      1      0      617    \n",
       "31041 999      1294    F      1      1      617    \n",
       "31042 999      1514    F      1      1      617    \n",
       "31043 999      1720    F      1      1      617    \n",
       "31044 999      1784    F      1      0      617    \n",
       "31045 999      2162    F      1      0      617    \n",
       "31046 999      2204    F      1      0      617    \n",
       "31047 999      2521    F      1      0      617    \n",
       "31048 999      2589    F      1      1      617    \n",
       "31049 999      2819    F      1      0      617    \n",
       "31050 999      2846    F      1      1      617    \n",
       "31051 999      2891    F      1      0      617    \n",
       "31052 999      3050    F      1      0      617    \n",
       "31053 999      3176    F      1      0      617    \n",
       "31054 999      3560    F      1      1      617    \n",
       "31055 999      3590    F      1      0      617    \n",
       "31056 999      4134    F      1      0      617    \n",
       "31057 999      4153    F      1      0      617    \n",
       "31058 999      4235    F      1      1      617    \n",
       "31059 999      4316    F      1      0      617    \n",
       "31060 999      4784    F      1      0      617    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Transform the data into aggregate data form\n",
    "\n",
    "Aggregate.Form <- function(n_customer, n_sessions, n_product){\n",
    "  \n",
    "  # Call the previous functions we need \n",
    "  \n",
    "  sessions2 <- Sessions.Table.Adjust(n_sessions = n_sessions, n_product = n_product, n_customer = n_customer)\n",
    "  customer <- Customer.Table(n_customer = n_customer)\n",
    "  \n",
    "  # Transform the first session data into new form\n",
    "  \n",
    "  for (i in 1:1){\n",
    "    \n",
    "    # Transform the new table\n",
    "    \n",
    "    Product <- sessions2[i, seq(3, 201, 2)]\n",
    "    Product <- Product[is.na(Product) == FALSE]\n",
    "    \n",
    "    Bought <- sessions2[i, seq(4, 202, 2)]\n",
    "    Bought <- Bought[is.na(Bought) == FALSE]\n",
    "    \n",
    "    Customer <- rep(sessions2[i,1], times = length(Product))\n",
    "    Gender <- rep(customer[sessions2[i,1],2], times = length(Product))\n",
    "    Viewed <- rep(1, times = length(Product))\n",
    "    Session <- rep(i, times = length(Product))\n",
    "    \n",
    "    new <- cbind(Customer, Product, Gender, Viewed, Bought, Session)\n",
    "    new <- new[order(new[,2]),]\n",
    "    row.names(new) <- NULL\n",
    "    new <- as.data.frame(new)\n",
    "    \n",
    "    # Check if the product is duplicated\n",
    "    unit <- unique(new$Product)\n",
    "    if (length(unit) != length(new$Product)){\n",
    "      \n",
    "      new <- cbind(tapply(new$Viewed, new$Product, sum), tapply(new$Bought, new$Product, sum))\n",
    "      Product <- as.integer(row.names(new))\n",
    "      Customer <- rep(sessions2[i,1], times = length(unit))\n",
    "      Gender <- rep(customer[sessions2[i,1],2], times = length(unit))\n",
    "      Session <- rep(i, times = length(unit))\n",
    "      new <- cbind(Customer, Product, Gender, new, Session)\n",
    "      row.names(new) <- NULL\n",
    "      colnames(new) <- c(\"Customer\", \"Product\", \"Gender\", \"Viewed\", \"Bought\", \"Session\")\n",
    "      new <- as.data.frame(new)\n",
    "      \n",
    "    } \n",
    "    \n",
    "  }\n",
    "  \n",
    "  # Transform the remaining sessions into the new form\n",
    "  \n",
    "  for (i in 2:n_sessions){\n",
    "    \n",
    "    # Transform the new table\n",
    "    \n",
    "    Product <- sessions2[i, seq(3, 201, 2)]\n",
    "    Product <- Product[is.na(Product) == FALSE]\n",
    "    \n",
    "    Bought <- sessions2[i, seq(4, 202, 2)]\n",
    "    Bought <- Bought[is.na(Bought) == FALSE]\n",
    "    \n",
    "    Customer <- rep(sessions2[i,1], times = length(Product))\n",
    "    Gender <- rep(customer[sessions2[i,1],2], times = length(Product))\n",
    "    Viewed <- rep(1, times = length(Product))\n",
    "    Session <- rep(i, times = length(Product))\n",
    "    \n",
    "    new2 <- cbind(Customer, Product, Gender, Viewed, Bought, Session)\n",
    "    row.names(new2) <- NULL\n",
    "    \n",
    "    if (length(new2[,2]) > 1){\n",
    "      new2 <- new2[order(new2[,2]),]\n",
    "      \n",
    "    }\n",
    "    new2 <- as.data.frame(new2)\n",
    "    \n",
    "    # Check if the product is duplicated\n",
    "    unit <- unique(new2$Product)\n",
    "    \n",
    "    if (length(unit) != length(new2$Product)){\n",
    "      \n",
    "      new2 <- cbind(tapply(new2$Viewed, new2$Product, sum), tapply(new2$Bought, new2$Product, sum))\n",
    "      Product <- as.integer(row.names(new2))\n",
    "      Customer <- rep(sessions2[i,1], times = length(unit))\n",
    "      Gender <- rep(customer[sessions2[i,1],2], times = length(unit))\n",
    "      Session <- rep(i, times = length(unit))\n",
    "      new2 <- cbind(Customer, Product, Gender, new2, Session)\n",
    "      row.names(new2) <- NULL\n",
    "      colnames(new2) <- c(\"Customer\", \"Product\", \"Gender\", \"Viewed\", \"Bought\", \"Session\")\n",
    "      new2 <- as.data.frame(new2)\n",
    "      \n",
    "    } \n",
    "    \n",
    "    new <- rbind(new, new2)\n",
    "    \n",
    "  }\n",
    "  \n",
    "  # Sort the data by Customer_id and product_id\n",
    "  new <- new[order(new$Customer, new$Product),]\n",
    "  \n",
    "  # Change the label of gender into letters\n",
    "  new$Gender <- ifelse(new$Gender == 1, \"F\", \"M\")\n",
    "  \n",
    "  return(new)\n",
    "  \n",
    "}\n",
    "\n",
    "# Build the aggregate data frame with 1000 sessions.\n",
    "Aggregate.Form(n_sessions = 1000, n_product = 5000, n_customer = 1000)"
   ]
  },
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