Base_Paperwise_RSNMF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creation of R matrix (User-Item rating matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[5,0,4,0,3,3],\n",
    "            [0,4,0,0,3,0],\n",
    "            [3,0,0,3,0,0],\n",
    "            [0,4,0,5,0,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "   1  2  3  4  5  6\n",
       "1  5  0  4  0  3  3\n",
       "2  0  4  0  0  3  0\n",
       "3  3  0  0  3  0  0\n",
       "4  0  4  0  5  0  1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Data = pd.DataFrame(data=x, index=[1,2,3,4], columns=[1,2,3,4,5,6])\n",
    "Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[5, 0, 4, 0, 3, 3],\n",
       "        [0, 4, 0, 0, 3, 0],\n",
       "        [3, 0, 0, 3, 0, 0],\n",
       "        [0, 4, 0, 5, 0, 1]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R = np.asmatrix(x)\n",
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_arr = np.array(R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization of f i.e. low rank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## U is No of users in User-Item rating matrix\n",
    "## I is No of items User-Item rating matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "U,I = R.shape\n",
    "f = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Factor matrices initialization randomly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#p = np.random.rand(U,f)\n",
    "#q = np.random.rand(f,I)\n",
    "p = np.array([[0.11,0.07,0.19],\n",
    "            [0.09,0.16,0.19],\n",
    "            [0.09,0.05,0.04],\n",
    "            [0.03,0.13,0.18]])\n",
    "q = np.array([[0.16,0.01,0.07,0.17,0.02,0.20],\n",
    "             [0.18,0.19,0.10,0.05,0.18,0.15],\n",
    "             [0.02,0.18,0.03,0.14,0.17,0.06]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = np.asmatrix(p)\n",
    "Q = np.asmatrix(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.11</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.09</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.09</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.03</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "      1     2     3\n",
       "1  0.11  0.07  0.19\n",
       "2  0.09  0.16  0.19\n",
       "3  0.09  0.05  0.04\n",
       "4  0.03  0.13  0.18"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=P, index=[1,2,3,4], columns=[1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.16</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.18</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      1     2     3     4     5     6\n",
       "1  0.16  0.01  0.07  0.17  0.02  0.20\n",
       "2  0.18  0.19  0.10  0.05  0.18  0.15\n",
       "3  0.02  0.18  0.03  0.14  0.17  0.06"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=Q, index=[1,2,3], columns=[1,2,3,4,5,6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularization Coefficient initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_p = 0.06\n",
    "lambda_q = 0.06"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting maximum training round"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 1\n",
    "max_training_round = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple error measure (Sum of elementwise squared error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_error(R, P, Q):\n",
    "    return np.sum(np.square(R - np.dot(P,Q)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auxiliary matrix to determine Ui and Iu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = R>0.01\n",
    "W[W == True] = 1\n",
    "W[W == False] = 0\n",
    "# To be consistent with our Q matrix\n",
    "W = W.astype(np.int64, copy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "l2 = lambda x : np.sqrt(sum(x**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Counting no of users who rated item i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ui = []\n",
    "for iterator in range(I):\n",
    "    Ui.append(W[:,iterator].sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "R.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ui = l2(R_arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Counting no of items which was being rated by user u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "Iu = []\n",
    "for iterator in range(U):\n",
    "    Iu.append(W[iterator].sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "Iu = l2(R_arr.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Ui)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Iu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.83095189, 5.65685425, 4.        , 5.83095189, 4.24264069,\n",
       "       3.16227766])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ui"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7.68114575, 5.        , 4.24264069, 6.4807407 ])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Iu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RSNMF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "error = []\n",
    "while t <= max_training_round:\n",
    "    UserUp = np.zeros((U,f), dtype=float)\n",
    "    UserDown = np.zeros((U,f), dtype=float)\n",
    "    ItemUp = np.zeros((f,I), dtype=float)\n",
    "    ItemDown = np.zeros((f,I), dtype=float)\n",
    "    for u in range(U):\n",
    "        for i in range(I):\n",
    "            if(R[u,i] != 0):\n",
    "                rui_cap = P[u,:]*Q[:,i]\n",
    "                for k in range(f):\n",
    "                    UserUp[u,k] = UserUp[u,k] + Q[k,i] * R[u,i]\n",
    "                    UserDown[u,k] = UserDown[u,k] + Q[k,i] * rui_cap\n",
    "                    ItemUp[k,i] = ItemUp[k,i] + P[u,k] * R[u,i]\n",
    "                    ItemDown[k,i] = ItemDown[k,i] + P[u,k]*rui_cap\n",
    "    for u in range(U):\n",
    "        for k in range(f):\n",
    "            UserDown[u,k] = UserDown[u,k] + Iu[u] * lambda_p * P[u,k]\n",
    "            P[u,k] = P[u,k] * (UserUp[u,k]/UserDown[u,k])\n",
    "    for i in range(I):\n",
    "        for k in range(f):\n",
    "            ItemDown[k,i] = ItemDown[k,i] + Ui[i] * lambda_q * Q[k,i]\n",
    "            Q[k,i] = Q[k,i] * (ItemUp[k,i]/ItemDown[k,i])\n",
    "    error.append(get_error(R, P, Q))\n",
    "    #print('{}th epoch is completed'.format(t))\n",
    "    t = t+1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## No of training epoch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of training epoch : 100\n"
     ]
    }
   ],
   "source": [
    "print(\"No of training epoch : %d\"%max_training_round)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## You could check the values by solving it by hand "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.626711</td>\n",
       "      <td>1.287679</td>\n",
       "      <td>1.001976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.332787</td>\n",
       "      <td>1.298760</td>\n",
       "      <td>1.513618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.730927</td>\n",
       "      <td>0.814009</td>\n",
       "      <td>0.926897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.200247</td>\n",
       "      <td>1.087277</td>\n",
       "      <td>1.808322</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "          1         2         3\n",
       "1  1.626711  1.287679  1.001976\n",
       "2  0.332787  1.298760  1.513618\n",
       "3  0.730927  0.814009  0.926897\n",
       "4  0.200247  1.087277  1.808322"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=P, index=[1,2,3,4], columns=[1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.381457</td>\n",
       "      <td>0.247884</td>\n",
       "      <td>1.161438</td>\n",
       "      <td>0.372386</td>\n",
       "      <td>0.447889</td>\n",
       "      <td>1.218432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.159731</td>\n",
       "      <td>1.152045</td>\n",
       "      <td>0.924362</td>\n",
       "      <td>1.161127</td>\n",
       "      <td>0.960357</td>\n",
       "      <td>0.602987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.009681</td>\n",
       "      <td>1.447950</td>\n",
       "      <td>0.745730</td>\n",
       "      <td>1.847967</td>\n",
       "      <td>0.976423</td>\n",
       "      <td>0.092706</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          1         2         3         4         5         6\n",
       "1  1.381457  0.247884  1.161438  0.372386  0.447889  1.218432\n",
       "2  1.159731  1.152045  0.924362  1.161127  0.960357  0.602987\n",
       "3  1.009681  1.447950  0.745730  1.847967  0.976423  0.092706"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=Q, index=[1,2,3], columns=[1,2,3,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.752269</td>\n",
       "      <td>3.337511</td>\n",
       "      <td>3.826808</td>\n",
       "      <td>3.952542</td>\n",
       "      <td>2.943570</td>\n",
       "      <td>2.851379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.494214</td>\n",
       "      <td>3.770365</td>\n",
       "      <td>2.715784</td>\n",
       "      <td>4.429065</td>\n",
       "      <td>2.874256</td>\n",
       "      <td>1.328934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.889646</td>\n",
       "      <td>2.461060</td>\n",
       "      <td>2.292579</td>\n",
       "      <td>2.930229</td>\n",
       "      <td>2.014156</td>\n",
       "      <td>1.467350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.363411</td>\n",
       "      <td>3.920590</td>\n",
       "      <td>2.586131</td>\n",
       "      <td>4.678755</td>\n",
       "      <td>2.899550</td>\n",
       "      <td>1.067244</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          1         2         3         4         5         6\n",
       "1  4.752269  3.337511  3.826808  3.952542  2.943570  2.851379\n",
       "2  3.494214  3.770365  2.715784  4.429065  2.874256  1.328934\n",
       "3  2.889646  2.461060  2.292579  2.930229  2.014156  1.467350\n",
       "4  3.363411  3.920590  2.586131  4.678755  2.899550  1.067244"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rp = np.dot(P,Q)\n",
    "R_estimated = pd.DataFrame(data=rp, index=[1,2,3,4], columns=[1,2,3,4,5,6])\n",
    "R_estimated.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total error of rated movies: 111.97620181864559\n"
     ]
    }
   ],
   "source": [
    "print('Total error of rated movies: {}'.format(get_error(R,P,Q)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19caa812c50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(error);\n",
    "plt.xlabel('Iteration Number');\n",
    "plt.ylabel('Sum of Squared Error');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[82.72553034625035,\n",
       " 1124.2342991137998,\n",
       " 73.4677806731767,\n",
       " 717.4042922837602,\n",
       " 69.23019506545775,\n",
       " 505.8826008266523,\n",
       " 68.01974918875938,\n",
       " 383.10351203143557,\n",
       " 68.8869609706766,\n",
       " 306.30489879655124,\n",
       " 71.15168393389403,\n",
       " 255.5951624126963,\n",
       " 74.28866884524078,\n",
       " 220.70637979181566,\n",
       " 77.89620386462892,\n",
       " 195.91129779436892,\n",
       " 81.67685443636245,\n",
       " 177.81976420437564,\n",
       " 85.41994941632875,\n",
       " 164.32854476068349,\n",
       " 88.9847627537385,\n",
       " 154.08194384142726,\n",
       " 92.28493395603005,\n",
       " 146.17771239058413,\n",
       " 95.27474649951552,\n",
       " 139.99872989824777,\n",
       " 97.93761736330522,\n",
       " 135.1127321862731,\n",
       " 100.276859069846,\n",
       " 131.21052405080263,\n",
       " 102.3085582140849,\n",
       " 128.06678495635092,\n",
       " 104.05628983082494,\n",
       " 125.51456728696984,\n",
       " 105.54733975098351,\n",
       " 123.4283251415851,\n",
       " 106.81011241794805,\n",
       " 121.71238821719385,\n",
       " 107.8724364791765,\n",
       " 120.29298727550429,\n",
       " 108.76052779514367,\n",
       " 119.112641784704,\n",
       " 109.49841846118535,\n",
       " 118.12614689796413,\n",
       " 110.10770507518711,\n",
       " 117.29766124312393,\n",
       " 110.60750722494167,\n",
       " 116.59856410840547,\n",
       " 111.01455747395966,\n",
       " 116.00585820534623,\n",
       " 111.34336754171292,\n",
       " 115.50096462504064,\n",
       " 111.60643292399311,\n",
       " 115.06880341800114,\n",
       " 111.81445101438902,\n",
       " 114.69708478295671,\n",
       " 111.97653692819875,\n",
       " 114.37575739984023,\n",
       " 112.10042760116126,\n",
       " 114.09657534170063,\n",
       " 112.1926690696323,\n",
       " 113.85275542278796,\n",
       " 112.25878470611218,\n",
       " 113.63870421293676,\n",
       " 112.3034240151859,\n",
       " 113.44979922079625,\n",
       " 112.3304927083743,\n",
       " 113.28221255897392,\n",
       " 112.34326540297377,\n",
       " 113.13276818701532,\n",
       " 112.3444825942288,\n",
       " 112.99882588161886,\n",
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