Task_2_Prediction_using_Unsupervised_ML (1).ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LIHyEzm6PQEH"
      },
      "source": [
        "#G.Vinay venkata sai"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gy2p2DNxPQEM"
      },
      "source": [
        "## Data Science and Business Analytics Intern @ The Sparks Foundation "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vKcy2EH4PQEN"
      },
      "source": [
        "### Task #2 : Prediction using Unsupervised ML "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lCRhtb_gPQEN"
      },
      "source": [
        "#### Dataset : Iris.csv (https://bit.ly/3kXTdox)\n",
        "#### Algorithm used here : K-Means Clustering"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XPiv_CrwPQEO"
      },
      "source": [
        "### Import Libraries "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WYSdsOxDPQEO"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "\n",
        "from sklearn.datasets import load_iris\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "\n",
        "from sklearn.cluster import KMeans\n",
        "from sklearn.decomposition import PCA\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6AZBHXQOPQEQ"
      },
      "source": [
        "### Load Dataset"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "yN5aJGeMPQEQ",
        "outputId": "dff8f229-1a09-405d-bec8-6326ab7f8802"
      },
      "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>Id</th>\n",
              "      <th>SepalLengthCm</th>\n",
              "      <th>SepalWidthCm</th>\n",
              "      <th>PetalLengthCm</th>\n",
              "      <th>PetalWidthCm</th>\n",
              "      <th>Species</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>146</td>\n",
              "      <td>6.7</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.2</td>\n",
              "      <td>2.3</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>147</td>\n",
              "      <td>6.3</td>\n",
              "      <td>2.5</td>\n",
              "      <td>5.0</td>\n",
              "      <td>1.9</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>148</td>\n",
              "      <td>6.5</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.2</td>\n",
              "      <td>2.0</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>149</td>\n",
              "      <td>6.2</td>\n",
              "      <td>3.4</td>\n",
              "      <td>5.4</td>\n",
              "      <td>2.3</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>149</th>\n",
              "      <td>150</td>\n",
              "      <td>5.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.1</td>\n",
              "      <td>1.8</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>150 rows × 6 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "      Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  \\\n",
              "0      1            5.1           3.5            1.4           0.2   \n",
              "1      2            4.9           3.0            1.4           0.2   \n",
              "2      3            4.7           3.2            1.3           0.2   \n",
              "3      4            4.6           3.1            1.5           0.2   \n",
              "4      5            5.0           3.6            1.4           0.2   \n",
              "..   ...            ...           ...            ...           ...   \n",
              "145  146            6.7           3.0            5.2           2.3   \n",
              "146  147            6.3           2.5            5.0           1.9   \n",
              "147  148            6.5           3.0            5.2           2.0   \n",
              "148  149            6.2           3.4            5.4           2.3   \n",
              "149  150            5.9           3.0            5.1           1.8   \n",
              "\n",
              "            Species  \n",
              "0       Iris-setosa  \n",
              "1       Iris-setosa  \n",
              "2       Iris-setosa  \n",
              "3       Iris-setosa  \n",
              "4       Iris-setosa  \n",
              "..              ...  \n",
              "145  Iris-virginica  \n",
              "146  Iris-virginica  \n",
              "147  Iris-virginica  \n",
              "148  Iris-virginica  \n",
              "149  Iris-virginica  \n",
              "\n",
              "[150 rows x 6 columns]"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df=pd.read_csv('Iris.csv')\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZEbyr_1GPQES"
      },
      "source": [
        "K-Means is considered an unsupervised learning algorthm. This means you only need a features matrix. In the iris dataset, there are four features. In this notebook, the features matrix will only be two features as it is easier to visualize clusters in two dimensions. KMeans is a popular clustering algorithm that we can use to find structure in our data.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9Jt-PL25PQES",
        "outputId": "b8816a98-4486-46bb-e8c8-10088983693e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 150 entries, 0 to 149\n",
            "Data columns (total 6 columns):\n",
            " #   Column         Non-Null Count  Dtype  \n",
            "---  ------         --------------  -----  \n",
            " 0   Id             150 non-null    int64  \n",
            " 1   SepalLengthCm  150 non-null    float64\n",
            " 2   SepalWidthCm   150 non-null    float64\n",
            " 3   PetalLengthCm  150 non-null    float64\n",
            " 4   PetalWidthCm   150 non-null    float64\n",
            " 5   Species        150 non-null    object \n",
            "dtypes: float64(4), int64(1), object(1)\n",
            "memory usage: 7.2+ KB\n"
          ]
        }
      ],
      "source": [
        "\n",
        "df.info()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NV_40_rhPQET"
      },
      "source": [
        "### Arrange Data into Feature Matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rLO1ylJmPQET"
      },
      "outputs": [],
      "source": [
        "features = ['PetalLengthCm','PetalWidthCm']\n",
        "\n",
        "# Create features matrix\n",
        "x = df.loc[:, features].values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "ONa0UQrPPQET",
        "outputId": "2944f8b6-5c81-41cc-deec-679c688e7e55"
      },
      "outputs": [
        {
          "data": {
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              "       [1.4, 0.2],\n",
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              "       [1.7, 0.4],\n",
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              "       [1.5, 0.2],\n",
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              "       [1.5, 0.1],\n",
              "       [1.5, 0.2],\n",
              "       [1.6, 0.2],\n",
              "       [1.4, 0.1],\n",
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              "       [1.2, 0.2],\n",
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              "       [1.3, 0.4],\n",
              "       [1.4, 0.3],\n",
              "       [1.7, 0.3],\n",
              "       [1.5, 0.3],\n",
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              "       [1.5, 0.4],\n",
              "       [1. , 0.2],\n",
              "       [1.7, 0.5],\n",
              "       [1.9, 0.2],\n",
              "       [1.6, 0.2],\n",
              "       [1.6, 0.4],\n",
              "       [1.5, 0.2],\n",
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              "       [1.6, 0.2],\n",
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              "       [1.5, 0.1],\n",
              "       [1.4, 0.2],\n",
              "       [1.5, 0.1],\n",
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              "       [1.3, 0.2],\n",
              "       [1.5, 0.1],\n",
              "       [1.3, 0.2],\n",
              "       [1.5, 0.2],\n",
              "       [1.3, 0.3],\n",
              "       [1.3, 0.3],\n",
              "       [1.3, 0.2],\n",
              "       [1.6, 0.6],\n",
              "       [1.9, 0.4],\n",
              "       [1.4, 0.3],\n",
              "       [1.6, 0.2],\n",
              "       [1.4, 0.2],\n",
              "       [1.5, 0.2],\n",
              "       [1.4, 0.2],\n",
              "       [4.7, 1.4],\n",
              "       [4.5, 1.5],\n",
              "       [4.9, 1.5],\n",
              "       [4. , 1.3],\n",
              "       [4.6, 1.5],\n",
              "       [4.5, 1.3],\n",
              "       [4.7, 1.6],\n",
              "       [3.3, 1. ],\n",
              "       [4.6, 1.3],\n",
              "       [3.9, 1.4],\n",
              "       [3.5, 1. ],\n",
              "       [4.2, 1.5],\n",
              "       [4. , 1. ],\n",
              "       [4.7, 1.4],\n",
              "       [3.6, 1.3],\n",
              "       [4.4, 1.4],\n",
              "       [4.5, 1.5],\n",
              "       [4.1, 1. ],\n",
              "       [4.5, 1.5],\n",
              "       [3.9, 1.1],\n",
              "       [4.8, 1.8],\n",
              "       [4. , 1.3],\n",
              "       [4.9, 1.5],\n",
              "       [4.7, 1.2],\n",
              "       [4.3, 1.3],\n",
              "       [4.4, 1.4],\n",
              "       [4.8, 1.4],\n",
              "       [5. , 1.7],\n",
              "       [4.5, 1.5],\n",
              "       [3.5, 1. ],\n",
              "       [3.8, 1.1],\n",
              "       [3.7, 1. ],\n",
              "       [3.9, 1.2],\n",
              "       [5.1, 1.6],\n",
              "       [4.5, 1.5],\n",
              "       [4.5, 1.6],\n",
              "       [4.7, 1.5],\n",
              "       [4.4, 1.3],\n",
              "       [4.1, 1.3],\n",
              "       [4. , 1.3],\n",
              "       [4.4, 1.2],\n",
              "       [4.6, 1.4],\n",
              "       [4. , 1.2],\n",
              "       [3.3, 1. ],\n",
              "       [4.2, 1.3],\n",
              "       [4.2, 1.2],\n",
              "       [4.2, 1.3],\n",
              "       [4.3, 1.3],\n",
              "       [3. , 1.1],\n",
              "       [4.1, 1.3],\n",
              "       [6. , 2.5],\n",
              "       [5.1, 1.9],\n",
              "       [5.9, 2.1],\n",
              "       [5.6, 1.8],\n",
              "       [5.8, 2.2],\n",
              "       [6.6, 2.1],\n",
              "       [4.5, 1.7],\n",
              "       [6.3, 1.8],\n",
              "       [5.8, 1.8],\n",
              "       [6.1, 2.5],\n",
              "       [5.1, 2. ],\n",
              "       [5.3, 1.9],\n",
              "       [5.5, 2.1],\n",
              "       [5. , 2. ],\n",
              "       [5.1, 2.4],\n",
              "       [5.3, 2.3],\n",
              "       [5.5, 1.8],\n",
              "       [6.7, 2.2],\n",
              "       [6.9, 2.3],\n",
              "       [5. , 1.5],\n",
              "       [5.7, 2.3],\n",
              "       [4.9, 2. ],\n",
              "       [6.7, 2. ],\n",
              "       [4.9, 1.8],\n",
              "       [5.7, 2.1],\n",
              "       [6. , 1.8],\n",
              "       [4.8, 1.8],\n",
              "       [4.9, 1.8],\n",
              "       [5.6, 2.1],\n",
              "       [5.8, 1.6],\n",
              "       [6.1, 1.9],\n",
              "       [6.4, 2. ],\n",
              "       [5.6, 2.2],\n",
              "       [5.1, 1.5],\n",
              "       [5.6, 1.4],\n",
              "       [6.1, 2.3],\n",
              "       [5.6, 2.4],\n",
              "       [5.5, 1.8],\n",
              "       [4.8, 1.8],\n",
              "       [5.4, 2.1],\n",
              "       [5.6, 2.4],\n",
              "       [5.1, 2.3],\n",
              "       [5.1, 1.9],\n",
              "       [5.9, 2.3],\n",
              "       [5.7, 2.5],\n",
              "       [5.2, 2.3],\n",
              "       [5. , 1.9],\n",
              "       [5.2, 2. ],\n",
              "       [5.4, 2.3],\n",
              "       [5.1, 1.8]])"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f3c2qlHdPQEU"
      },
      "outputs": [],
      "source": [
        "from sklearn import preprocessing\n",
        "le=preprocessing.LabelEncoder()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "akghIhP6PQEU",
        "outputId": "96a38eed-55f3-465a-9367-c940b1da9607"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0      0\n",
              "1      0\n",
              "2      0\n",
              "3      0\n",
              "4      0\n",
              "      ..\n",
              "145    2\n",
              "146    2\n",
              "147    2\n",
              "148    2\n",
              "149    2\n",
              "Name: Species, Length: 150, dtype: int32"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df.Species=le.fit_transform(df.Species.values)\n",
        "df.Species"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SrJqJe0OPQEU",
        "outputId": "89c26467-fd29-4e47-9653-543185ac8e53"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0      0\n",
              "1      0\n",
              "2      0\n",
              "3      0\n",
              "4      0\n",
              "      ..\n",
              "145    2\n",
              "146    2\n",
              "147    2\n",
              "148    2\n",
              "149    2\n",
              "Name: Species, Length: 150, dtype: int32"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y=df.Species\n",
        "y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H0hKgFL0PQEV"
      },
      "source": [
        "### Standardize the data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qWijK74ZPQEV"
      },
      "outputs": [],
      "source": [
        "x=StandardScaler().fit_transform(x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "voIGG0thPQEV"
      },
      "source": [
        "### Plot data to estimate number of clusters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Qi3dWIO7PQEV",
        "outputId": "381af698-0324-4024-d083-d2f5ceca5d3e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'K-Means Clustering')"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "X=pd.DataFrame(x,columns=features)\n",
        "plt.figure(figsize=(6,5))\n",
        "plt.scatter(X['PetalLengthCm'], X['PetalWidthCm'])\n",
        "plt.xlabel('petal length (cm)')\n",
        "plt.ylabel('petal width (cm)');\n",
        "plt.title('K-Means Clustering')\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8gSYudC9PQEW"
      },
      "source": [
        "###  Finding the optimum number of clusters for K-means clustering"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4chg9XefPQEW"
      },
      "outputs": [],
      "source": [
        "# Finding the optimum number of clusters for k-means classification\n",
        "wcss = []\n",
        "\n",
        "for i in range(1, 11):\n",
        "    kmeans = KMeans(n_clusters = i, init = 'k-means++', \n",
        "                    max_iter = 300, n_init = 10, random_state = 0)\n",
        "    kmeans.fit(x)\n",
        "    wcss.append(kmeans.inertia_)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PjuaWvQZPQEW",
        "outputId": "d5980669-2870-49f8-9008-f43b741d8945"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plotting the results onto a line graph, \n",
        "# `allowing us to observe 'The elbow'\n",
        "plt.plot(range(1, 11), wcss)\n",
        "plt.title('The elbow method')\n",
        "plt.xlabel('Number of clusters')\n",
        "plt.ylabel('WCSS') # Within cluster sum of squares\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8ZuRau80PQEW"
      },
      "source": [
        "It is called 'The elbow method' from the above graph, the optimum clusters is where the elbow occurs. This is when the within cluster sum of squares (WCSS) doesn't decrease significantly with every iteration.\n",
        "\n",
        "From this we choose the number of clusters as **'3'**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aUNsdjAkPQEX"
      },
      "source": [
        "### K-Means Clustering "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "W_tYoyPsPQEX",
        "outputId": "1f882fd5-a53d-4434-fdd1-d6264547c7ff"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
              "       n_clusters=3, n_init=10, n_jobs=None, precompute_distances='auto',\n",
              "       random_state=1, tol=0.0001, verbose=0)"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Make an instance of KMeans with 3 clusters\n",
        "kmeans = KMeans(n_clusters=3, random_state=1)\n",
        "\n",
        "# Fit only on a features matrix\n",
        "kmeans.fit(x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LpGq78UhPQEX"
      },
      "outputs": [],
      "source": [
        "# Get labels and cluster centroids\n",
        "labels = kmeans.labels_\n",
        "centroids = kmeans.cluster_centers_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RqTeOmJ1PQEX",
        "outputId": "1c8dcc4d-40d5-4ceb-cd8e-4b210505ba0a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
              "       2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
              "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "labels"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dkgPcR3pPQEY",
        "outputId": "8f16b348-d4a5-48ec-89a8-c41cc1fd220c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1.02813193,  1.12749028],\n",
              "       [-1.30487835, -1.25512862],\n",
              "       [ 0.30564587,  0.16609419]])"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "centroids"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nxYiFVvtPQEY"
      },
      "source": [
        "### Visually Evaluate the clusters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RTa8KMEGPQEY",
        "outputId": "39e333c4-49a1-49b3-fa9b-1fcb7d2745b5"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "colormap = np.array(['r', 'g', 'b'])\n",
        "plt.scatter(X['PetalLengthCm'], X['PetalWidthCm'], c=colormap[labels])\n",
        "plt.scatter(centroids[:,0], centroids[:,1], s = 300, marker = 'x', c = 'k')\n",
        "\n",
        "plt.xlabel('petal length (cm)')\n",
        "plt.ylabel('petal width (cm)');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SzZOjXykPQEY"
      },
      "source": [
        "### Visually Evaluate the clusters and compare the species"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "s1fOFGflPQEY",
        "outputId": "59df39db-cebd-495b-d270-6c9cc6d3729e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(10,4))\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.scatter(X['PetalLengthCm'], X['PetalWidthCm'], c=colormap[labels])\n",
        "plt.scatter(centroids[:,0], centroids[:,1], s = 300, marker = 'x', c = 'k')\n",
        "plt.xlabel('petal length (cm)')\n",
        "plt.ylabel('petal width (cm)');\n",
        "plt.title('K-Means Clustering (k = 3)')\n",
        " \n",
        "plt.subplot(1, 2, 2)\n",
        "plt.scatter(X['PetalLengthCm'], X['PetalWidthCm'], c=colormap[y], s=40)\n",
        "plt.xlabel('petal length (cm)')\n",
        "plt.ylabel('petal width (cm)');\n",
        "plt.title('Flower Species')\n",
        "\n",
        "\n",
        "plt.tight_layout()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qsFUW6UUPQEZ"
      },
      "source": [
        "\n",
        "They look pretty similar. Looks like KMeans picked up flower differences with only two features and not the labels. The colors are different in the two graphs simply because KMeans gives out a arbitrary cluster number and the iris dataset has an arbitrary number in the target column."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XY45vLxuPQEZ"
      },
      "source": [
        "### PCA Projection in 2D "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HrGo_8tlPQEZ"
      },
      "source": [
        "The original data has 4 columns (sepal length, sepal width, petal length, and petal width). The code below projects the original data which is 4 dimensional into 2 dimensions. Note that after dimensionality reduction, there usually isn’t a particular meaning assigned to each principal component. The new components are just the two main dimensions of variation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GvUr5NgVPQEZ"
      },
      "outputs": [],
      "source": [
        "pca = PCA(n_components=2)\n",
        "\n",
        "# Fit and transform the data\n",
        "principalComponents = pca.fit_transform(x)\n",
        "\n",
        "principalDf = pd.DataFrame(data = principalComponents, columns = ['principal component 1', 'principal component 2'])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_xaE1vnpPQEa"
      },
      "outputs": [],
      "source": [
        "df=pd.read_csv('Iris.csv')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "esf_ZkMSPQEa"
      },
      "source": [
        "### 2D Projection"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yiuGiT2vPQEa"
      },
      "outputs": [],
      "source": [
        "finalDf = pd.concat([principalDf, df[['Species']]], axis = 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BcceB9msPQEa",
        "outputId": "2972dbf3-34c8-4d3c-cee7-5c0da1106c6c"
      },
      "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>principal component 1</th>\n",
              "      <th>principal component 2</th>\n",
              "      <th>Species</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-1.876838</td>\n",
              "      <td>0.020008</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-1.876838</td>\n",
              "      <td>0.020008</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.917048</td>\n",
              "      <td>0.060218</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-1.836627</td>\n",
              "      <td>-0.020202</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.876838</td>\n",
              "      <td>0.020008</td>\n",
              "      <td>Iris-setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>1.603421</td>\n",
              "      <td>0.444297</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>1.151139</td>\n",
              "      <td>0.152856</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>1.324525</td>\n",
              "      <td>0.165401</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>1.683841</td>\n",
              "      <td>0.363877</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>149</th>\n",
              "      <td>1.098384</td>\n",
              "      <td>0.019680</td>\n",
              "      <td>Iris-virginica</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>150 rows × 3 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "     principal component 1  principal component 2         Species\n",
              "0                -1.876838               0.020008     Iris-setosa\n",
              "1                -1.876838               0.020008     Iris-setosa\n",
              "2                -1.917048               0.060218     Iris-setosa\n",
              "3                -1.836627              -0.020202     Iris-setosa\n",
              "4                -1.876838               0.020008     Iris-setosa\n",
              "..                     ...                    ...             ...\n",
              "145               1.603421               0.444297  Iris-virginica\n",
              "146               1.151139               0.152856  Iris-virginica\n",
              "147               1.324525               0.165401  Iris-virginica\n",
              "148               1.683841               0.363877  Iris-virginica\n",
              "149               1.098384               0.019680  Iris-virginica\n",
              "\n",
              "[150 rows x 3 columns]"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "finalDf"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qmS5URomPQEa",
        "outputId": "7c686ffa-616c-4773-b17d-82137e20912d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (8,8));\n",
        "targets = df.loc[:, 'Species'].unique()\n",
        "colors = ['r', 'g', 'b']\n",
        "\n",
        "for target, color in zip(targets,colors):\n",
        "    indicesToKeep = finalDf['Species'] == target\n",
        "    ax.scatter(finalDf.loc[indicesToKeep, 'principal component 1']\n",
        "               , finalDf.loc[indicesToKeep, 'principal component 2']\n",
        "               , c = color\n",
        "               , s = 50)\n",
        "\n",
        "ax.set_xlabel('Principal Component 1', fontsize = 15)\n",
        "ax.set_ylabel('Principal Component 2', fontsize = 15)\n",
        "ax.set_title('2 Component PCA', fontsize = 20)    \n",
        "ax.legend(targets)\n",
        "ax.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WICSCwhVPQEb"
      },
      "source": [
        "\n",
        "From the graph, it looks like the setosa class is well separated from the versicolor and virginica classes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9htFP42SPQEb"
      },
      "source": [
        "### Explained Varience"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aO0bJ3lfPQEb"
      },
      "source": [
        "The explained variance tells us how much information (variance) can be attributed to each of the principal components. This is important as while you can convert 4 dimensional space to 2 dimensional space, you lose some of the variance (information) when you do this."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RcitYnLRPQEb",
        "outputId": "1c6a61ed-a970-4654-8c18-71b4d062ba8b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0.98137855, 0.01862145])"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pca.explained_variance_ratio_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SlTyB8jePQEb",
        "outputId": "46fabbf1-d8dd-4ce0-cd43-d9f3b1e9ce38"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sum(pca.explained_variance_ratio_)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MHoWWHDZPQEc"
      },
      "source": [
        "Together, the two principal components contain 100% of the information. The first principal component contains about 98% of the variance. The second principal component contains about 1.8% of the variance.\n",
        "\n",
        "PCA can be used to help visualize our data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uUN9KiIWPQEc"
      },
      "source": [
        "**Thank you!**"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.6"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}