PCA/PCA_Iris_DataSet.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1><b> Dimensionality Reduction - Principal Component Analysis </b></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importing required packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np  #for matrix calculation\n",
    "import matplotlib.pyplot as plt #for scatter plot\n",
    "import pandas as pd #for data frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Storing file paths of each file in a separate variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file_name = 'https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Implementing and explaining PCA method step by step on one file."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Reading the file - pca_a.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\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>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>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>4.6</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>5.0</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>5</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0    1    2    3            4\n",
       "0  5.1  3.5  1.4  0.2  Iris-setosa\n",
       "1  4.9  3.0  1.4  0.2  Iris-setosa\n",
       "2  4.7  3.2  1.3  0.2  Iris-setosa\n",
       "3  4.6  3.1  1.5  0.2  Iris-setosa\n",
       "4  5.0  3.6  1.4  0.2  Iris-setosa\n",
       "5  5.4  3.9  1.7  0.4  Iris-setosa\n",
       "6  4.6  3.4  1.4  0.3  Iris-setosa\n",
       "7  5.0  3.4  1.5  0.2  Iris-setosa\n",
       "8  4.4  2.9  1.4  0.2  Iris-setosa\n",
       "9  4.9  3.1  1.5  0.1  Iris-setosa"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(file_name, sep=',',header=None)\n",
    "df.head(n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Storing the disease labels in Y_label dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will separate the labels given in the last column, for easy calculations on the data frame.\n",
    "Extracting the last column of the disease label from the df_a and storing it into Y_label data frame for further use.\n",
    "Displaying first 10 rows of Y_label data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th>label</th>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <th>6</th>\n",
       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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       "      <td>Iris-setosa</td>\n",
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      "text/plain": [
       "         label\n",
       "0  Iris-setosa\n",
       "1  Iris-setosa\n",
       "2  Iris-setosa\n",
       "3  Iris-setosa\n",
       "4  Iris-setosa\n",
       "5  Iris-setosa\n",
       "6  Iris-setosa\n",
       "7  Iris-setosa\n",
       "8  Iris-setosa\n",
       "9  Iris-setosa"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class_label = pd.DataFrame(df.iloc[:,-1])\n",
    "class_label.columns = ['label']\n",
    "class_label.head(n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After deleting the last column of the data frame, we will have data frame of only features of data as df_a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
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       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
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       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
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       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.4</td>\n",
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       "      <td>0.4</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
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      "text/plain": [
       "     0    1    2    3\n",
       "0  5.1  3.5  1.4  0.2\n",
       "1  4.9  3.0  1.4  0.2\n",
       "2  4.7  3.2  1.3  0.2\n",
       "3  4.6  3.1  1.5  0.2\n",
       "4  5.0  3.6  1.4  0.2\n",
       "5  5.4  3.9  1.7  0.4\n",
       "6  4.6  3.4  1.4  0.3\n",
       "7  5.0  3.4  1.5  0.2\n",
       "8  4.4  2.9  1.4  0.2\n",
       "9  4.9  3.1  1.5  0.1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.iloc[:, :-1]\n",
    "df.head(n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean Normalization on Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df = df.sub(df.mean(axis=0), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Converting dataframe to matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To perform mathematical operations, we will convert our features data frame into matrix form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "matrix([[ -7.43333333e-01,   4.46000000e-01,  -2.35866667e+00,\n",
       "          -9.98666667e-01],\n",
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       "        [ -8.43333333e-01,   4.46000000e-01,  -2.45866667e+00,\n",
       "          -8.98666667e-01],\n",
       "        [ -1.34333333e+00,  -7.54000000e-01,  -2.45866667e+00,\n",
       "          -8.98666667e-01],\n",
       "        [ -1.44333333e+00,   1.46000000e-01,  -2.45866667e+00,\n",
       "          -9.98666667e-01],\n",
       "        [ -8.43333333e-01,   4.46000000e-01,  -2.15866667e+00,\n",
       "          -5.98666667e-01],\n",
       "        [ -7.43333333e-01,   7.46000000e-01,  -1.85866667e+00,\n",
       "          -7.98666667e-01],\n",
       "        [ -1.04333333e+00,  -5.40000000e-02,  -2.35866667e+00,\n",
       "          -8.98666667e-01],\n",
       "        [ -7.43333333e-01,   7.46000000e-01,  -2.15866667e+00,\n",
       "          -9.98666667e-01],\n",
       "        [ -1.24333333e+00,   1.46000000e-01,  -2.35866667e+00,\n",
       "          -9.98666667e-01],\n",
       "        [ -5.43333333e-01,   6.46000000e-01,  -2.25866667e+00,\n",
       "          -9.98666667e-01],\n",
       "        [ -8.43333333e-01,   2.46000000e-01,  -2.35866667e+00,\n",
       "          -9.98666667e-01],\n",
       "        [  1.15666667e+00,   1.46000000e-01,   9.41333333e-01,\n",
       "           2.01333333e-01],\n",
       "        [  5.56666667e-01,   1.46000000e-01,   7.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [  1.05666667e+00,   4.60000000e-02,   1.14133333e+00,\n",
       "           3.01333333e-01],\n",
       "        [ -3.43333333e-01,  -7.54000000e-01,   2.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [  6.56666667e-01,  -2.54000000e-01,   8.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [ -1.43333333e-01,  -2.54000000e-01,   7.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [  4.56666667e-01,   2.46000000e-01,   9.41333333e-01,\n",
       "           4.01333333e-01],\n",
       "        [ -9.43333333e-01,  -6.54000000e-01,  -4.58666667e-01,\n",
       "          -1.98666667e-01],\n",
       "        [  7.56666667e-01,  -1.54000000e-01,   8.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [ -6.43333333e-01,  -3.54000000e-01,   1.41333333e-01,\n",
       "           2.01333333e-01],\n",
       "        [ -8.43333333e-01,  -1.05400000e+00,  -2.58666667e-01,\n",
       "          -1.98666667e-01],\n",
       "        [  5.66666667e-02,  -5.40000000e-02,   4.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [  1.56666667e-01,  -8.54000000e-01,   2.41333333e-01,\n",
       "          -1.98666667e-01],\n",
       "        [  2.56666667e-01,  -1.54000000e-01,   9.41333333e-01,\n",
       "           2.01333333e-01],\n",
       "        [ -2.43333333e-01,  -1.54000000e-01,  -1.58666667e-01,\n",
       "           1.01333333e-01],\n",
       "        [  8.56666667e-01,   4.60000000e-02,   6.41333333e-01,\n",
       "           2.01333333e-01],\n",
       "        [ -2.43333333e-01,  -5.40000000e-02,   7.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [ -4.33333333e-02,  -3.54000000e-01,   3.41333333e-01,\n",
       "          -1.98666667e-01],\n",
       "        [  3.56666667e-01,  -8.54000000e-01,   7.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [ -2.43333333e-01,  -5.54000000e-01,   1.41333333e-01,\n",
       "          -9.86666667e-02],\n",
       "        [  5.66666667e-02,   1.46000000e-01,   1.04133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  2.56666667e-01,  -2.54000000e-01,   2.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [  4.56666667e-01,  -5.54000000e-01,   1.14133333e+00,\n",
       "           3.01333333e-01],\n",
       "        [  2.56666667e-01,  -2.54000000e-01,   9.41333333e-01,\n",
       "           1.33333333e-03],\n",
       "        [  5.56666667e-01,  -1.54000000e-01,   5.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [  7.56666667e-01,  -5.40000000e-02,   6.41333333e-01,\n",
       "           2.01333333e-01],\n",
       "        [  9.56666667e-01,  -2.54000000e-01,   1.04133333e+00,\n",
       "           2.01333333e-01],\n",
       "        [  8.56666667e-01,  -5.40000000e-02,   1.24133333e+00,\n",
       "           5.01333333e-01],\n",
       "        [  1.56666667e-01,  -1.54000000e-01,   7.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [ -1.43333333e-01,  -4.54000000e-01,  -2.58666667e-01,\n",
       "          -1.98666667e-01],\n",
       "        [ -3.43333333e-01,  -6.54000000e-01,   4.13333333e-02,\n",
       "          -9.86666667e-02],\n",
       "        [ -3.43333333e-01,  -6.54000000e-01,  -5.86666667e-02,\n",
       "          -1.98666667e-01],\n",
       "        [ -4.33333333e-02,  -3.54000000e-01,   1.41333333e-01,\n",
       "           1.33333333e-03],\n",
       "        [  1.56666667e-01,  -3.54000000e-01,   1.34133333e+00,\n",
       "           4.01333333e-01],\n",
       "        [ -4.43333333e-01,  -5.40000000e-02,   7.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [  1.56666667e-01,   3.46000000e-01,   7.41333333e-01,\n",
       "           4.01333333e-01],\n",
       "        [  8.56666667e-01,   4.60000000e-02,   9.41333333e-01,\n",
       "           3.01333333e-01],\n",
       "        [  4.56666667e-01,  -7.54000000e-01,   6.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [ -2.43333333e-01,  -5.40000000e-02,   3.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [ -3.43333333e-01,  -5.54000000e-01,   2.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [ -3.43333333e-01,  -4.54000000e-01,   6.41333333e-01,\n",
       "           1.33333333e-03],\n",
       "        [  2.56666667e-01,  -5.40000000e-02,   8.41333333e-01,\n",
       "           2.01333333e-01],\n",
       "        [ -4.33333333e-02,  -4.54000000e-01,   2.41333333e-01,\n",
       "           1.33333333e-03],\n",
       "        [ -8.43333333e-01,  -7.54000000e-01,  -4.58666667e-01,\n",
       "          -1.98666667e-01],\n",
       "        [ -2.43333333e-01,  -3.54000000e-01,   4.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [ -1.43333333e-01,  -5.40000000e-02,   4.41333333e-01,\n",
       "           1.33333333e-03],\n",
       "        [ -1.43333333e-01,  -1.54000000e-01,   4.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [  3.56666667e-01,  -1.54000000e-01,   5.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [ -7.43333333e-01,  -5.54000000e-01,  -7.58666667e-01,\n",
       "          -9.86666667e-02],\n",
       "        [ -1.43333333e-01,  -2.54000000e-01,   3.41333333e-01,\n",
       "           1.01333333e-01],\n",
       "        [  4.56666667e-01,   2.46000000e-01,   2.24133333e+00,\n",
       "           1.30133333e+00],\n",
       "        [ -4.33333333e-02,  -3.54000000e-01,   1.34133333e+00,\n",
       "           7.01333333e-01],\n",
       "        [  1.25666667e+00,  -5.40000000e-02,   2.14133333e+00,\n",
       "           9.01333333e-01],\n",
       "        [  4.56666667e-01,  -1.54000000e-01,   1.84133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  6.56666667e-01,  -5.40000000e-02,   2.04133333e+00,\n",
       "           1.00133333e+00],\n",
       "        [  1.75666667e+00,  -5.40000000e-02,   2.84133333e+00,\n",
       "           9.01333333e-01],\n",
       "        [ -9.43333333e-01,  -5.54000000e-01,   7.41333333e-01,\n",
       "           5.01333333e-01],\n",
       "        [  1.45666667e+00,  -1.54000000e-01,   2.54133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  8.56666667e-01,  -5.54000000e-01,   2.04133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  1.35666667e+00,   5.46000000e-01,   2.34133333e+00,\n",
       "           1.30133333e+00],\n",
       "        [  6.56666667e-01,   1.46000000e-01,   1.34133333e+00,\n",
       "           8.01333333e-01],\n",
       "        [  5.56666667e-01,  -3.54000000e-01,   1.54133333e+00,\n",
       "           7.01333333e-01],\n",
       "        [  9.56666667e-01,  -5.40000000e-02,   1.74133333e+00,\n",
       "           9.01333333e-01],\n",
       "        [ -1.43333333e-01,  -5.54000000e-01,   1.24133333e+00,\n",
       "           8.01333333e-01],\n",
       "        [ -4.33333333e-02,  -2.54000000e-01,   1.34133333e+00,\n",
       "           1.20133333e+00],\n",
       "        [  5.56666667e-01,   1.46000000e-01,   1.54133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [  6.56666667e-01,  -5.40000000e-02,   1.74133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  1.85666667e+00,   7.46000000e-01,   2.94133333e+00,\n",
       "           1.00133333e+00],\n",
       "        [  1.85666667e+00,  -4.54000000e-01,   3.14133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [  1.56666667e-01,  -8.54000000e-01,   1.24133333e+00,\n",
       "           3.01333333e-01],\n",
       "        [  1.05666667e+00,   1.46000000e-01,   1.94133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [ -2.43333333e-01,  -2.54000000e-01,   1.14133333e+00,\n",
       "           8.01333333e-01],\n",
       "        [  1.85666667e+00,  -2.54000000e-01,   2.94133333e+00,\n",
       "           8.01333333e-01],\n",
       "        [  4.56666667e-01,  -3.54000000e-01,   1.14133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  8.56666667e-01,   2.46000000e-01,   1.94133333e+00,\n",
       "           9.01333333e-01],\n",
       "        [  1.35666667e+00,   1.46000000e-01,   2.24133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  3.56666667e-01,  -2.54000000e-01,   1.04133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  2.56666667e-01,  -5.40000000e-02,   1.14133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  5.56666667e-01,  -2.54000000e-01,   1.84133333e+00,\n",
       "           9.01333333e-01],\n",
       "        [  1.35666667e+00,  -5.40000000e-02,   2.04133333e+00,\n",
       "           4.01333333e-01],\n",
       "        [  1.55666667e+00,  -2.54000000e-01,   2.34133333e+00,\n",
       "           7.01333333e-01],\n",
       "        [  2.05666667e+00,   7.46000000e-01,   2.64133333e+00,\n",
       "           8.01333333e-01],\n",
       "        [  5.56666667e-01,  -2.54000000e-01,   1.84133333e+00,\n",
       "           1.00133333e+00],\n",
       "        [  4.56666667e-01,  -2.54000000e-01,   1.34133333e+00,\n",
       "           3.01333333e-01],\n",
       "        [  2.56666667e-01,  -4.54000000e-01,   1.84133333e+00,\n",
       "           2.01333333e-01],\n",
       "        [  1.85666667e+00,  -5.40000000e-02,   2.34133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [  4.56666667e-01,   3.46000000e-01,   1.84133333e+00,\n",
       "           1.20133333e+00],\n",
       "        [  5.56666667e-01,   4.60000000e-02,   1.74133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  1.56666667e-01,  -5.40000000e-02,   1.04133333e+00,\n",
       "           6.01333333e-01],\n",
       "        [  1.05666667e+00,   4.60000000e-02,   1.64133333e+00,\n",
       "           9.01333333e-01],\n",
       "        [  8.56666667e-01,   4.60000000e-02,   1.84133333e+00,\n",
       "           1.20133333e+00],\n",
       "        [  1.05666667e+00,   4.60000000e-02,   1.34133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [ -4.33333333e-02,  -3.54000000e-01,   1.34133333e+00,\n",
       "           7.01333333e-01],\n",
       "        [  9.56666667e-01,   1.46000000e-01,   2.14133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [  8.56666667e-01,   2.46000000e-01,   1.94133333e+00,\n",
       "           1.30133333e+00],\n",
       "        [  8.56666667e-01,  -5.40000000e-02,   1.44133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [  4.56666667e-01,  -5.54000000e-01,   1.24133333e+00,\n",
       "           7.01333333e-01],\n",
       "        [  6.56666667e-01,  -5.40000000e-02,   1.44133333e+00,\n",
       "           8.01333333e-01],\n",
       "        [  3.56666667e-01,   3.46000000e-01,   1.64133333e+00,\n",
       "           1.10133333e+00],\n",
       "        [  5.66666667e-02,  -5.40000000e-02,   1.34133333e+00,\n",
       "           6.01333333e-01]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_mat = np.asmatrix(df)\n",
    "df_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculating covariance "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to achieve PCA on the dataset, lets start by calculating covariance matrix of the feature matrix. We will denote covariance matrix as sigma.\n",
    "\n",
    "$S = (1/n) * XX^T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.68569351, -0.03926846,  1.27368233,  0.5169038 ],\n",
       "       [-0.03926846,  0.18800403, -0.32171275, -0.11798121],\n",
       "       [ 1.27368233, -0.32171275,  3.11317942,  1.29638747],\n",
       "       [ 0.5169038 , -0.11798121,  1.29638747,  0.58241432]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sigma = 1/df_a_mat.shape[0] * np.dot(df_a_mat.transpose(),df_a_mat)\n",
    "sigma = np.cov(df_mat.T)\n",
    "sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigma.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculating eigen values and eigen vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eigVals, eigVec = np.linalg.eig(sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sorting eigen values in decreasing order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sorted_index = eigVals.argsort()[::-1] \n",
    "eigVals = eigVals[sorted_index]\n",
    "eigVec = eigVec[:,sorted_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.22484077,  0.24224357,  0.07852391,  0.02368303])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigVals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.36158968, -0.65653988, -0.58099728,  0.31725455],\n",
       "       [-0.08226889, -0.72971237,  0.59641809, -0.32409435],\n",
       "       [ 0.85657211,  0.1757674 ,  0.07252408, -0.47971899],\n",
       "       [ 0.35884393,  0.07470647,  0.54906091,  0.75112056]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigVec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Selecting top k eigen vectors : k=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.36158968, -0.65653988],\n",
       "       [-0.08226889, -0.72971237],\n",
       "       [ 0.85657211,  0.1757674 ],\n",
       "       [ 0.35884393,  0.07470647]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigVec = eigVec[:,:2]\n",
    "eigVec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transforming data on new subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eigVec = pd.DataFrame(np.real(eigVec))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "transformed = df_mat.dot(eigVec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-2.68420713, -0.32660731],\n",
       "        [-2.71539062,  0.16955685],\n",
       "        [-2.88981954,  0.13734561],\n",
       "        [-2.7464372 ,  0.31112432],\n",
       "        [-2.72859298, -0.33392456],\n",
       "        [-2.27989736, -0.74778271],\n",
       "        [-2.82089068,  0.08210451],\n",
       "        [-2.62648199, -0.17040535],\n",
       "        [-2.88795857,  0.57079803],\n",
       "        [-2.67384469,  0.1066917 ],\n",
       "        [-2.50652679, -0.65193501],\n",
       "        [-2.61314272, -0.02152063],\n",
       "        [-2.78743398,  0.22774019],\n",
       "        [-3.22520045,  0.50327991],\n",
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       "        [-2.38386932, -1.34475434],\n",
       "        [-2.6225262 , -0.81808967],\n",
       "        [-2.64832273, -0.31913667],\n",
       "        [-2.19907796, -0.87924409],\n",
       "        [-2.58734619, -0.52047364],\n",
       "        [-2.3105317 , -0.39786782],\n",
       "        [-2.54323491, -0.44003175],\n",
       "        [-3.21585769, -0.14161557],\n",
       "        [-2.30312854, -0.10552268],\n",
       "        [-2.35617109,  0.03120959],\n",
       "        [-2.50791723,  0.13905634],\n",
       "        [-2.469056  , -0.13788731],\n",
       "        [-2.56239095, -0.37468456],\n",
       "        [-2.63982127, -0.31929007],\n",
       "        [-2.63284791,  0.19007583],\n",
       "        [-2.58846205,  0.19739308],\n",
       "        [-2.41007734, -0.41808001],\n",
       "        [-2.64763667, -0.81998263],\n",
       "        [-2.59715948, -1.10002193],\n",
       "        [-2.67384469,  0.1066917 ],\n",
       "        [-2.86699985, -0.0771931 ],\n",
       "        [-2.62522846, -0.60680001],\n",
       "        [-2.67384469,  0.1066917 ],\n",
       "        [-2.98184266,  0.48025005],\n",
       "        [-2.59032303, -0.23605934],\n",
       "        [-2.77013891, -0.27105942],\n",
       "        [-2.85221108,  0.93286537],\n",
       "        [-2.99829644,  0.33430757],\n",
       "        [-2.4055141 , -0.19591726],\n",
       "        [-2.20883295, -0.44269603],\n",
       "        [-2.71566519,  0.24268148],\n",
       "        [-2.53757337, -0.51036755],\n",
       "        [-2.8403213 ,  0.22057634],\n",
       "        [-2.54268576, -0.58628103],\n",
       "        [-2.70391231, -0.11501085],\n",
       "        [ 1.28479459, -0.68543919],\n",
       "        [ 0.93241075, -0.31919809],\n",
       "        [ 1.46406132, -0.50418983],\n",
       "        [ 0.18096721,  0.82560394],\n",
       "        [ 1.08713449, -0.07539039],\n",
       "        [ 0.64043675,  0.41732348],\n",
       "        [ 1.09522371, -0.28389121],\n",
       "        [-0.75146714,  1.00110751],\n",
       "        [ 1.04329778, -0.22895691],\n",
       "        [-0.01019007,  0.72057487],\n",
       "        [-0.5110862 ,  1.26249195],\n",
       "        [ 0.51109806,  0.10228411],\n",
       "        [ 0.26233576,  0.5478933 ],\n",
       "        [ 0.98404455,  0.12436042],\n",
       "        [-0.174864  ,  0.25181557],\n",
       "        [ 0.92757294, -0.46823621],\n",
       "        [ 0.65959279,  0.35197629],\n",
       "        [ 0.23454059,  0.33192183],\n",
       "        [ 0.94236171,  0.54182226],\n",
       "        [ 0.0432464 ,  0.58148945],\n",
       "        [ 1.11624072,  0.08421401],\n",
       "        [ 0.35678657,  0.06682383],\n",
       "        [ 1.29646885,  0.32756152],\n",
       "        [ 0.92050265,  0.18239036],\n",
       "        [ 0.71400821, -0.15037915],\n",
       "        [ 0.89964086, -0.32961098],\n",
       "        [ 1.33104142, -0.24466952],\n",
       "        [ 1.55739627, -0.26739258],\n",
       "        [ 0.81245555,  0.16233157],\n",
       "        [-0.30733476,  0.36508661],\n",
       "        [-0.07034289,  0.70253793],\n",
       "        [-0.19188449,  0.67749054],\n",
       "        [ 0.13499495,  0.31170964],\n",
       "        [ 1.37873698,  0.42120514],\n",
       "        [ 0.58727485,  0.48328427],\n",
       "        [ 0.8072055 , -0.19505396],\n",
       "        [ 1.22042897, -0.40803534],\n",
       "        [ 0.81286779,  0.370679  ],\n",
       "        [ 0.24519516,  0.26672804],\n",
       "        [ 0.16451343,  0.67966147],\n",
       "        [ 0.46303099,  0.66952655],\n",
       "        [ 0.89016045,  0.03381244],\n",
       "        [ 0.22887905,  0.40225762],\n",
       "        [-0.70708128,  1.00842476],\n",
       "        [ 0.35553304,  0.50321849],\n",
       "        [ 0.33112695,  0.21118014],\n",
       "        [ 0.37523823,  0.29162202],\n",
       "        [ 0.64169028, -0.01907118],\n",
       "        [-0.90846333,  0.75156873],\n",
       "        [ 0.29780791,  0.34701652],\n",
       "        [ 2.53172698,  0.01184224],\n",
       "        [ 1.41407223,  0.57492506],\n",
       "        [ 2.61648461, -0.34193529],\n",
       "        [ 1.97081495,  0.18112569],\n",
       "        [ 2.34975798,  0.04188255],\n",
       "        [ 3.39687992, -0.54716805],\n",
       "        [ 0.51938325,  1.19135169],\n",
       "        [ 2.9320051 , -0.35237701],\n",
       "        [ 2.31967279,  0.24554817],\n",
       "        [ 2.91813423, -0.78038063],\n",
       "        [ 1.66193495, -0.2420384 ],\n",
       "        [ 1.80234045,  0.21615461],\n",
       "        [ 2.16537886, -0.21528028],\n",
       "        [ 1.34459422,  0.77641543],\n",
       "        [ 1.5852673 ,  0.53930705],\n",
       "        [ 1.90474358, -0.11881899],\n",
       "        [ 1.94924878, -0.04073026],\n",
       "        [ 3.48876538, -1.17154454],\n",
       "        [ 3.79468686, -0.25326557],\n",
       "        [ 1.29832982,  0.76101394],\n",
       "        [ 2.42816726, -0.37678197],\n",
       "        [ 1.19809737,  0.60557896],\n",
       "        [ 3.49926548, -0.45677347],\n",
       "        [ 1.38766825,  0.20403099],\n",
       "        [ 2.27585365, -0.33338653],\n",
       "        [ 2.61419383, -0.55836695],\n",
       "        [ 1.25762518,  0.179137  ],\n",
       "        [ 1.29066965,  0.11642525],\n",
       "        [ 2.12285398,  0.21085488],\n",
       "        [ 2.3875644 , -0.46251925],\n",
       "        [ 2.84096093, -0.37274259],\n",
       "        [ 3.2323429 , -1.37052404],\n",
       "        [ 2.15873837,  0.21832553],\n",
       "        [ 1.4431026 ,  0.14380129],\n",
       "        [ 1.77964011,  0.50146479],\n",
       "        [ 3.07652162, -0.68576444],\n",
       "        [ 2.14498686, -0.13890661],\n",
       "        [ 1.90486293, -0.04804751],\n",
       "        [ 1.16885347,  0.1645025 ],\n",
       "        [ 2.10765373, -0.37148225],\n",
       "        [ 2.31430339, -0.18260885],\n",
       "        [ 1.92245088, -0.40927118],\n",
       "        [ 1.41407223,  0.57492506],\n",
       "        [ 2.56332271, -0.2759745 ],\n",
       "        [ 2.41939122, -0.30350394],\n",
       "        [ 1.94401705, -0.18741522],\n",
       "        [ 1.52566363,  0.37502085],\n",
       "        [ 1.76404594, -0.07851919],\n",
       "        [ 1.90162908, -0.11587675],\n",
       "        [ 1.38966613,  0.28288671]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transformed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "final_df = np.hstack((transformed, class_label))\n",
    "final_df = pd.DataFrame(final_df)\n",
    "final_df.columns = ['x','y','label']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.68421</td>\n",
       "      <td>-0.326607</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.71539</td>\n",
       "      <td>0.169557</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.88982</td>\n",
       "      <td>0.137346</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.74644</td>\n",
       "      <td>0.311124</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.72859</td>\n",
       "      <td>-0.333925</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-2.2799</td>\n",
       "      <td>-0.747783</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-2.82089</td>\n",
       "      <td>0.0821045</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-2.62648</td>\n",
       "      <td>-0.170405</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-2.88796</td>\n",
       "      <td>0.570798</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-2.67384</td>\n",
       "      <td>0.106692</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-2.50653</td>\n",
       "      <td>-0.651935</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-2.61314</td>\n",
       "      <td>-0.0215206</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-2.78743</td>\n",
       "      <td>0.22774</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-3.2252</td>\n",
       "      <td>0.50328</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-2.64354</td>\n",
       "      <td>-1.18619</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-2.38387</td>\n",
       "      <td>-1.34475</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-2.62253</td>\n",
       "      <td>-0.81809</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-2.64832</td>\n",
       "      <td>-0.319137</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-2.19908</td>\n",
       "      <td>-0.879244</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-2.58735</td>\n",
       "      <td>-0.520474</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-2.31053</td>\n",
       "      <td>-0.397868</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>-2.54323</td>\n",
       "      <td>-0.440032</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>-3.21586</td>\n",
       "      <td>-0.141616</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-2.30313</td>\n",
       "      <td>-0.105523</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>-2.35617</td>\n",
       "      <td>0.0312096</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-2.50792</td>\n",
       "      <td>0.139056</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>-2.46906</td>\n",
       "      <td>-0.137887</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>-2.56239</td>\n",
       "      <td>-0.374685</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-2.63982</td>\n",
       "      <td>-0.31929</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>-2.63285</td>\n",
       "      <td>0.190076</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>120</th>\n",
       "      <td>2.42817</td>\n",
       "      <td>-0.376782</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>121</th>\n",
       "      <td>1.1981</td>\n",
       "      <td>0.605579</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>122</th>\n",
       "      <td>3.49927</td>\n",
       "      <td>-0.456773</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>123</th>\n",
       "      <td>1.38767</td>\n",
       "      <td>0.204031</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>2.27585</td>\n",
       "      <td>-0.333387</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125</th>\n",
       "      <td>2.61419</td>\n",
       "      <td>-0.558367</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>126</th>\n",
       "      <td>1.25763</td>\n",
       "      <td>0.179137</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>1.29067</td>\n",
       "      <td>0.116425</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>128</th>\n",
       "      <td>2.12285</td>\n",
       "      <td>0.210855</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>2.38756</td>\n",
       "      <td>-0.462519</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>130</th>\n",
       "      <td>2.84096</td>\n",
       "      <td>-0.372743</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131</th>\n",
       "      <td>3.23234</td>\n",
       "      <td>-1.37052</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>132</th>\n",
       "      <td>2.15874</td>\n",
       "      <td>0.218326</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>133</th>\n",
       "      <td>1.4431</td>\n",
       "      <td>0.143801</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>134</th>\n",
       "      <td>1.77964</td>\n",
       "      <td>0.501465</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>3.07652</td>\n",
       "      <td>-0.685764</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>2.14499</td>\n",
       "      <td>-0.138907</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>137</th>\n",
       "      <td>1.90486</td>\n",
       "      <td>-0.0480475</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>138</th>\n",
       "      <td>1.16885</td>\n",
       "      <td>0.164502</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>139</th>\n",
       "      <td>2.10765</td>\n",
       "      <td>-0.371482</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>2.3143</td>\n",
       "      <td>-0.182609</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>1.92245</td>\n",
       "      <td>-0.409271</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>1.41407</td>\n",
       "      <td>0.574925</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>2.56332</td>\n",
       "      <td>-0.275975</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>2.41939</td>\n",
       "      <td>-0.303504</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>1.94402</td>\n",
       "      <td>-0.187415</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>1.52566</td>\n",
       "      <td>0.375021</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>1.76405</td>\n",
       "      <td>-0.0785192</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>1.90163</td>\n",
       "      <td>-0.115877</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>1.38967</td>\n",
       "      <td>0.282887</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           x          y           label\n",
       "0   -2.68421  -0.326607     Iris-setosa\n",
       "1   -2.71539   0.169557     Iris-setosa\n",
       "2   -2.88982   0.137346     Iris-setosa\n",
       "3   -2.74644   0.311124     Iris-setosa\n",
       "4   -2.72859  -0.333925     Iris-setosa\n",
       "5    -2.2799  -0.747783     Iris-setosa\n",
       "6   -2.82089  0.0821045     Iris-setosa\n",
       "7   -2.62648  -0.170405     Iris-setosa\n",
       "8   -2.88796   0.570798     Iris-setosa\n",
       "9   -2.67384   0.106692     Iris-setosa\n",
       "10  -2.50653  -0.651935     Iris-setosa\n",
       "11  -2.61314 -0.0215206     Iris-setosa\n",
       "12  -2.78743    0.22774     Iris-setosa\n",
       "13   -3.2252    0.50328     Iris-setosa\n",
       "14  -2.64354   -1.18619     Iris-setosa\n",
       "15  -2.38387   -1.34475     Iris-setosa\n",
       "16  -2.62253   -0.81809     Iris-setosa\n",
       "17  -2.64832  -0.319137     Iris-setosa\n",
       "18  -2.19908  -0.879244     Iris-setosa\n",
       "19  -2.58735  -0.520474     Iris-setosa\n",
       "20  -2.31053  -0.397868     Iris-setosa\n",
       "21  -2.54323  -0.440032     Iris-setosa\n",
       "22  -3.21586  -0.141616     Iris-setosa\n",
       "23  -2.30313  -0.105523     Iris-setosa\n",
       "24  -2.35617  0.0312096     Iris-setosa\n",
       "25  -2.50792   0.139056     Iris-setosa\n",
       "26  -2.46906  -0.137887     Iris-setosa\n",
       "27  -2.56239  -0.374685     Iris-setosa\n",
       "28  -2.63982   -0.31929     Iris-setosa\n",
       "29  -2.63285   0.190076     Iris-setosa\n",
       "..       ...        ...             ...\n",
       "120  2.42817  -0.376782  Iris-virginica\n",
       "121   1.1981   0.605579  Iris-virginica\n",
       "122  3.49927  -0.456773  Iris-virginica\n",
       "123  1.38767   0.204031  Iris-virginica\n",
       "124  2.27585  -0.333387  Iris-virginica\n",
       "125  2.61419  -0.558367  Iris-virginica\n",
       "126  1.25763   0.179137  Iris-virginica\n",
       "127  1.29067   0.116425  Iris-virginica\n",
       "128  2.12285   0.210855  Iris-virginica\n",
       "129  2.38756  -0.462519  Iris-virginica\n",
       "130  2.84096  -0.372743  Iris-virginica\n",
       "131  3.23234   -1.37052  Iris-virginica\n",
       "132  2.15874   0.218326  Iris-virginica\n",
       "133   1.4431   0.143801  Iris-virginica\n",
       "134  1.77964   0.501465  Iris-virginica\n",
       "135  3.07652  -0.685764  Iris-virginica\n",
       "136  2.14499  -0.138907  Iris-virginica\n",
       "137  1.90486 -0.0480475  Iris-virginica\n",
       "138  1.16885   0.164502  Iris-virginica\n",
       "139  2.10765  -0.371482  Iris-virginica\n",
       "140   2.3143  -0.182609  Iris-virginica\n",
       "141  1.92245  -0.409271  Iris-virginica\n",
       "142  1.41407   0.574925  Iris-virginica\n",
       "143  2.56332  -0.275975  Iris-virginica\n",
       "144  2.41939  -0.303504  Iris-virginica\n",
       "145  1.94402  -0.187415  Iris-virginica\n",
       "146  1.52566   0.375021  Iris-virginica\n",
       "147  1.76405 -0.0785192  Iris-virginica\n",
       "148  1.90163  -0.115877  Iris-virginica\n",
       "149  1.38967   0.282887  Iris-virginica\n",
       "\n",
       "[150 rows x 3 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scatter plot of new data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AuOCCC3jppZfavG/Dhg00NjZy/PHHAzBu3DheeOGF1tfPOeeckL+lYArd40ilCvgo7vka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\nqKZ1iwWNHWwTpo4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FnFxPR5AdAH+mqo2q+ghwAHCIqhbff4F55rcXRzLJtpVNZ1tb0wF5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\nhGKBwxhjTCgWOIwxxoRigcMYY0wo/x9p3RfhQA314QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2107230d8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "groups = final_df.groupby('label')\n",
    "figure, axes = plt.subplots()\n",
    "axes.margins(0.05)\n",
    "for name, group in groups:\n",
    "    axes.plot(group.x, group.y, marker='o', linestyle='', ms=6, label=name)\n",
    "    axes.set_title(\"PCA on IRIS data set\")\n",
    "axes.legend()\n",
    "plt.xlabel(\"principal component 1\")\n",
    "plt.ylabel(\"principal component 2\")\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}