{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright (c) 2015, 2016 [Sebastian Raschka](sebastianraschka.com)\n",
    "\n",
    "https://github.com/rasbt/python-machine-learning-book\n",
    "\n",
    "[MIT License](https://github.com/rasbt/python-machine-learning-book/blob/master/LICENSE.txt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Machine Learning - Code Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 5 - Compressing Data via Dimensionality Reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka \n",
      "last updated: 2016-07-26 \n",
      "\n",
      "CPython 3.5.1\n",
      "IPython 5.0.0\n",
      "\n",
      "numpy 1.11.1\n",
      "scipy 0.17.1\n",
      "matplotlib 1.5.1\n",
      "scikit-learn 0.17.1\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,scipy,matplotlib,scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "*The use of `watermark` is optional. You can install this IPython extension via \"`pip install watermark`\". For more information, please see: https://github.com/rasbt/watermark.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Unsupervised dimensionality reduction via principal component analysis 128](#Unsupervised-dimensionality-reduction-via-principal-component-analysis-128)\n",
    "  - [Total and explained variance](#Total-and-explained-variance)\n",
    "  - [Feature transformation](#Feature-transformation)\n",
    "  - [Principal component analysis in scikit-learn](#Principal-component-analysis-in-scikit-learn)\n",
    "- [Supervised data compression via linear discriminant analysis](#Supervised-data-compression-via-linear-discriminant-analysis)\n",
    "  - [Computing the scatter matrices](#Computing-the-scatter-matrices)\n",
    "  - [Selecting linear discriminants for the new feature subspace](#Selecting-linear-discriminants-for-the-new-feature-subspace)\n",
    "  - [Projecting samples onto the new feature space](#Projecting-samples-onto-the-new-feature-space)\n",
    "  - [LDA via scikit-learn](#LDA-via-scikit-learn)\n",
    "- [Using kernel principal component analysis for nonlinear mappings](#Using-kernel-principal-component-analysis-for-nonlinear-mappings)\n",
    "  - [Kernel functions and the kernel trick](#Kernel-functions-and-the-kernel-trick)\n",
    "  - [Implementing a kernel principal component analysis in Python](#Implementing-a-kernel-principal-component-analysis-in-Python)\n",
    "    - [Example 1 – separating half-moon shapes](#Example-1-–-separating-half-moon-shapes)\n",
    "    - [Example 2 – separating concentric circles](#Example-2-–-separating-concentric-circles)\n",
    "  - [Projecting new data points](#Projecting-new-data-points)\n",
    "  - [Kernel principal component analysis in scikit-learn](#Kernel-principal-component-analysis-in-scikit-learn)\n",
    "- [Summary](#Summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised dimensionality reduction via principal component analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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AIhBRBJRYIgqnFqYIKAKKgCKgxKLvgCKgCCgCikBEEVBiiSicWpgioAgoAoqAEou+A4qA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\nHKK1WOKj4ZlGaJMCZMhrTLYN9GAT5uGJ8nMmQ5T+oUcfJzymJvlJhH0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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "image/png": {
       "width": 400
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./images/05_01.png', width=400) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Class label</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315 of diluted wines</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Class label  Alcohol  Malic acid   Ash  Alcalinity of ash  Magnesium  \\\n",
       "0            1    14.23        1.71  2.43               15.6        127   \n",
       "1            1    13.20        1.78  2.14               11.2        100   \n",
       "2            1    13.16        2.36  2.67               18.6        101   \n",
       "3            1    14.37        1.95  2.50               16.8        113   \n",
       "4            1    13.24        2.59  2.87               21.0        118   \n",
       "\n",
       "   Total phenols  Flavanoids  Nonflavanoid phenols  Proanthocyanins  \\\n",
       "0           2.80        3.06                  0.28             2.29   \n",
       "1           2.65        2.76                  0.26             1.28   \n",
       "2           2.80        3.24                  0.30             2.81   \n",
       "3           3.85        3.49                  0.24             2.18   \n",
       "4           2.80        2.69                  0.39             1.82   \n",
       "\n",
       "   Color intensity   Hue  OD280/OD315 of diluted wines  Proline  \n",
       "0             5.64  1.04                          3.92     1065  \n",
       "1             4.38  1.05                          3.40     1050  \n",
       "2             5.68  1.03                          3.17     1185  \n",
       "3             7.80  0.86                          3.45     1480  \n",
       "4             4.32  1.04                          2.93      735  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/'\n",
    "                      'machine-learning-databases/wine/wine.data',\n",
    "                      header=None)\n",
    "\n",
    "df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',\n",
    "                   'Alcalinity of ash', 'Magnesium', 'Total phenols',\n",
    "                   'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',\n",
    "                   'Color intensity', 'Hue',\n",
    "                   'OD280/OD315 of diluted wines', 'Proline']\n",
    "\n",
    "df_wine.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "### Note:\n",
    "\n",
    "\n",
    "If the link to the Wine dataset provided above does not work for you, you can find a local copy in this repository at [./../datasets/wine/wine.data](./../datasets/wine/wine.data).\n",
    "\n",
    "Or you could fetch it via\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Class label</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315 of diluted wines</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Class label  Alcohol  Malic acid   Ash  Alcalinity of ash  Magnesium  \\\n",
       "0            1    14.23        1.71  2.43               15.6        127   \n",
       "1            1    13.20        1.78  2.14               11.2        100   \n",
       "2            1    13.16        2.36  2.67               18.6        101   \n",
       "3            1    14.37        1.95  2.50               16.8        113   \n",
       "4            1    13.24        2.59  2.87               21.0        118   \n",
       "\n",
       "   Total phenols  Flavanoids  Nonflavanoid phenols  Proanthocyanins  \\\n",
       "0           2.80        3.06                  0.28             2.29   \n",
       "1           2.65        2.76                  0.26             1.28   \n",
       "2           2.80        3.24                  0.30             2.81   \n",
       "3           3.85        3.49                  0.24             2.18   \n",
       "4           2.80        2.69                  0.39             1.82   \n",
       "\n",
       "   Color intensity   Hue  OD280/OD315 of diluted wines  Proline  \n",
       "0             5.64  1.04                          3.92     1065  \n",
       "1             4.38  1.05                          3.40     1050  \n",
       "2             5.68  1.03                          3.17     1185  \n",
       "3             7.80  0.86                          3.45     1480  \n",
       "4             4.32  1.04                          2.93      735  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wine = pd.read_csv('https://raw.githubusercontent.com/rasbt/python-machine-learning-book/master/code/datasets/wine/wine.data', header=None)\n",
    "\n",
    "df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash', \n",
    "'Alcalinity of ash', 'Magnesium', 'Total phenols', \n",
    "'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins', \n",
    "'Color intensity', 'Hue', 'OD280/OD315 of diluted wines', 'Proline']\n",
    "df_wine.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Splitting the data into 70% training and 30% test subsets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "\n",
    "X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values\n",
    "\n",
    "X_train, X_test, y_train, y_test = \\\n",
    "    train_test_split(X, y, test_size=0.3, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standardizing the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "sc = StandardScaler()\n",
    "X_train_std = sc.fit_transform(X_train)\n",
    "X_test_std = sc.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Note**\n",
    "\n",
    "Accidentally, I wrote `X_test_std = sc.fit_transform(X_test)` instead of `X_test_std = sc.transform(X_test)`. In this case, it wouldn't make a big difference since the mean and standard deviation of the test set should be (quite) similar to the training set. However, as remember from Chapter 3, the correct way is to re-use parameters from the training set if we are doing any kind of transformation -- the test set should basically stand for \"new, unseen\" data.\n",
    "\n",
    "My initial typo reflects a common mistake is that some people are *not* re-using these parameters from the model training/building and standardize the new data \"from scratch.\" Here's simple example to explain why this is a problem.\n",
    "\n",
    "Let's assume we have a simple training set consisting of 3 samples with 1 feature (let's call this feature \"length\"):\n",
    "\n",
    "- train_1: 10 cm -> class_2\n",
    "- train_2: 20 cm -> class_2\n",
    "- train_3: 30 cm -> class_1\n",
    "\n",
    "mean: 20, std.: 8.2\n",
    "\n",
    "After standardization, the transformed feature values are\n",
    "\n",
    "- train_std_1: -1.21 -> class_2\n",
    "- train_std_2: 0 -> class_2\n",
    "- train_std_3: 1.21 -> class_1\n",
    "\n",
    "Next, let's assume our model has learned to classify samples with a standardized length value < 0.6 as class_2 (class_1 otherwise). So far so good. Now, let's say we have 3 unlabeled data points that we want to classify:\n",
    "\n",
    "- new_4: 5 cm -> class ?\n",
    "- new_5: 6 cm -> class ?\n",
    "- new_6: 7 cm -> class ?\n",
    "\n",
    "If we look at the \"unstandardized \"length\" values in our training datast, it is intuitive to say that all of these samples are likely belonging to class_2. However, if we standardize these by re-computing standard deviation and and mean you would get similar values as before in the training set and your classifier would (probably incorrectly) classify samples 4 and 5 as class 2.\n",
    "\n",
    "- new_std_4: -1.21 -> class 2\n",
    "- new_std_5: 0 -> class 2\n",
    "- new_std_6: 1.21 -> class 1\n",
    "\n",
    "However, if we use the parameters from your \"training set standardization,\" we'd get the values:\n",
    "\n",
    "- sample5: -18.37 -> class 2\n",
    "- sample6: -17.15 -> class 2\n",
    "- sample7: -15.92 -> class 2\n",
    "\n",
    "The values 5 cm, 6 cm, and 7 cm are much lower than anything we have seen in the training set previously. Thus, it only makes sense that the standardized features of the \"new samples\" are much lower than every standardized feature in the training set.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eigendecomposition of the covariance matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvalues \n",
      "[ 4.8923083   2.46635032  1.42809973  1.01233462  0.84906459  0.60181514\n",
      "  0.52251546  0.08414846  0.33051429  0.29595018  0.16831254  0.21432212\n",
      "  0.2399553 ]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "cov_mat = np.cov(X_train_std.T)\n",
    "eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)\n",
    "\n",
    "print('\\nEigenvalues \\n%s' % eigen_vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: \n",
    "\n",
    "Above, I used the [`numpy.linalg.eig`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html) function to decompose the symmetric covariance matrix into its eigenvalues and eigenvectors.\n",
    "    <pre>>>> eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)</pre>\n",
    "    This is not really a \"mistake,\" but probably suboptimal. It would be better to use [`numpy.linalg.eigh`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eigh.html) in such cases, which has been designed for [Hermetian matrices](https://en.wikipedia.org/wiki/Hermitian_matrix). The latter always returns real  eigenvalues; whereas the numerically less stable `np.linalg.eig` can decompose nonsymmetric square matrices, you may find that it returns complex eigenvalues in certain cases. (S.R.)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Total and explained variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tot = sum(eigen_vals)\n",
    "var_exp = [(i / tot) for i in sorted(eigen_vals, reverse=True)]\n",
    "cum_var_exp = np.cumsum(var_exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ECd6tW7fwclFRkWdlZfkbb7zh7u5t2rTxV155Jeq93n333X7eeeeFl80sfO4RI0b4qFGj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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103cf438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "plt.bar(range(1, 14), var_exp, alpha=0.5, align='center',\n",
    "        label='individual explained variance')\n",
    "plt.step(range(1, 14), cum_var_exp, where='mid',\n",
    "         label='cumulative explained variance')\n",
    "plt.ylabel('Explained variance ratio')\n",
    "plt.xlabel('Principal components')\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/pca1.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])\n",
    "               for i in range(len(eigen_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eigen_pairs.sort(key=lambda k: k[0], reverse=True)\n",
    "\n",
    "# Note: I added the `key=lambda k: k[0]` in the sort call above\n",
    "# just like I used it further below in the LDA section.\n",
    "# This is to avoid problems if there are ties in the eigenvalue\n",
    "# arrays (i.e., the sorting algorithm will only regard the\n",
    "# first element of the tuples, now)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[ 0.14669811  0.50417079]\n",
      " [-0.24224554  0.24216889]\n",
      " [-0.02993442  0.28698484]\n",
      " [-0.25519002 -0.06468718]\n",
      " [ 0.12079772  0.22995385]\n",
      " [ 0.38934455  0.09363991]\n",
      " [ 0.42326486  0.01088622]\n",
      " [-0.30634956  0.01870216]\n",
      " [ 0.30572219  0.03040352]\n",
      " [-0.09869191  0.54527081]\n",
      " [ 0.30032535 -0.27924322]\n",
      " [ 0.36821154 -0.174365  ]\n",
      " [ 0.29259713  0.36315461]]\n"
     ]
    }
   ],
   "source": [
    "w = np.hstack((eigen_pairs[0][1][:, np.newaxis],\n",
    "               eigen_pairs[1][1][:, np.newaxis]))\n",
    "print('Matrix W:\\n', w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "Depending on which version of NumPy and LAPACK you are using, you may obtain the the Matrix W with its signs flipped. E.g., the matrix shown in the book was printed as:\n",
    "\n",
    "```\n",
    "[[ 0.14669811  0.50417079]\n",
    "[-0.24224554  0.24216889]\n",
    "[-0.02993442  0.28698484]\n",
    "[-0.25519002 -0.06468718]\n",
    "[ 0.12079772  0.22995385]\n",
    "[ 0.38934455  0.09363991]\n",
    "[ 0.42326486  0.01088622]\n",
    "[-0.30634956  0.01870216]\n",
    "[ 0.30572219  0.03040352]\n",
    "[-0.09869191  0.54527081]\n",
    "```\n",
    "\n",
    "Please note that this is not an issue: If $v$ is an eigenvector of a matrix $\\Sigma$, we have\n",
    "\n",
    "$$\\Sigma v = \\lambda v,$$\n",
    "\n",
    "where $\\lambda$ is our eigenvalue,\n",
    "\n",
    "\n",
    "then $-v$ is also an eigenvector that has the same eigenvalue, since\n",
    "\n",
    "$$\\Sigma(-v) = -\\Sigma v = -\\lambda v = \\lambda(-v).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IiMSWkpSIiMSWklSNDAwM8LGPfYyOjg5mzpzJggUL+OlPfxp1WCIiiaIkVSOD\ng4MccMABPPTQQ2zevJlrr72Ws88+m/Xr10cdmohIYjRkklq+HB59NPh9cBCuvBL++Mdw32PatGlc\nc801vPGNbwTg/e9/PwceeCCPPfZYuG8kIpJiqUtSr70G114LAwPB/f/4j2D103xvfCOccQY88ggs\nXgy/+hWMXaljW95qVzt3wvbt1cX10ksv8fzzz3PEEUdUtyMRkQaSuiTV1ASPPQZnnw3PPQfvLrBK\n1emnQ08PnHgi/PjHcM89MHXq7ufXrIG3vhXWrw8S1KJF8JWvTDymwcFBzjvvPC644AIOOeSQie9I\nRKTBpC5JNTfD974XtKDe/Ga47DJYsmT0NoODsHJl8Ls7/OY3o59fsAAuuSRIYieeGLTOPvvZicXj\n7px33nnstddefO1rX5vYTkREGlTqkhTAiy/Cpk3B79ns7q6/nMsvh76+IPmsXBl0/Y2tZ1iyBDZs\ngF/+Em64Afbaa2KxdHZ2smnTJu6++26tyCsiUqHUzYK+eXPQVXf55fDxjwfdfq2t8N3v7t5m3Tp4\n3et2d/E9+ywccgjkFtDNdfG99hq8613wzW9Cby8ccEBlcV988cU88cQTrFq1imnTpo13jJoFXUQa\nRqJW5h1PpUt1rFkTdNlB0Ip69lk4quCav4U98QT83d/BbbcFLagbboBJk+CTnyx/H+vXr6ejo4OW\nlpaRFpSZsXz5chYuXFj2sYiIpFFDJ6kkStOxSDSGhiC/R3nsfZE40XpSIg1kaCgo8slmg/vZbHB/\naCjKqESqF3mSMrPPmNkuM5sddSwiSTV5Mlx3HZx1FnR3Bz+vu04tKUm+SJOUmc0FTgXWRRmHSBpk\nMkFV6rJlwc9MJuqIRKoXdUvqeuDyiGMQSYVsNphdpasr+Jnr+hNJsqao3tjMzgA2uPuTZuOOnYlI\nCUNDsHQp3Hln0ILKZIL7Dz+sLj9JtppW95nZ/cB++Q8BDnweuBI41d23mtl/AH/h7n8qsh9V94mM\nQ9V9kiTlVvfVtCXl7qcWetzMjgQ6gN9Y0IyaCzxmZse6e8H5yLu7u0d+z2QyZNThLjLK2ISkBCVx\nks1myU6gDzoW10kNt6QWuPsrRZ5XS0pEJEWSdp2UE3QFioiIjIhFknL3g9z95ajjCNtHPvIRXv/6\n17P33ntz6KGH0tPTE3VIIiKJEovuvvEktbvv6aef5qCDDqKlpYXnnnuOk046iZ/85CfMnz9/j23j\nfiwiImG1ozeKAAAIF0lEQVRKWndfXW3bto2zzz2bvdv3puOQDu69996avM/hhx9OS0sLEKwrZWb8\n9re/rcl7iYikUSqT1OOPP86C4xew/wH7c9ais/jzn/886vlzP3ouP3zmh2z+yGbWHbeODy38EE8+\n+eSobXbu3MnPfvYzfvCDH9DX1zfhWJYsWcL06dM57LDDeMMb3sDpp58+4X2JiDSa1HX3/eEPf+DQ\now5ly4lbYC40/2szx7Yey0MPPDSyTcv0FnZ8YgcML/HUfF8z1515HZ/+9KcB2L59Oye++0Se3fgs\nk2ZMwjYaD/c+zJFHHjmh+N2dX/ziF2SzWa644oqCix+qu09EGknDdvc9+OCD+FyH+UA7DLxvgEcf\neZRXX311ZJtpM6ZBrnHl0LSliZkzZ448f/PNN/PU1qfYdv42tpy5hS1v38JHL/rohGMyM97xjnew\nYcMGvvGNb0x4PyIijSZ1SWr69On4Ng+K2gH6gx/Nzc0j21z/leuZdtc07AGj5e4W5jCHc845Z+T5\n3637HdvfsH3k0/EDnA2/31B1bIODgxqTEhGpQOqS1Hvf+14OmnUQLXe3wCMw/fbpfPaKzzJlypSR\nbRafv5j77rmPqzNX8+WPf5k1j65h+vTpI8+/8x3vZNoz0+BVYBc0/6qZtx//9ori6Ovr44477uDV\nV19l165d3HfffaxcuZJTTjklrEMVEUm91I1JAbz22mt8/etfZ+2GtWTemeFDH/oQlUxi6+5cfsXl\n3HjjjUxqmsTR84/m3h/ey+zZ5S95tWnTJs4880yeeOIJdu3axbx587j00ku58MILix2jxqREpGFo\n+fgQ9Pf3s337dmbNmlWz98hRkhKRRqIklTBpOhYRkfE0bHWfiIikh5KUiIjElpKUiIjElpKUiIjE\nlpKUiIjElpKUiIjEVlPUAVRj3rx5FV2kG2fz5s2LOgQRkdiJ7DopM+sCPg78cfihK939p0W2LXid\nlIiIJFNSrpP6qrsvGL4VTFCNLJvNRh1CZBr12Bv1uKFxj71Rj7tcUSepdPTV1Ugj/+Nt1GNv1OOG\nxj32Rj3uckWdpD5hZo+b2T+a2czxNxcRkUZS0yRlZveb2RN5tyeHf34A+DpwkLsfDWwEvlrLWERE\nJHliMcGsmc0DfuTubynyfPRBiohIqMopnIisBN3M9nf3jcN3/wr4t2LblnMgIiKSPlFeJ/VlMzsa\n2AWsBS6KMBYREYmhWHT3iYiIFBJ1dV9FzOwSM3tmuADjS1HHU09m9hkz22Vm5a9hn2Bm9uXhv/Xj\nZvZ9M2uLOqZaM7PTzOzfzew5M7si6njqwczmmtkDZvbU8P/rT0YdUz2Z2SQzW2NmP4w6lnoys5lm\ndufw//GnzOy4YtsmJkmZWQb4AHCUux8F/O9oI6ofM5sLnAqsizqWOvoZcMRw9efzwNKI46kpM5sE\n3AS8FzgCWGhmh0YbVV0MAp929yOAtwNLGuS4cy4Fno46iAjcCPzE3Q8D3go8U2zDxCQp4G+AL7n7\nIIC7b4o4nnq6Hrg86iDqyd1Xufuu4buPAnOjjKcOjgWed/d17r4TWAn8t4hjqjl33+jujw//vo3g\nZDUn2qjqY/jL5+nAP0YdSz0N94q8092/DeDug+6+pdj2SUpShwDvMrNHzazXzP4i6oDqwczOADa4\n+5NRxxKhC4F7ow6ixuYAG/Lu/54GOVnnmFkHcDTwr9FGUje5L5+NVhhwILDJzL493NX5TTObWmzj\nWM2Cbmb3A/vlP0TwB/w8Qayz3P14MzsG+B5wUP2jDN84x30lQVdf/nOpUOK4r3L3Hw1vcxWw091v\njyBEqRMzmwHcBVw63KJKNTN7P/CSuz8+PJSRmv/XZWgCFgBL3P1XZnYD8Dmgq9jGseHupxZ7zswu\nBu4e3m71cBHBPu7+p7oFWCPFjtvMjgQ6gN9YsCbJXOAxMzvW3f9Y6DVJUurvDWBmFxB0h7ynLgFF\n60XggLz7c4cfSz0zayJIUN9193uijqdOTgDOMLPTgalAq5nd5u7nRxxXPfyeoHfoV8P37wKKFgol\nqbvv/zJ8sjKzQ4ApaUhQpbj7v7n7/u5+kLsfSPDHnZ+GBDUeMzuNoCvkDHffEXU8dbAaONjM5plZ\nM3AO0CgVX7cAT7v7jVEHUi/ufqW7H+DuBxH8rR9okASFu78EbBg+jwOcTInikVi1pMbxbeAWM3sS\n2AE0xB90DKdxugW+BjQD9w8vbPmou/+PaEOqHXcfMrNPEFQ1TgJ63L1oxVNamNkJwLnAk2b2a4J/\n40XXlpPU+CTwz2Y2Bfgd8NFiG+piXhERia0kdfeJiEiDUZISEZHYUpISEZHYUpISEZHYUpISEZHY\nUpISEZHYUpISqQMzGxqep+xJM7vDzFqGH9/PzFaY2fNmttrMfmxmBxd4fY+ZvWRmT9Q/epHoKEmJ\n1Mer7r5geJmZncDFw4//gGC2gf/i7scQLEmyX4HXf5tgGQ+RhpKkGSdE0uIh4Cgzezcw4O7fyj1R\nbLZ7d3/YzObVK0CRuFBLSqQ+DEYmU30f8CRwJPBYlEGJxJ2SlEh9TDWzNcAvgbVAT7ThiCSDuvtE\n6uM1d1+Q/4CZPQWcGVE8IomglpRIfewxe727PwA0m9nHRjYyO2p4ZvBi+2iUWfBFACUpkXopttzA\nfwdONbMXhpeh+SKwcexGZnY78C/AIWa23syKLm0gkiZaqkNERGJLLSkREYktJSkREYktJSkREYkt\nJSkREYktJSkREYktJSkREYktJSkREYktJSkREYmt/wQjFzx9PIZopAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11041b5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train_pca = X_train_std.dot(w)\n",
    "colors = ['r', 'b', 'g']\n",
    "markers = ['s', 'x', 'o']\n",
    "\n",
    "for l, c, m in zip(np.unique(y_train), colors, markers):\n",
    "    plt.scatter(X_train_pca[y_train == l, 0], \n",
    "                X_train_pca[y_train == l, 1], \n",
    "                c=c, label=l, marker=m)\n",
    "\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/pca2.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.59891628,  0.00484089])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_std[0].dot(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal component analysis in scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.37329648,  0.18818926,  0.10896791,  0.07724389,  0.06478595,\n",
       "        0.04592014,  0.03986936,  0.02521914,  0.02258181,  0.01830924,\n",
       "        0.01635336,  0.01284271,  0.00642076])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA()\n",
    "X_train_pca = pca.fit_transform(X_train_std)\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110c335f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(range(1, 14), pca.explained_variance_ratio_, alpha=0.5, align='center')\n",
    "plt.step(range(1, 14), np.cumsum(pca.explained_variance_ratio_), where='mid')\n",
    "plt.ylabel('Explained variance ratio')\n",
    "plt.xlabel('Principal components')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "X_train_pca = pca.fit_transform(X_train_std)\n",
    "X_test_pca = pca.transform(X_test_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Q9ikzuwB4E5gGbo6xLCIiqdURTUP1qGlIRKRxHd80JCIinUGBQEQk5RQIRERS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\ngYhIyikQiIiknAKBiEjK/X+vMr41JwdU9wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110629898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train_pca[:, 0], X_train_pca[:, 1])\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "def plot_decision_regions(X, y, classifier, resolution=0.02):\n",
    "\n",
    "    # setup marker generator and color map\n",
    "    markers = ('s', 'x', 'o', '^', 'v')\n",
    "    colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')\n",
    "    cmap = ListedColormap(colors[:len(np.unique(y))])\n",
    "\n",
    "    # plot the decision surface\n",
    "    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),\n",
    "                           np.arange(x2_min, x2_max, resolution))\n",
    "    Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)\n",
    "    Z = Z.reshape(xx1.shape)\n",
    "    plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)\n",
    "    plt.xlim(xx1.min(), xx1.max())\n",
    "    plt.ylim(xx2.min(), xx2.max())\n",
    "\n",
    "    # plot class samples\n",
    "    for idx, cl in enumerate(np.unique(y)):\n",
    "        plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],\n",
    "                    alpha=0.8, c=cmap(idx),\n",
    "                    marker=markers[idx], label=cl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training logistic regression classifier using the first 2 principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "lr = LogisticRegression()\n",
    "lr = lr.fit(X_train_pca, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r05WNLCdZRpaTY00fhoJfaSmLJvxA2z+vUuoNpVTof4U1APrpGgtROtINOnZN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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110406748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_regions(X_train_pca, y_train, classifier=lr)\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/pca3.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qi6655hpOOeUUTjjhBM466yyWLl3quyQRkUgpyJA6dOgQCxYtYOKFE5n2v6bx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105d1748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_regions(X_test_pca, y_test, classifier=lr)\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/pca4.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.37329648,  0.18818926,  0.10896791,  0.07724389,  0.06478595,\n",
       "        0.04592014,  0.03986936,  0.02521914,  0.02258181,  0.01830924,\n",
       "        0.01635336,  0.01284271,  0.00642076])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=None)\n",
    "X_train_pca = pca.fit_transform(X_train_std)\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supervised data compression via linear discriminant analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4IlGoolpNnTXNOYBevfhu6uTpNl7KqJ4z6xJ2eEqzcrRgCx+Yi+Soq9dPrbw5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\nt2/DezT3c7zyacta6mGBrPynXyHq3ZdurPQAHEBveb3e0eX3cHXI1HvSJ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nkg02gE9TN1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\nPIPA/wO575rfoXikyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 25,
     "metadata": {
      "image/png": {
       "width": 400
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./images/05_06.png', width=400) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the scatter matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the mean vectors for each class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MV 1: [ 0.9259 -0.3091  0.2592 -0.7989  0.3039  0.9608  1.0515 -0.6306  0.5354\n",
      "  0.2209  0.4855  0.798   1.2017]\n",
      "\n",
      "MV 2: [-0.8727 -0.3854 -0.4437  0.2481 -0.2409 -0.1059  0.0187 -0.0164  0.1095\n",
      " -0.8796  0.4392  0.2776 -0.7016]\n",
      "\n",
      "MV 3: [ 0.1637  0.8929  0.3249  0.5658 -0.01   -0.9499 -1.228   0.7436 -0.7652\n",
      "  0.979  -1.1698 -1.3007 -0.3912]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=4)\n",
    "\n",
    "mean_vecs = []\n",
    "for label in range(1, 4):\n",
    "    mean_vecs.append(np.mean(X_train_std[y_train == label], axis=0))\n",
    "    print('MV %s: %s\\n' % (label, mean_vecs[label - 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the within-class scatter matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Within-class scatter matrix: 13x13\n"
     ]
    }
   ],
   "source": [
    "d = 13  # number of features\n",
    "S_W = np.zeros((d, d))\n",
    "for label, mv in zip(range(1, 4), mean_vecs):\n",
    "    class_scatter = np.zeros((d, d))  # scatter matrix for each class\n",
    "    for row in X_train_std[y_train == label]:\n",
    "        row, mv = row.reshape(d, 1), mv.reshape(d, 1)  # make column vectors\n",
    "        class_scatter += (row - mv).dot((row - mv).T)\n",
    "    S_W += class_scatter                          # sum class scatter matrices\n",
    "\n",
    "print('Within-class scatter matrix: %sx%s' % (S_W.shape[0], S_W.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Better: covariance matrix since classes are not equally distributed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class label distribution: [40 49 35]\n"
     ]
    }
   ],
   "source": [
    "print('Class label distribution: %s' \n",
    "      % np.bincount(y_train)[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled within-class scatter matrix: 13x13\n"
     ]
    }
   ],
   "source": [
    "d = 13  # number of features\n",
    "S_W = np.zeros((d, d))\n",
    "for label, mv in zip(range(1, 4), mean_vecs):\n",
    "    class_scatter = np.cov(X_train_std[y_train == label].T)\n",
    "    S_W += class_scatter\n",
    "print('Scaled within-class scatter matrix: %sx%s' % (S_W.shape[0],\n",
    "                                                     S_W.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the between-class scatter matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Between-class scatter matrix: 13x13\n"
     ]
    }
   ],
   "source": [
    "mean_overall = np.mean(X_train_std, axis=0)\n",
    "d = 13  # number of features\n",
    "S_B = np.zeros((d, d))\n",
    "for i, mean_vec in enumerate(mean_vecs):\n",
    "    n = X_train[y_train == i + 1, :].shape[0]\n",
    "    mean_vec = mean_vec.reshape(d, 1)  # make column vector\n",
    "    mean_overall = mean_overall.reshape(d, 1)  # make column vector\n",
    "    S_B += n * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T)\n",
    "\n",
    "print('Between-class scatter matrix: %sx%s' % (S_B.shape[0], S_B.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Selecting linear discriminants for the new feature subspace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve the generalized eigenvalue problem for the matrix $S_W^{-1}S_B$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eigen_vals, eigen_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**:\n",
    "    \n",
    "Above, I used the [`numpy.linalg.eig`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html) function to decompose the symmetric covariance matrix into its eigenvalues and eigenvectors.\n",
    "    <pre>>>> eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)</pre>\n",
    "    This is not really a \"mistake,\" but probably suboptimal. It would be better to use [`numpy.linalg.eigh`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eigh.html) in such cases, which has been designed for [Hermetian matrices](https://en.wikipedia.org/wiki/Hermitian_matrix). The latter always returns real  eigenvalues; whereas the numerically less stable `np.linalg.eig` can decompose nonsymmetric square matrices, you may find that it returns complex eigenvalues in certain cases. (S.R.)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sort eigenvectors in decreasing order of the eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in decreasing order:\n",
      "\n",
      "452.721581245\n",
      "156.43636122\n",
      "7.20678700076e-14\n",
      "3.94081990073e-14\n",
      "3.94081990073e-14\n",
      "2.51053275902e-14\n",
      "2.46878288879e-14\n",
      "2.46878288879e-14\n",
      "1.97651922798e-14\n",
      "5.31966277392e-15\n",
      "3.27314649699e-15\n",
      "2.7136147327e-15\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])\n",
    "               for i in range(len(eigen_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eigen_pairs = sorted(eigen_pairs, key=lambda k: k[0], reverse=True)\n",
    "\n",
    "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "\n",
    "print('Eigenvalues in decreasing order:\\n')\n",
    "for eigen_val in eigen_pairs:\n",
    "    print(eigen_val[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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904CHgO8TmoZ+kZnNcvcVMcrdBcyrSvAiIpK49PT0Go1NmAqJjN03B3gXWAZU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129d5b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tot = sum(eigen_vals.real)\n",
    "discr = [(i / tot) for i in sorted(eigen_vals.real, reverse=True)]\n",
    "cum_discr = np.cumsum(discr)\n",
    "\n",
    "plt.bar(range(1, 14), discr, alpha=0.5, align='center',\n",
    "        label='individual \"discriminability\"')\n",
    "plt.step(range(1, 14), cum_discr, where='mid',\n",
    "         label='cumulative \"discriminability\"')\n",
    "plt.ylabel('\"discriminability\" ratio')\n",
    "plt.xlabel('Linear Discriminants')\n",
    "plt.ylim([-0.1, 1.1])\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/lda1.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.0662 -0.3797]\n",
      " [ 0.0386 -0.2206]\n",
      " [-0.0217 -0.3816]\n",
      " [ 0.184   0.3018]\n",
      " [-0.0034  0.0141]\n",
      " [ 0.2326  0.0234]\n",
      " [-0.7747  0.1869]\n",
      " [-0.0811  0.0696]\n",
      " [ 0.0875  0.1796]\n",
      " [ 0.185  -0.284 ]\n",
      " [-0.066   0.2349]\n",
      " [-0.3805  0.073 ]\n",
      " [-0.3285 -0.5971]]\n"
     ]
    }
   ],
   "source": [
    "w = np.hstack((eigen_pairs[0][1][:, np.newaxis].real,\n",
    "              eigen_pairs[1][1][:, np.newaxis].real))\n",
    "print('Matrix W:\\n', w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Projecting samples onto the new feature space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x129d5f0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train_lda = X_train_std.dot(w)\n",
    "colors = ['r', 'b', 'g']\n",
    "markers = ['s', 'x', 'o']\n",
    "\n",
    "for l, c, m in zip(np.unique(y_train), colors, markers):\n",
    "    plt.scatter(X_train_lda[y_train == l, 0] * (-1),\n",
    "                X_train_lda[y_train == l, 1] * (-1),\n",
    "                c=c, label=l, marker=m)\n",
    "\n",
    "plt.xlabel('LD 1')\n",
    "plt.ylabel('LD 2')\n",
    "plt.legend(loc='lower right')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/lda2.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LDA via scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Sebastian/miniconda3/lib/python3.5/site-packages/sklearn/lda.py:4: DeprecationWarning: lda.LDA has been moved to discriminant_analysis.LinearDiscriminantAnalysis in 0.17 and will be removed in 0.19\n",
      "  \"in 0.17 and will be removed in 0.19\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.lda import LDA\n",
    "\n",
    "lda = LDA(n_components=2)\n",
    "X_train_lda = lda.fit_transform(X_train_std, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qpNcMdzsjA6iosBbsvvWW9bWiIrn2+Hto/mHK887jbhJkLs5JEQUJPoyvsLD9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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129eceeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "lr = LogisticRegression()\n",
    "lr = lr.fit(X_train_lda, y_train)\n",
    "\n",
    "plot_decision_regions(X_train_lda, y_train, classifier=lr)\n",
    "plt.xlabel('LD 1')\n",
    "plt.ylabel('LD 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./images/lda3.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qY+/evaxZs4avfvWr9O3bl9WrV7Ny5UpWrlyZ032JiJQiHR/ficOHD3P48GEq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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129ed1ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_test_lda = lda.transform(X_test_std)\n",
    "\n",
    "plot_decision_regions(X_test_lda, y_test, classifier=lr)\n",
    "plt.xlabel('LD 1')\n",
    "plt.ylabel('LD 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./images/lda4.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Using kernel principal component analysis for nonlinear mappings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Pi05pj8GPVGaMIZNw+6k7R8nzFybjxWuwf3o0XNGtMMiG7zkaN9QQ3nfvnrD1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\n9nPg6DZwvfuy4e8fJlTx0nTR1TbY2lGJo9euMN+newsL4S0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ptizTrT1nw1j9a8MEG2P7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\nrkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 39,
     "metadata": {
      "image/png": {
       "width": 500
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./images/05_11.png', width=500) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing a kernel principal component analysis in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import pdist, squareform\n",
    "from scipy import exp\n",
    "from scipy.linalg import eigh\n",
    "import numpy as np\n",
    "\n",
    "def rbf_kernel_pca(X, gamma, n_components):\n",
    "    \"\"\"\n",
    "    RBF kernel PCA implementation.\n",
    "\n",
    "    Parameters\n",
    "    ------------\n",
    "    X: {NumPy ndarray}, shape = [n_samples, n_features]\n",
    "        \n",
    "    gamma: float\n",
    "      Tuning parameter of the RBF kernel\n",
    "        \n",
    "    n_components: int\n",
    "      Number of principal components to return\n",
    "\n",
    "    Returns\n",
    "    ------------\n",
    "     X_pc: {NumPy ndarray}, shape = [n_samples, k_features]\n",
    "       Projected dataset   \n",
    "\n",
    "    \"\"\"\n",
    "    # Calculate pairwise squared Euclidean distances\n",
    "    # in the MxN dimensional dataset.\n",
    "    sq_dists = pdist(X, 'sqeuclidean')\n",
    "\n",
    "    # Convert pairwise distances into a square matrix.\n",
    "    mat_sq_dists = squareform(sq_dists)\n",
    "\n",
    "    # Compute the symmetric kernel matrix.\n",
    "    K = exp(-gamma * mat_sq_dists)\n",
    "\n",
    "    # Center the kernel matrix.\n",
    "    N = K.shape[0]\n",
    "    one_n = np.ones((N, N)) / N\n",
    "    K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)\n",
    "\n",
    "    # Obtaining eigenpairs from the centered kernel matrix\n",
    "    # numpy.eigh returns them in sorted order\n",
    "    eigvals, eigvecs = eigh(K)\n",
    "\n",
    "    # Collect the top k eigenvectors (projected samples)\n",
    "    X_pc = np.column_stack((eigvecs[:, -i]\n",
    "                            for i in range(1, n_components + 1)))\n",
    "\n",
    "    return X_pc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 1: Separating half-moon shapes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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19y/3vj8t6VZ3P59yf/Wq4jt6VHriiaTcdnFR2r1b2r+/6lFhQJPfb6c0xHoh2haLlZaZ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\nlEhQAIAo/T/h7ILNFIJKUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ebc0b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=100, random_state=123)\n",
    "\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='red', marker='^', alpha=0.5)\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/half_moon_1.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5BCJSBZp2tUSrV4cm9ET2ibuHlcpuuy2b1NbQEGrlmuBl+BYtgsWL4bzzYtmaoZq4SDwl\ntiZeCxK9CIpZCOJKaiudcgtEJAKRz9iWdKtWhdbUb30rfF+9OuoSDYNmaSsfTZYjIhFQEC9Bbnb6\nzJnh++23h/2JoMBTHpq9TUQioub0EhRaBGXHjrA/9kPMiq2NraS24ctNboPs7G179ui9FJGKUhAv\nQaKz0ydMgKuugtGjs/s0S9vIaPY2EYmImtNLkOhFULZuDX0BLS2JX3Y0lQpD3GPRjaE8AxGpItXE\nSzR7dpih7eWXw+Np06Itz5AtWQKbNsVmdrGRit20tzGdvU1EapNq4mXw/PMhkN94Y2ihjn2Geo3U\nFmOXWFgowe3xx5XgJiIVo5p4iRI5f3qN1BZjl1iYn+AGIblNeQYiUiGD1sTNbLyZvbXA/uMrU6Rk\nKRRIenpiXPmqodpibmIhxCCxMJPglskxaGkJn/C2bo2oQCJS6wasiZvZhcAtwDYzawY+6u4r0k9/\nF5hT2eLFX+Iy1GsoKz2TWHj77aEGnukTj00LSI3kHYhIfA04d7qZPQ2c4+6vmNlJwPeBBe7+EzNb\n6e7vrFZBhyKq+ZkTNX96ZyfccAMsWFAT04KmUv2TCmMTwDs7w3s8bVoo4A03RP5+a+50kXgq5d4c\nrDm90d1fAXD3J4AzgC+a2aeBstyRZna2ma0zs2fN7Joix3zDzDaY2dNmdmI5zltOmQz1668P32Mb\nwKF/7TDhVq0KjQo33hje940boy5RDs2GJ8PV3d3/K7NvKN8H21ft7Wqeb6B9A33PfZ87O8M/lMcG\nXO06lgYL4q/n9oenA3obcD7wjlJPbmYNwG3AWenXu9jM3p53zDnAW939aOAy4NulnrcSWltDE3pX\nV0zGKxdSI1npEMPM9Fw1lHcgVdLZCVdeCZddFr6uvDIEleuuG/x7Z2f4Krav2tuZ66nG+QZ6Dwb6\n/tnPZt/nhx6Cd78b5syBU06B73wn2r+FYRosO/1/AP2q+O7+upmdDVxYhvOfBGxw980AZnY34QPC\nupxjzic04+Puj5vZBDOb4u6xyhaK3XjlQmokKx1imJmeKz9LPZWCceMSmXcgVbJkCTz5ZFhR0Awm\nT4avfz38UQ/2PdPKs2lT4X3V3r700je3+FVqe6D3YKDvTz8d3uuDD4a1a8NsXZnunuuug098ouiv\nKm4G6xM/Cpji7o/k7T8V6HT350s6udkFwFnu/jfpx38JnOTun8455mfADe7+2/TjB4Gr3f13BV4v\nkn63VCo06+YOM+vujtkws64uuPrqEPkaG8Nc6c3NcPPNMc7CKy4R7znEKgeh3vrE16yBX/4y/KlP\nnRr+zA89NPzfnjABdu4Mx02YkP3w3dOTvR26urL7Cj1X6Lhiz+dvt7aGv+GuLpi4byt84Qt0PbOZ\nidueDccdchQT+7ZDWxtdv17FxPceD8uX03XSmUx8YimcdlrYf857aN3+Iqneg+iaeAQT2++Hs86i\na8vrTGzZDUceSde6zmFvNzf00nP40UzsWBPKM/0dNG/eQM+BJia+fSps3EjX/jE0HzmTno1baG7o\nZedhx8K2bUy44iP0fGsRzYcdws4N29jd28KYtx7GtG1P09q0D446Cp57LrwhpWxPnRqmNv7gB7Mt\nAJl9p58O//Efhb//+7+HSsyrr4ZfxiuvwL59/f947rijqoG8kuuJ3wIsKLB/V/q5D43kpJW0cOHC\nN7bb2tpoa2ur+DljXSvMyNQOX389W6iEZqVDAjLTMyLMUG9vb6e9vb2q54yLz30ObrklW7nKaGwM\n/7dHjQp/MxAqvkccEeLAMceE/+8QekHWrw9xIf+58eNh167+xxV7Pn+7uRnmzQtT7Pf0wK5nUrDp\nrxm/5w/s2tMMDTC+Yze7GA/3H8R4zmDX/eOg71zG/2ovu/a9D+5vZDxn0LxkLPNGL2fZzrn0NI9h\n1/aT4f5xjD+wk129Y2DtoYx/bRO7ekfDuimM375pgP1hu7dzO+v3zOKYmXto2v4uwOg9eCrrt4zm\nmNEv0vT8wbBtG73eyPrHjmXq/s1s2ncYPnoM9PZhv+rjiHEfZ9O+qexL9ZE6MIqJj/cyt3klX571\nfWYf2xwCJ8Cxx458e8+e8D/shReyXVWZfU8+Gb6vWPHmx3v2hDe+oSEM/8wP4JCo2vhgNfEV7j63\nyHOr3b2kBmMzOxlY6O5npx9fC7i735RzzLeBh939nvTjdcDphZrTVRMfRIxqheUQ28z0jJhlqNdL\nTXzNGjjxxBBcC2loCMF2/PjwOFOsWbPCdk9PCOyZgPzSSyHvIvNcY2M2CGcatBobQ+9JJjZknof+\n2/Pnh7/bZcvC/tbGvSy5cyukUszzZSzrPR2AM3mQpZwJBvNaH2FZ6lRobGKeLWOZz4O+XuaP/w0p\nb2XZ7lOYN/oRWhv3sCTVBhhnjlnO0t2nwZjR4Wd2nwqjxnBmw4MsTZ0Ko0cxr+HBN/bPawjH9I1q\npXlvN430cWDMWHpS+8CN5rEtNOzups8b6B09Dt+zh2brw0aP4sXXJ8GBAzQc1IQ7eG8f3tgMGLt7\nmpjQ8Dre1Myh3slJo1bzjXk/p3V1OoFszhz4XbpR9Z3vhJUrh7bd1xfe6Az38NXQEJ7bvh0mTQqf\n8DPJShMnhsfusHdvmMdh9+7if0gPPADnnDPYn1tZVLImPlA76+gBnhuqFcBRZnY48ApwEXBx3jGL\ngcuBe9JBvytu/eH5tUKAi/OvIg5qaNyychCkmKee6j9pXr5M0D5wIPzPNwsB/6CDQkNV5pj9+0Og\nP3Cg/3MNDaFmnYkXPT2hQevVV8PPNTVln4f+23v3hoDf2xu+7+UgGqYfBj372TXrPBrWjwNg5xHn\n0rBlKhjsescf0bBmNDQ1sest59Ow8RDo62PvSYfQaND7yCQaTz2LvUDDU+GTyc5jz6Nh7VhobmLX\nUR+iYd1YaGpm59EfouH3b96/66jzaFjXSp+30NPby4SJvbyaGoX39ADG/uYmDmndyx+6mrDmJujp\npQcYN7GBvg2NNDU5NDRigB3oY19PI03NwG5omjCBXm/kwLgWUkf+EV1feA+tlv70PWVKdjKk4Wxn\nfonub1606cCBEMQnT4bXXuv/ffv28EvbsSP80p57LowRfv75cJ82NITjTj4ZPvCBIf7FRWuwIP6k\nmX3C3ful65nZx4GnSj25u/eZ2aeApYRM+UXuvtbMLgtP+x3u/oCZfdDMngNSwCWlnrcSMsPMHn0U\nfvjD8HXvvTEKLvmZ6fPnJ7Y2noipbrVee2T+5E/C/+JigTzzPz8TWN1DQN23L9u3bRa29+4Nx+U+\nd+BANrhDdrKnlpbCz+dujxoV/n6bmsKfRGurcaCxBRpbGH/CWA5sC8dNePchHEj32Y8/ZiIHXkxv\nzx7LgXT376gjJ4TXGgt9h46mtRUO/D79828by4FN6Z85euob2xOOnsKBF968f/zRU8J2HzS3ttDd\nAC2t0NPTkr3GhhZaJoQ/aW9uobkZ9gGNB4XxxtaQrhBbI02ZSnID9DY0hkpyaxOth7cycTbQOjP7\nCzniiJFvy6DN6VOAnwD7yQbtdwEtwJ+5e6zGKEU9oUSsm9UXLQpjIKdPD+t2nnxyYmuFHR2he39m\nzv+BLVvCOP3p06MrVz/uoaD5GerTp0e23Gu9NKcDfP7zIQk5EX3iRY4bynY5X2ug6xlo39SpoYEv\n815n3s9Nm8KHn1QqvOdz54b7NhaVmpipWHN6utn6FDM7AzguvXuJuz80kpPVutgmuNVYrTARU91m\n5lGHEAG+9rXQP57A9dqT6J/+CS65JN7Z6WefPfhx1X6tga5nsPen0Pu5c2fodh4zJqZ5KzVgsJr4\nKOCTwFHAakJzd5F0keipJl5EplaYn5keYa2wVIma6nbRIli8GM47L9LWj3qqiYskSSn35mBB/B6g\nB/gNcA6wyd2vHFEpqyAO/yhiG1yUmR6NGGWoK4iLxFMls9P/ODOMzMwWAU+M5CT1JJPglhtgYkGZ\n6dFQhrqIVNBgc6f3ZDbi3IweN88/HwL5jTeG5vXVqyMukOZMj4bmUBeRChusJn6CmaVzFjFgdPqx\nEYaAja9o6RIolsOfaqg2GNvkwULy51CHRM+SJyLxM1h2emO1ClIrYhdklJkendwMdcgWWkSkTAar\nicswxS7I1GBt8MMfDpPpxHrO9Hw1llgoIvGgIF5msVuYI782mGC5CW0QprZ9z3sSEMChphILRSQ+\nBhxiljRxGsaSWWYwd4KERASbmIrtGPyhiMkwMw0xE4mnSg4xkxFqbQ1Z6okZChVzscs1GI4aSiwU\nkXgZbIhZxZjZJDNbambrzexXZvamTlozm2FmD5nZGjNbbWafjqKsI5GooVAJkJtrADHINRgqDTMT\nkQqKsiZ+LfCgu99sZtcAC9L7cvUCn3P3p81sLPCUmS1193XVLuxwJbrmGEOxyzUYqvzEwsxCKAlO\nLBSR+IgyiJ8PnJ7e/h7QTl4QT6+S1pne7jaztcB0IPZBPHZZ6gmXSoVlfq+/PmE5BloIRUQqKLLm\ndODQ9CppmWB96EAHm9kRwInA4xUvWRlkao7d3WGZzB07wtAoGb5Vq0JS25e/HL5eey0hATxfboa6\niEgZVDQ73cyWAVNydxHWj/8i8F13n5xz7HZ3P7jI64wl1NT/wd1/OsD5YpcBm0rBo4+Gcc2gBLfh\nSnRWeq4YZKgrO10knmKbne7u84o9Z2ZbzWyKu281s6nAtiLHNQH3Aj8YKIBnLFy48I3ttrY22tra\nhlvssrv3Xpg0KUbTsCZIzeQWRJCh3t7eTnt7e0XPISLRimycuJndBLzm7jelE9smuXt+Yhtm9n3g\nVXf/3BBeM3af9js6QhPwzJnZfVu2hL7d6dOjK1dS1ERNvKsLrr46fBppbAxT3zY3w803VzVJQjVx\nkXiKbU18EDcBPzKzjwGbgQsBzOww4Dvufq6ZnQr8d2C1ma0kNMX/nbv/MqpCD5cS3EqXyGlWc+Vm\nqKdSofAJn/pWROJBM7ZVwerVoQk9kdOFRijR06wWEvH86aqJi8RTKfdmlNnpdWP27ND8e/HF4fEP\nfxiTdcZjLH+ynEmTQm5Boik7XUTKTEG8ijIJbprBbXCFEtp6ehI80VlnJyxfDscdF753dkZdIhGp\nAQriVVJzQanCEjvNajGFstNFREqkIF4lNReUquDDHw7JbFu2hPcrcQltGZo/XUQqRIltVaQEt6Gp\nuYQ29zDWMDN/OoTs9OnTqzr9qhLbROKplHtTQbzKUin47W/h7rvDY83g1l9NjAsfTGa8YZUpiIvE\nk7LTE+a++5TgVkzN5w50dsJ11ymxTUTKQkG8ymo+SJWouRn27w994VCDuQMaZiYiZaQgXmX5CW47\ndoSg1dwcbbniYNWqMLFZdzcsWwbPPJPwhLZ8GmYmImWmIF5luUuUPvNMCFbd3SF41fPkL7mTu5xw\nAsybF7avv76G8gU0zExEykxBPAKzZ4fgNHZsCFYnnKC+8fxuhkmToKUlm6GeeBpmJiIVENkCKGY2\nCbgHOBzYBFzo7juLHNsAPAm85O7nVa2QFdTTE4LUpEnhcWKX2CyTml8oRougiEgFRFkTvxZ40N2P\nAR4CFgxw7GeA31elVFWiyV+yUqnw4eVjHwvvQ+IndynEDGbMCJ/cvv3t8H3GjKqOExeR2hPlUqTn\nA6ent78HtBMCez9mNgP4IPA/gUHXFE+KTN/47bdnl9i85JJs62rNBK9B5E7sknkPZswIH2Zq8j3I\nzU6/9NKoSyMiCRfZZC9m9pq7Ty72OGf/jwkBfAJw1UDN6UmcUCJTC33pJbjzzmwwq4cJYOpiYpdc\nnZ1hGdJp0+Dll8OypFVcklSTvYjEU2wnezGzZWa2Kudrdfp7oUD8pjvczOYDW939acDSXzWltTXU\nOu+8M7vsZr0kub38cvgA09ISHtf8mHllp4tImVW0Od3d5xV7zsy2mtkUd99qZlOBbQUOOxU4z8w+\nCIwGxpnZ9939r4q97sKFC9/Ybmtro62tbaTFr5pCE8DUepLbqlVw663w9NOwdi2cckq41prNC8jP\nTu/rC48vuKBiF9ze3k57e3tFXltE4iHK5vSbgNfc/SYzuwaY5O5v6hPPOf50arA5Hd7crLxjB7z2\nWmhWPvQ/KNNNAAAN50lEQVTQqEtXfrnXm5lLft8+OPVUuPLKGu1GiMEiKGpOF4mn2DanD+ImYJ6Z\nrQfeD9wIYGaHmdnPIyxX1dXbBDC5LQ9TpsD8+XDiiXDttTUawCGbnT5rFkyeHL4rO11EShRZEHf3\n19z9A+5+jLuf6e5d6f2vuPu5BY7/j1oZI15IvUwAk0rB7t1hOzO8bv/+0KI8bVp05aoaLYAiImUU\n5RAzyVNoApht20Kf8bHHJr9/PHc42a5d4Wv8+Gw2ftKvb0g0xExEykhBPEbyZy174QV48kn4l3+B\n0aOTPewsd270zHCyHTtCE/q0aXUSwPMXQJk/v6pDzESk9mju9BjJ7RvfuBFWrIC5c+Etb0l203oq\nFVoT9uzpn4EPMGZMnQRw0BAzESk7BfGYmT07ZKV/+tPZAA4h6O3ZE4JhkgL5qlUhE/0b3wgfSl54\nIeyvu2lmtQCKiFSAmtNjqLU19IGPHt2/aX3FihAMx4xJRtN6bhP61KkhEXvFivBcpnugbmrhmQVQ\nXn89e9FaAEVESqSaeEzlNq1nAvjcuXDkkcloWi/UhP6Wt8C73gVXXBFaG+L+IaSszEITembxEw0x\nE5EyUBCPsUzT+hVXhOCXlKb1gZrQx4ypjUz7EcnNTBcRKQM1p8dcpml9zJhkNK2rCb0IZaaLSAWo\nJp4AgzWt33ILbNgQfa0804S+e7ea0N9EmekiUgGRzZ1eCbU+P3MmSH7jGyGAA2zdCg8/HKYtnTgx\nulp5ZiKXPXv6D42r+eVFh6KrC66+Osxy09gYFj9pboabb65qer7mTheJp1LuTTWnJ0h+03pLS1g8\n5KCDQlDfvz/Uyqs5gUoqFZYUvfXWMNNcpoV4xYqw5kemub9uAzhkM9PzFz9RZrqIlEg18QRavTpk\np3d1haU8zzgjLCRS7Vp5pvadXw4Izf5XXFHHSWzFZBIbIqCauEg8JXIVMzObZGZLzWy9mf3KzApW\nS8xsgpn92MzWmtkaM3t3tcsaN5ms9X/4h7B8Z2trqIXn1sor2VeeSoXXvfXWcJ4jjwzn/e1vQzm6\nu0MSmwJ4Hi1+IiJlFmVi27XAg+5+DPAQsKDIcbcCD7j7scAJwNoqlS/WWlvh6KPD+tuZaVr37YNT\nTgnN7KkUPPIIfOlLYbjXE0+E5axHGtBTqfDzjz8eXu9LXwqvn0qF851ySjj/xo2hPHXfhF6IhpiJ\nSJlF1pxuZuuA0919q5lNBdrd/e15x4wHVrr7W4f4mnXZZJfpl77xxtAv3dKSjRPz54fgu2JFyBIf\nMwYuuSTMMzJxYgi0qVRoEs/kWOVvb9kC3/1uyDp/8smQtDZ9ev9z7N9fhwuaDEdnJyxYEN6cl1+G\nG26o+hAzNaeLxFNSE9sOdfetAO7eaWaHFjjmLcCrZnYnoRb+JPAZd99TxXLGXm6tPNNXvm9f6KMG\nWLMmJEUfcghs3x6C+Ny5ocl73jxYtiy7PCiE5UEz22PGZLPNDzkkvM6aNSGIn3JK6IPfuDEE/Suv\nDOWQAgoNMdNSpCJSoooGcTNbBkzJ3QU48MUChxf6mN4EzAEud/cnzewWQjP8V4qdc+HChW9st7W1\n0dbWNuxyJ1WmrzxTK29thb17w9eoUSEhes2a8P3gg8NIpy99KQTyyZNDLRvC48z2e9+b/bm2ttD3\nnXnN1tbQJ6/a9yDyFz/p6wuPL7igokPM2tvbaW9vr9jri0j0omxOXwu05TSnP5zu9849ZgrwqLsf\nmX58GnCNu3+oyGuqyS4tk8GeO2774INDrfugg+DMM0Mg/vnP4dxzw888/HD4Pndudpa1006DRx8N\nNft580JNPvN6SV/jvGrcQ59G/uIn06dXde50NaeLxFNSm9MXAx8FbgL+Gvhp/gHpAL/FzN7m7s8C\n7wd+X9VSJlSmVt7VFSp/d94Jr74aKoHveEc2+a2pKexrbc0OYx4/Prs9blw4fsWK8PNjxoTXyu1T\nl0HkLn6yYIGmWxWRsomyJj4Z+BEwE9gMXOjuXWZ2GPAddz83fdwJwP8BmoGNwCXuvrPIa+rTfhGZ\n5LWODvjXfw194M3Ng/eJjx8fjvvYx0LFUYF7hBYtgsWL4bzzIusLV01cJJ5KuTc12Usdys1GH0p2\nugJ3iWKQmQ4K4iJxldTmdIlIa2v/oFzocaFtGSFlpotIhWgVM5FKys9M7+0Nj7u6oi6ZiNQANaeL\nVFJMMtNBzekicZXIudNF6kJuZnpLC8yaFVL7qxzARaQ2KYiLVJrmTBeRClEQF6mkzk5YvhyOOy58\n1wpmIlJGCuIilVQoM11EpEwUxEUqRZnpIlJhyk4XqZRMZnpmDluILDMdlJ0uEleasS1N/yhEilMQ\nF4knDTETERGpQ5EFcTObZGZLzWy9mf3KzCYUOe6zZvafZrbKzP6vmbVUu6wiIiJxFGVN/FrgQXc/\nBngIWJB/gJlNA64A5rj78YS53i+qainztLe36xw6RyLPUetq5fekc9TfOUoRZRA/H/heevt7wJ8W\nOa4RaDWzJmAM8HIVylZUrfzR6Bz1d45aVyu/J52j/s5RiiiD+KHuvhXA3TuBQ/MPcPeXga8BLwId\nQJe7P1jVUoqIiMRURZciNbNlwJTcXYADXyxw+JtSV81sIqHGfjiwE7jXzP7C3e+qQHFFREQSJbIh\nZma2Fmhz961mNhV42N2PzTvmw8BZ7v6J9OOPAO92908VeU2NYREZQJRDzKI4r0hSjPTerGhNfBCL\ngY8CNwF/Dfy0wDEvAieb2ShgH/B+YEWxF4zqH5SIDEz3pkhlRFkTnwz8CJgJbAYudPcuMzsM+I67\nn5s+7iuEjPQeYCXwcXfviaTQIiIiMVJTM7aJiIjUk8TO2GZmN5vZWjN72szuM7PxRY4728zWmdmz\nZnbNCM7z4fRkM31mNmeA4zaZ2TNmttLMnqjQOUZ8LcOYXGdY1zGUMpnZN8xsQ/p3deJwyj2Uc5jZ\n6WbWZWa/S38VSpwc7ByLzGyrma0a4JhSr2PAc5TpOmaY2UNmtsbMVpvZpytxLUMoR8XvT92bQ3rt\nxN+fujcH4e6J/AI+ADSkt28EbihwTAPwHCG7vRl4Gnj7MM9zDHA0YUKaOQMctxGYNMJrGfQcpV4L\nIffg6vT2NcCNpV7HUMoEnAMsSW+/G3hsmO/NUM5xOrC4xL+n04ATgVVFni/pOoZ4jnJcx1TgxPT2\nWGB9uX8nQyxHxe9P3ZtluXdif3/q3hz4dRNbE3f3B909szzUY8CMAoedBGxw980e+tHvJgxZG855\n1rv7BsLwuIEYI2zZGOI5Sr2WoU6uM5zrGEqZzge+D+DujwMTzGwKQzfU6y4pccrdlwM7Bjik1OsY\nyjmg9OvodPen09vdwFpget5hJV/LEMpR8ftT9+agauL+1L058LUkNojn+RjwiwL7pwNbch6/xJvf\ntHJxYJmZrTCzT1Tg9Uu9lkEn10kbznUMpUz5x3QUOKbUcwC8J938tMTM/ngYrz/Scgz3OoaqbNdh\nZkcQaheP5z1VrWvJiPr+rMd7c6jlqoX7s67vzSiHmA3Kik8Wc527/yx9zHVAj5cwAcxQzjMEp7r7\nK2b2R4QbbW360105zzGgAc4xpMl10ga8jph6Cpjl7rvN7BzgfuBtEZdpJMp2HWY2FrgX+Ez6U3/Z\nVeP+1L3ZTxLvTaiN+zO292asg7i7zxvoeTP7KPBB4H1FDukAZuU8npHeN6zzDIW7v5L+/gcz+wmh\nmWl5zvOlnmPQaxnoHOmkjSmenVxnW6HjBruO4ZYp/XjmIMcMZCjX3Z2z/Qsz+6aZTXb314ZxnqGU\no5TrGFS5rsPCOgP3Aj9w90LzL5TlWqpxf+re7Pcaw7k3h1QuauP+rOt7M7HN6WZ2NvAF4Dx331fk\nsBXAUWZ2uIUlTC8iTDIz4tMWKcuY9KcrzKwVOBP4z3Keg9KvJTO5DhSZXGcE1zGUMi0G/ir9micT\n5r/fOoxyD3qO3D4jMzuJMHRyJP8gjOLvf6nXMeg5yngd/wr83t1vLfJ8ua6lqAjuT92bIytXUu5P\n3ZvFDJb5FtcvYANhkpjfpb++md5/GPDznOPOJmQBbgCuHcF5/pTQR7EHeAX4Rf55gLcQsjJXAquH\ne56hnKPUawEmAw+mf34pMLEc11GoTMBlwN/kHHMbIYP1GQbIIh7pOYDLCf/QVgK/JUzNO9xz3EVY\nIW8fYabASypwHQOeo0zXcSrQl/N7/F36/SvrtQyhHBW/P3Vvln7vlOnvuqL3p+7NgV9Xk72IiIgk\nVGKb00VEROqdgriIiEhCKYiLiIgklIK4iIhIQimIi4iIJJSCuIiISEIpiMuIWFia8XfpJfXuMbNR\n6f1TzOyH6aX0VpjZz83sqPRzvzCzHWZWyoQ7IjII3Z/1Q0FcRirl7nPcfTbQA3wyvf8nwEPufrS7\nzwUWkJ0z+mbgL6tfVJG6o/uzTiiISzn8hjD14hnAfnf/TuYJd1/t7o+ktx8GKrIYh4gUpfuzhimI\ny0gZvDGh/zmEqSCPI6z2IyLR0v1ZJxTEZaRGm9nvgCeATcCiaIsjIjl0f9aJWC9FKrG2293n5O4w\nszXAhyMqj4hk6f6sE6qJy0i9ack+d38IaDGzj79xkNlsMzs17+eKLSkoIuWh+7NOKIjLSBVb/u7P\ngHlm9pyZrQb+F9AJYGa/Bu4B3mdmL5rZvOoUVaTu6P6sE1qKVEREJKFUExcREUkoBXEREZGEUhAX\nERFJKAVxERGRhFIQFxERSSgFcRERkYRSEBcREUkoBXEREZGE+v8gTItYO/FI1AAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1147b2d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scikit_pca = PCA(n_components=2)\n",
    "X_spca = scikit_pca.fit_transform(X)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))\n",
    "\n",
    "ax[0].scatter(X_spca[y == 0, 0], X_spca[y == 0, 1],\n",
    "              color='red', marker='^', alpha=0.5)\n",
    "ax[0].scatter(X_spca[y == 1, 0], X_spca[y == 1, 1],\n",
    "              color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[1].scatter(X_spca[y == 0, 0], np.zeros((50, 1)) + 0.02,\n",
    "              color='red', marker='^', alpha=0.5)\n",
    "ax[1].scatter(X_spca[y == 1, 0], np.zeros((50, 1)) - 0.02,\n",
    "              color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[0].set_xlabel('PC1')\n",
    "ax[0].set_ylabel('PC2')\n",
    "ax[1].set_ylim([-1, 1])\n",
    "ax[1].set_yticks([])\n",
    "ax[1].set_xlabel('PC1')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/half_moon_2.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4RUoSM4sgvmEDPP20MtNFZNgUxBusaMlthTreoiWJFe14RST3FMQbrGjJbYU6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\nOqCHHO4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129fab2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.ticker import FormatStrFormatter\n",
    "\n",
    "X_kpca = rbf_kernel_pca(X, gamma=15, n_components=2)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1,ncols=2, figsize=(7,3))\n",
    "ax[0].scatter(X_kpca[y==0, 0], X_kpca[y==0, 1], \n",
    "            color='red', marker='^', alpha=0.5)\n",
    "ax[0].scatter(X_kpca[y==1, 0], X_kpca[y==1, 1],\n",
    "            color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[1].scatter(X_kpca[y==0, 0], np.zeros((50,1))+0.02, \n",
    "            color='red', marker='^', alpha=0.5)\n",
    "ax[1].scatter(X_kpca[y==1, 0], np.zeros((50,1))-0.02,\n",
    "            color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[0].set_xlabel('PC1')\n",
    "ax[0].set_ylabel('PC2')\n",
    "ax[1].set_ylim([-1, 1])\n",
    "ax[1].set_yticks([])\n",
    "ax[1].set_xlabel('PC1')\n",
    "ax[0].xaxis.set_major_formatter(FormatStrFormatter('%0.1f'))\n",
    "ax[1].xaxis.set_major_formatter(FormatStrFormatter('%0.1f'))\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/half_moon_3.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2: Separating concentric circles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MpuCFIJvAb7019LXEUZ6+tWvX0tq1a11pS2jRPCQiEkIkEtFuIrqAiGqI6GMi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\n3YwNsmrLeF9LShBiUFCAz5KS4N+9XqQ+8nhwbEMD/l+3Tr6DZgLX7Pw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8hBBCSLmpaeh3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\nEEJILqFAEUIIySUUKEIIIbnk/03qfDwSxhncAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1147b2c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_circles\n",
    "\n",
    "X, y = make_circles(n_samples=1000, random_state=123, noise=0.1, factor=0.2)\n",
    "\n",
    "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='red', marker='^', alpha=0.5)\n",
    "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/circles_1.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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u2sRkqdWrOTGIUEw1MGbt8bB53KRJ/NvhYA7XoUOsrluzhttNmsThjxtnlbSn\npVnWuPldX0/L/J//pC7u398DYuQuF3DLLZyRDB3K6z1sGN0TMTE8MVpbpYfr1vGACgpYX757N/D2\n28176AuCIHQSscTbSiiLuKDAWg/cdHAz/wdbGSs7mzf7wIUwNm6k4o0b1/zxbrbcgmWZjxrF5zZs\noF6lpDBS0NDAofp8dInn5zM6UFtrdSMtKWnebdReZVRbS4vcRA9cLuDBB6M0Rq4UZxsXXMBMPbeb\nJ2DiRIp0ejpPyowZPEE/+AFzG3btAj77jDXjxcU8aK3FGhcEISyIJd4WQlnEBw4Av/kNfckNDXSb\n3nsv8KMf0RoPXBkrP58x8vXrGftuaOD/H31EkSgspJVuHl+2rFstN68X+P3vT80oB4CvfY3hYJPY\nBnC+4nBQxD//nCXyplze4bBc6aHw+zlHKS6m1m3cyGq9ffv4WFRZ58adHh/P2IDDYa0Bf845QL9+\nnNFMm8bPxJe+RA/LggV0WxxtWudn5Upe/+XLZQU6QRA6jVjibSFYlrHbTRMyJobqtrtpCfTcXOD2\n24MveJGWBpx/Ppu9mBryt9+mgl12GdO5jx9nfVZODvcZbI3rLmLNGnry4+OtZcvr6ugyf+89Hqbf\nz/mG1pxruFzUMa0puCkpfH1NDX9qa5nPV1V16vspxVORksIKu4oKatvdd/M0jB3LyURUZLAH9gOo\nquIB9+9Pd8NzzzH34dAhXi+l2Et/9Wpa6VVVjJWbBjHnny8LoAiC0GnEEm+NYOuBA8Df/sabdEMD\n3aW1tbzBL11KMTa14+bH6WQ3r40brXi4z0eL3O+ngpWU0GL79FM+3tgYfI3rMBAY9/Z6mWXe0EAB\nLSzk/OLTT4HHH2fSvdacszQ0WPupr+dhKMVTUFHBfWnNeYvW1K/Atu9K8fBqariP8nKOx5zypCSe\nivh4q7482Li7DXs/gLg44M9/Zmx8+HBO3NLTmeAWG2uFQrKzeeAXXkg3/OTJdKt/4Qv0uBQVdfNB\nCIJwuiGWeGsErmSVnc3srZdeovm4dy+VyO/nTTw/nxb6/Pk0MU0cPTubQWV73NusUe3300J77jm2\nat25ky75vn2tcYSxVjwvj25zr5dZ4Q8+SGv5yBEm05v5SH09Bbumht5iI94m+1xrinZKCodWVmZF\nFZxODrmxkdsGutWV4oQAoHd6504+lpjI1/ftS2GPieE4PB56r195hdslJUXQQrd7Zr7xDWsFOvta\n4VdcwV7gXT0qAAAgAElEQVT5Ph8nbKNHW7HxuLhu864IgnB6IyLeEvYlQu036I8+suKilZVUnbo6\n/l9dzZv0vHkU5lmzuK9ly6y49969NDHXr2c8PT0d+Phjy5qrqaHp2wU3eK8X+OUvOQSHg+L64IOc\nW6xbx8NIT2cFnBFLpSjQDoeVl2Wnqoo/Tqe1qJv5Me8RiHkuJob7BCzrvLCQzzmdPBWxsYyT33MP\nt4+PB847L0I15oGemauvbu5mB6xkgb59mfhWVATcdhvLzox3xXyWzAI4giAIHUBEvCUC46AAY54/\n+AFdqdXVtMpjYpj59eGHtLzOOYdWVmqq5Vo1XdsOHqRb9aabLOvaTBZ8vi6/wR8/Tou2d2/ONcrK\n6BAw63NozSTrxkbLy5+RQWE1K66Gwu5mt58ys99g29tfA/CUApxkxMVxcjBnDudEDgfnOHV1bCpz\n7rkRqDEP9Mx88MGpk62qKvbP37OHLvj0dCZBPvII8Ic/AHfdxbh4hDvxCYLQ8xERbwkTB7Xz/vsU\nblNmNHky8J3vAP/5D4O4aWn0TZeW8ub96ae8WcfG0gW7YgVF/4c/tATa5eKNvZtv8KakWSm6xE3y\nWVWVJcL19Twsh4PlYGVltI7bQ1sXr7JvZ1bvLC9n+kFKitU3JS6ODhCtu9mIDeWZsU+2TMXC1q3c\n/t13gUsuodfFtNVdt675IimCIAgdRES8PezZwzW/zzuPKpKQwNphr5fucr+fJuvKldy+qIim48SJ\ntLwfesiqv7ILtFJ0n5eVMUnqppu6rEvboEGMI5u8OeMeP3KEfzc0hHZ/m8Sz7sBY/TU1zJpPS6N4\nJyZabvv77utmKzwmJrjr3FxLU7FgkgnGjGGFwdlnAzfcwDyKESOAl19mE6CJE7tx8IIgnI6IiLeH\nVauogtOmUWgB3sT/8x/+HRPDG3dpKUvIYmKoRPv2USVzc3lD37qVPm1zE7fHWZcupWr96ldd0l87\nOZk69OKLnDMUFPBtSkr4fLQs+WwS4ozVb37HxbFd69NPM8m/2zAL3LTU9zwri7Mj02ze56PHZtky\noFcvuhJ27eJsaM4cLlErCILQCVotMVNKpSmlzgry+JllRhihnT6dqdSmjWpKCt2jhw8zmOzxcAGU\nhx/mT1wc8M1vcpEMh4P/Oxxss2qwx1kLC1mGZmLpYSCwLGvCBBqFjz/OcuWqKhqO9fUtN2eJNPHx\nHGdsLJ0h3Yo9Iz0YbjcXRHG5GH8oKmJio1L8/e67FPbcXD62fDk9O4IgCJ2gRRFXSn0LwG4Ai5RS\nO5RS021Pv96VA4s6gpWaAVY8e9Ag4Lrr+Pv73wf+8Q+uEHLoEHDrreyYUldnZYitXctyNHucde9e\nPq8UY+lh6NKWl8e5xBNP8Pe2bXw8OZlzkJISJrU5nfzpDF256Jrfb7Vzzc21+rV3C6F6BdiZP58n\n04RLGhro1hg5kl6Z4cN5wpOSOMmrrbWWfxMEQeggrVniPwMwVWs9CcD3AfxdKXVD03PRsU5mdxCY\n0GRvvmLi2enpLClKT6eA5+XR3HW76beOjwe+/W2uM/3mm8Df/84Md5MB/9RTvNlPm8Ys9qSkTlvj\nXi/7oKek0KurNd3oxiKvr2dXNKWa13R3FHvtd1u2bS92L8Hf/96NDV9CTeAMe/awfKyhgSc6NZXi\nPWUK3e+//S3dHuvWcR+moH7+/JYb+ARrcycIgmCjNdsrRmtdCABa6/VKqcsALFFKDQUQluipUuor\nAF4EJxTztNbPBdnmJQBXAfAC+J7Wems43rvNBCs1CywPMwJfVcX1ph0OFlufPMkbv9fLuqgHHjg1\npjpkCPezfz+T5cwyl50sM/N4KNReL7u4NjYyTLtmDXuRpKez1CwpiUM3bcEDy77aSntc8cZgratr\n33tozVO6ciWdG9dd18XJbW3JSF+5kgcUE0MBv/BCpvJXVHAyd9NNVqWDy8U15QcNost92zYmuQXS\nlhj8mY59USIz4UlJ4bmzt/grLaUnJD+fv81zpaXWvpKS2NGopIQel+3brccBhkhOnGD8qbqaP337\n8sPn9fL5qVOtfQ8YwHLS5GRrIYIDB/h3UZH1urPO4ngPH2bS4+HDHIf9Q11cbI333HP596ZNLGVN\nTubnY+1avt7r5Xts3879DBjQ/PyYDk/mXBUVcRvTRtgcv3nN4cP8/+BBVs2YtsEAw4pmPOZ9q6qs\nz6u5DuY9d++2llg2mHNhjttsO2AAKzrOPdc6N2Zf/ftb2wPWuTT7SUqyrm1SEn/27uX/9hve5Mk8\nXnPezW/g1GtgGneZz5z98xZhlG4hk0kp9TmA72qtD9geSwWwGMDFWuv4Tr25Ug4AewFcDuA4gA0A\nbtZa77ZtcxWA+7TW1yilZgL4vdb6ghD70y0dT5egNQPORsEWLGCi26pVfKyhwWpGPmQI8LOfBW/i\nErgfgCpnCrg7gNfLPuQbN1JbAIr0tGkM0R84wMYvmzaxfryxseMCbkcpvl9Dg5UBH2yb9lwqe9MY\n05q8b1/eE+64g7rZJWLe2nVxu9ldb9cuzphqa5k3kZrKg6+vt3Ih7rmHIZYtW3jz2LWLs6k33jj1\nfefNYznj9deHremPUgpa64h40ML+3bRPcgB6OpSit+uHP+TzprzB9AtubOR1MKGOwPGY50aPZjKq\neb6lD2tCgpV1mZ5uNX0aN44JrLGxwJe/zGVs77yTj2/bxg+rzwc8/zyzNI8dYwlGeTlLMHr3ttoV\nFhfz/f1+fugbGzmTjY/n5/CWW5go2bs333/UKE4e4+OBzEyOMTeXz3k8HGdcHEVr82Z6jPbv52ey\npoZtgfv352y/uJhj3rvXMlr69eO+yspYfZOQwBvL1KncPiuL5+OGG3gdamt5Turr6W0cN47n9ORJ\nri0QF0fRNUkvCQmcbO3cyXNSUcHj9nr5fEoKxxEfbxlTlZX8/8SJU69VqOtnVmgy72GOD7CugdPJ\n7WbOBB57jN/LO+6gl1Up3kDDMMnuzHezNRE/H4BXa70/4PFYAN/SWv+jI29q288FAJ7UWl/V9P9j\nALTdGldK/QnAcq31wqb/dwHI1Fqf0ng6IiIOWLMzjwd49FFmIxcUWOoVF2cltF19NRW0Gwqc163j\n4mvr1/PzppT1eXvhBWDJEt5HVq1i6N7QmVNoLOykJKuHemfd9EBzETfd3LTm+/TqxUXDIrKM6bx5\nFGGPh/kMQ4awb4CpXnj7bfr+lWKToLw83qi3bOHNqrqa7vmxY619ut0Up0GDOLt65pmI3yjC8N7h\n/W7aJzkAy/YAiuP69eGZjXYGu3D06kVBMFae+UKY7kWmNKSlfYTCiEywmTJAMTIi29jI/Zm4l2mR\naBZEMO8VE0NhO3myfcfrdPL9bmiKuP7jH8Gvw5Ah3L60lDegaMZ0X8zIAC6/nOekVy9O0ADg/vvD\nMsnuzHezNXe6F8AAAPsDHp8BYG1H3jCAwQCO2v4vaNp3S9sca3osOlaPyMvjDWXWLLqAbrmFLVTN\nrG7gQM7sv/c9PtZNq1etXcvF1AAaAw0NnEe4XJxs/+Mf/N7v2MHPZVxceLLTTWy9pia891EzLhNz\nj43lezidVtig29uwejxs3uN2U5h9Poru9u20Bmtq2C/fWH0rVwI//SmTFhsbeWP/7DPgn/+0LMqq\nquAxeOmxbhFYkunz8QPi81mLEkUau/h6PPwx3YoAeJGE4/6BQAngRCIKMARpqMBoHIQXSViLGdit\nz0YNklCBBORiEpLgxQjkYxW+gP0YDQ0gocGHmIZG1CMWdYiDAuCHE340ohrJgE+jr8+Dc7Ad+Tgb\nJ5CCRh2PpIZKOFGPBsQCfsCHJDjgRyzqoRs1fCfTkIgqJKEaNUhEA5zwIwax8CEZPvjhhAMNGIzj\nGIfdaNBxOFo/FKn1Xlzwzi6cq3ahvOE76INSXID16A9b6KK4mF/kaBdwwGpYcfIkv7f/8z/8nZDA\n67l0KXDNNRENebUm4i8CmBXk8Yqm564L+4g6yezZs//7d2ZmJjIzM7vuzfLyeAFHjGB50b330i11\n/vl0P/XpQ1Px+ecZf+nK9G0bXi8FLSaGQwAY0jLfm4suoqdqyxZr7Rbj8W1vNzY7Zl0PY2i012Ue\nCoeDjg6vlxP96mrep5Xi8TQ20it49tnd3IbV5aL4HjjADMK+felifOABPrdoEa1zk/ZfWMiF13Nz\neQFSUynaf/gD8PWv8zWzZ/Ox2NhOt+DNyclBTk5O2A874gSWZBYW8lyeOBHaIo0k5kvQJOB5GI9f\n4nFswwRUIhUepAPwIxZ+DMMhHMVQeNAbbckdrmzD25ciDaswrNljNejd6uvq4EJ5kMftqZjHMBbr\ncVmz57Orb/jv3woafVGMP+JufAPvNe24rtvuhWHBhGXKyxmbNDedvn352YvwJLs1ER+gtd4W+KDW\neptSakQY3v8Y0OzTNaTpscBthrayzX+xi3iXM2cOXWFeL5cFO/983nBLSniRk5J4Q169mnEneyJO\nF2KS5uPj+X3p04eftT59GJ6rrqaOmMeNJy0xseMirhRDRpdeSq8x0NxF3xn8fo7LfO9jY60Jh9/P\n+3dcHI2w2NjwvGebKCpiaGT4cLq+Bw/mQLZuZcKSsdIBa03WDRvYEOjIEV6IsWOZ8LNkCUX6+HG2\naf3Wt6z36WAL3sBJ7FNPPdXJA44C7ImGBw8ylmyW3isvj55uRSHwIgm/xwPYizFIQRXyMRx1iEMC\nahAHH7ZhIijep8cq0RoaZeiLn+I5fBGrLYs8yq/TKTQ28vu6f79lPTid/E6vWBHRhYxaE/GWRpUY\nhvffAGC0Umo4gEIANwP4dsA27wO4F8DCphi6J1g8vNvJy2PDjthY3jwaG1lm9OijFPdBg6zEibw8\nKsyrr9JKO+uU3jlhJT2d84fzzqO7vLaWYZzx4+kVys+nuBcVWTk/AD1EpvVqe+PYMTHUspkzOZdZ\ntiy8x2Qm78aFPn48j6O2lpMRh4N6WF8f3vdtkexsely2bOE1tVvOX/86u+4dP35qMP/llznzKCjg\nzaB/fyZEjhrFoP6OHZwMSFb6qdgrRbTmLLSkhB/wXbs4gTp+nNnix45ZC9abpBClrLhRY6PlLnI4\n+AUwWZMNDXysqsr6UJnEDLO8n1mqz7wOoBvI5eLrU1N5DcvLGQfWGp7SeHg3joCjIQ1aN0JXOpvs\nbUfTj8LpV72rUI1UHBkwA/0HFPBajRlD4+fAASaVVVY2j+WZe2dMTPO1jc31U4rfEa1pGPl8vBmY\nVSXNNqFuCCaXQCnrepmJhclf6tWL123kSN5UR460MvOVYoJfTAzv9RFcyKg1Ed+olPqh1vo1+4NK\nqR8A2NTZN9daNyql7gOwFFaJ2S6l1J18Wv9Fa/2BUupqpdR+MEb//c6+b1h49ll+cMwNoaaGMc9Z\ns+g+t38gTfbY7t3WWuMZGV1mmScn07P/yius0NCafcbHj+f97Wc/4/3L6aS1Xl/Pz+J993Htjvh4\nfq/ag8vFZLnLLgO++lXL62SSasPVCc5k0B86xETXkSN5DzVZ8N02GTZx2cmTOTu/916e+ORk3gDS\n0znBGzq0+evmzbMa0Xu9nN0PHEjRiY211po3Lrpu8t70GAIXJRo+3Pr74ou7fzztJN0LJD8A+DcC\nMbGA2gHoOgAJsfzshMhx67nEAA4gaeQgDPs8G+gf6fGcfrQm4g8C+JdS6hZYoj0NQByAG0K+qh1o\nrT8CMDbgsT8H/H9fON6rQwS7iebnsy7L+KuNDzc1la5zk5lsalaffpozRKeTVlZWFjOY7XXAYb5Z\nT5jAJC9TUWLixElJFOyMDHoh6+utyepf/mKt3dFeKio4gf3hD5mE6/FYSXQNDZ2LtdtxNHkZjf55\nvRTv2FhLR7sFE5c12YIrVvBzYTwtweq8CwpopdfW8nonJFjlah4PLUqTvLBuHUXp1VelVvw0IjmZ\nVRRPP20tCWyqmurquJzCkSMt9wDqSShFT9lzz1lGrBBeWiwx++9GbPLS1AEAO7TWYXaWhocurUW1\n30T9fnZPeeEFZiKbso2EBJqH8fH8+5e/5M3+5Zf5f1UV9zlyJOtZP/uMJTLXXNNtjT28XurMxo3U\nj8pK3jSSkjhsj6f9DVgMMTFM0G9ooBXu9XKfJj7fmUYygTidfK8LL6Rzo8vqxINhSgmNC6OxkW7B\n2Fge7Pz5vO72Om/zWfp//4+14kuX0oq/8UarAQjA629a6H30ETvahKlW/LQqMevheL30igH8LBcU\nsKpr9Gg+t3YtHXc1NVbL/aQk5tCuWkXnj9a8rZhychNyMp6v6mruv29f9oXJz2fun0nXcTqt76PP\nZ62YrDX/T0zkdmYi7vfz+eRkKxl28GA6jxoa6ExKTQUuuIAewPJyCvgFF4iAt0ZX1oknALgLwGgA\n20B3dxTUbwSnS2tRA2+iWvObFxjz/Owz1m8pBdx2G9Vy1y5uC1gLYp91FusOjx+n2WwEvRuyHLdt\nYx/19es5nLo6OgFMsnRHrQDjkEhPtzLITZmlw2HldrWXuLhTJxZK8X0GD+YN6vXXu1HEAxvAFBcz\nhFJVxZP73e8yVtu3L90djz/OSd/77zPzb9s23rE//pix8GBLknZBrbiIuCBEJ535braWAvkG6D7f\nBrY9faEjb9IjaW3RC6UY75w5kyJ84YWMz61dawWCzQIX559vrd4xeDCfLy3l/3V1LEVqaXGNMDNq\nFId+2WVck8Ph4Gy/pqbjpZsxMbQK6us5CTBubmORm/3Gx1sNYdqK6UeRmNg8+3zQIE48tm2zrJpu\nwcRlhw3jT24uB3b8OMX51VdpWa9YQXPke9+j5T1+PK91dTWD+l4v/YzBZjat9WsXBEFA6yJ+rtb6\n1qYY9Y0ALumGMUUHbb2Jut1si+Z2M9a9bp3lXj96lD6s/fupWjEx9C25XDQjS0oYQC4rszLNuuFm\nbZqjHD3KmFxGBodcVmYlgrYX0/wJCJ4Q2tBAraqttdx9bRVy010xMZHuxvh4WuemrXWX0prrwJQ8\nHT7MmUp5OcV5/Xp+JvLyWBN+9ChPUFERrfLt2+k6WLKEq97ZJ28tLbgjCIJgo7Xb6H9vx9HsRg87\n7bmJmnWm330XWLiQN/HiYlpbSUk0FV0uWuDJyXx86lSWWNx+O633iRMp6N10s05Pp2jX1tL6Limx\nKjhiYzvWJrWhwYrBtYbxqrY1Y91MLCoraeyarPraWurlhAm0ysOOfYJmCBR1l4u904cP5zWNieG1\n9vnYG6Cujm71khImH/TqxYGnpXE7h4PeG/vkzb6ynf13BMtYBEGITlqLiTeCZV0AixcTAVQ3/a21\n1mldPsJ2ELa4W1sXI7HHLbdt48/06dbKIw4H8Otf03c9cCDjpFOmMHvd4bDinWFc9KStrFvHHCuz\nPkFiolVqGU2hS1MampREPTQJMuecQ01LS+vCnumBORGBiY6mosB8Xv78Z/ZKNzXLQ4bQLTF8OIV8\n9Gha5rt3W13Gqqt5gJdeysYxXZjYKDFxQYhOuiwmrrWO0VqnNf2kaq2dtr+jSsDDSmDMc9gwq2m/\nHbvLfdcuWuE1NdYykwcP0o165Ah91QkJXB0pLY37czja9j5dwMyZTK7v3dtqZZqQYEUC4uKarw0e\niS6Jqak8vX6/5Uo3fTVMlON//7eLBDxYToTxumRnN7fSlaKYf/YZJ3C7dlkdxRoaeP1N0mNaGj8f\nDgc/K4MH8//SUol7C4LQbjoQ/RQAWC53n4/xzaIiKsuOHTQbly+n+lx/PW/8tbXAI4/Q0ooSt+hl\nl/Fn3z4eilkK2TSsMpjKqY6WnrUXpSja/ftz7lNfzyosl4s5ZDExVrL/Cy90UWZ6YE5EVhY9LUbU\ny8stQb/jDn4OMjJYdfDJJ8x9KCsDfvxjHkhSEq14j4eN3gFmE6am8j1MIlwE2zcKgtDzOD0a9EaC\nmBiWkMXF0Xru04clY9On02V+/vm8cffpwxv+7t1Uym6ytNtCcjIt2eJiDjUlpXmdqfHyNzaGZznR\nlujf3+pqOHgwcO21PJWmZPr4ceYI1tTwFPbqxfF3SWZ6sJyIxYt5EsxKVPaKggMHgA8+4CyjrIwn\ns7aWgl5cTLfH+PHAk0/SlZCSQvfBZZexX8Cbb3K50l/9KmomeIIg9AzEEu8Ibjdrf82KGwUFvLGv\nWsXFK3bs4HYOB3trFxYyE+v3vwe++MXgdcERYsgQaozWbEJXV0eLPCbGylI3JV6BFjrQ9pXKzHam\nN4r9cdP0LC2N7v2xYzkWv5+hZNPO2uulsZuaGr7jD4q9PzfASdgzz/B6FhQ0ryioq2OC4tCh3H7P\nHv7etYsDNSuQ1dSwp/6mTTyooiImOJaVsVuGWN+CIHQAEfGOkJ0NrFlDcZ48mf7eESMYAz37bJq3\nAFVrwQKrLnzPHmDuXPp/DRHujZ2eTtd1Sgpw1VXAe+/ReBw5kpqVn0/hHjmSQlpZyTC/32+tGWDW\nhWgJs/KYcckbgU5P536KimhZX3ABXee1tdx2fFOfwJoanm7z/mYJ6S7JTA/sz6211Q/fCPqAAVaJ\nYEEBvTAmU7CkhJb1gw8yodEsS5qXx0UTvvAFbjd5MtvvivUtCEIHEXd6e3G72bijvGml3d27eXM/\ncoQ39mXLrIUv0tKs/oiHD9MH/PnnFHOzr8ASpm7GLJZSVcUVzsaPZwSgsZHiPHMmf5sOoxddZLU4\nNVGBUAKekEDhBvh6h4NVWDNmsNPsrbey6+g3vkFtmzKFp7CqirrWr5/V4M6sxvnEE8C0abTWp03j\n/2GPhweWkdkTHcePZ25DejrwzW9yBnH99ZzAxcfzhBUVcdaRl8fXFRXxc6EU+14WFfHk7N9vxTAE\nQRA6gFji7SU7m4JdU0NxPnHCKrJOT6d7dP583uiN6mRl8UadkUGrbeVKqpA929m0W42AZR64WMr2\n7cAf/mCVdt1yC9t4K8VcrPx8ayXIQEwM2zRj8floacfEcE5zwQXNu9Qa63zyZD5mFvN68EH+/8or\nnFyYBU4mTOASq4ELu4SNUP3y7Qe4ZQuv84IFHESfPvw8ZGdzdrJ8uRUvv+YaPp6YyBi48d6YMkOx\nwgVB6AQi4u3B42EGcVmZZUGZdWvHjaOl7fPRXX7ddRTqlBRaXAkJtMB27KDF9sUvNi9huuYavsdT\nTzEBqptXrTKraAJWHpZdKL/2NR7Gz35G8TaHbRfy2FgeWv/+VlfZtDRqVV0dnReffUaNHDOmuUA/\n8QTbwQaKc7CV2OxjDTvBJlZ2TOnZ6NFcnGTyZB6cw8H4t9vNNa0zMji5e+cdZt81NnIGZC8zNMF+\nIOJhFUEQeiYi4u3B5WIG8bZtFOrbbmNg1+GgH1gpdm2rqeGNfuxYmqAmSWrhQsZLJ02iNa5187au\n5eXAf/7DuPpDD0X0UAOF8sABev5XrmS8OpiIK8XDGT3aalpnVjIbOZJW98UXc92Pr3wltEC3NI4u\nJbA2/JprTp1MmdKzlBT680ePpnflnntobd99t5Xdbpq7PPggk9y8Xmu9cZ+Pa9LPmsX9dtMqdoIg\nnF5ITLw9mEVPCgupZEVF9A/PmMGuXHFxLGSePp0ikJfHLHaz7vTOndx2yxbgww/ZX3vvXvqbly9n\nty+nk0lQEYyTB+L1MrE+P586ZbLD/X7LkDSrlJ17Ll3i11/PePewYZZb/qKLaKWbRVKSk61utFFB\na/3y7aVnx45xdpKTw89Dbi5T6417PT2d/v8nn+RJiYsD/vQnqyTxgw8si99u/QuCILQDEfH20tLq\nZllZFOjaWorAc881v1EbgUhMtHpsT55MF/qoUYyvm6znrKyIHWIgZlUyp5NzmLg4GqKJiUw+GzmS\n4d733gNefJFzmLPPpiPia1/jNpMmWUlrsbFRWFHVln759p7mDz9Mke7bl9dw1SquWufx0BNTXt68\nL0BgtzfzGVq61FrhrJtWsRME4fRB3OntJZi1dscdvHkvXswaqHXraI3l5ABf/7qVmWxqyisrGTe9\n7jpa5z4ftwUYNwW4r9tvjwq1M+5u0/506FAewqRJwE9/Sit70CBu4/VyG3uId8oUa1E3k6AWNda3\nIbA2HDg18cxkqbvdjAX07s168FGjGPN++23mSyQn82Bfegm44gruwz7xKy+3PkOFhdz3uHHNP0+C\nIAhtIGIirpTqBWAhgOEADgP4lta6PMh2hwGUA/ADqNdaz+jGYTYn0FprbLSaeZi2mxMn0s3u81HN\nli9nXfCkScC3vsX9LFxISzwlhaK9dCnFITmZweexY+mzjpIFI5KTGdZ9+mmmAwDMEp8169S+5aZk\nrS1Ja1FFYG14S2RnU7z376fXZOVKusy15vXPyAA2bOC1XbmS+zai3djICdpZZ/FaG8v74EF+Jszn\nKQomb4IgRD8trmLWpW+s1HMAyrTWzyulfgqgl9b6sSDbHQQwVWt9sg377NqVklpa3eyvf+WSkv36\nMft4xQretD0e3uAnTWLDEAB49FFrxRGzjvittzJzzOFgz9HvfKdbVjNrD16v1eLUWN4tbRvVot1R\n3G4uPbp7N0sNU1MZ6P/Nb4DXXuNnY8sWXl+fjzkT6en8LMTEcAJYV8cZUFqaJeIZGVZ9Xhddd1nF\nTBCik858NyPpTv8qgEub/n4DQA6AU0QcXPY0OmL3oaw1Y6FXVLCZS2Iif+LjeaP2+4G77rJcs3fd\nxULsu+6iwqWm0hV7+DB7ru/a1bz8KEpITmasu63b9mjxDlXylZ1NF3hBAa93ejp/b97MSVpWFhMa\nTWF8eTmQmWl5YYDmQj18eLcdkiAIpx+RFMf+WusiANBauwH0D7GdBvCxUmqDUuqH3Ta69mBvJda/\nP2/g/frxOafTEnelmjcLWbGCGcsnTjApqraWKeB1dZKpHElCddLzeBgeMXkNWjN00tjIrD6vl1nq\nDgevb3y8VTfucHT7crOCIJz+dKmIK6U+Vkrl2X62Nf2+PsjmoXxtF2mtpwC4GsC9SqmLu27EHcTE\nPAMA8msAABygSURBVHfuZE/SgQN5ox4zhhZdQwNd7R5P88zkRYvY/OXZZ5kIVVfHLimHD5+aGS10\nH6FKvlwuhkXOOcdqOJ+QwKS0IUOA99/n4336UOArKthebtQoWumBk4LA9q6CIAjtpEvd6VrrK0M9\np5QqUkoN0FoXKaUyABSH2Edh0+8SpdS/AMwAsCrUfmfPnv3fvzMzM5GZmdmxwbcXk7UeF8eyo3PO\noRv9wAE+f/751kIYTiet7sJCCvy+fYyZ9u7NWGr//oy7hmrJKd29uo5gDV9SUvhTXs66/vJyXuOE\nBJaTTZ9Ol/m993LitmePNSErLKSnJSWleeZ5a+1dw0BOTg5yTNWDIAinJZFObDuhtX4uVGKbUioJ\ngENrXaWUSgawFMBTWuulIfYZmeQZj4fJamaVkMZG/u31WiI+bhzTu3/7Wz63fz8FwedjXDUjg2Jw\n4gRrsh55hK8PFOtuuPmf9rQ0CZo3j16TwYNpjU+cyBDHrFkM8h85wiVFfT66y/1+1thNnQr861/s\naLNmDXDoEPc3ahSt8/HjKejPPMPrNm8eLffrr++2kjJJbBOE6KQz381IxsSfA3ClUmoPgMsBPAsA\nSqmBSqklTdsMALBKKbUFwFoA/w4l4BHF3gTE/D7/fFpiTid/CgtZbvTEE2yp2rcvb+6DBrEWy6x0\n5ffTMt+yJXhcVrp7dY6WVo6zlxDu3Usxf/ttXo+sLHbf692bE6xevdhq9dFH6VX55BO6zz/6yFqG\nzeXiBMDjoYfG1IG31DBIEAShHUQsO11rfQLAFUEeLwRwbdPfhwBM6uahtZ/ArHWPh0uBFRXxf615\nY1+5kr1IXS5abAkJbGN26JBVejRtGtem/slPuN9Fi+imBdrW2xsQd3tLtLTAicvFTmyJiSwX++wz\nCu+XvsTrkJLCdqkASw2ffhq4+mpWE1RX8zqXl/O6uVz0yJiVYA4c4L7WraMVH6xhkCAIQjuRjm1d\ngVko5fhxWtbV1RSAQYN4A3/qKQptQgJ/O50UAtPBzetlHbLDwT6mX/wi3bqhusXZEXd7aFqbBBUV\nAa++ynO6bBknVQcPUrBLSnhdlzY5gmJiOFErK+MEzO3mRC4xkaGThx7iNS8rY6XCwIEU98pKXtNg\nDYOkwYsgCO1ERLwrMAulDB16qqjOm0dxv+QS1g4XFwP338+GMCkp3H7+fAp4aSmFfu5c3vhDdYuz\n3/xbW0rzTKa1SZA5d3Pm8DrU1lrlfr17U+Q9Hk7Mamp4nY8do2hXV3OS1q8fcxquvDJ4GZnWXBSl\npfaugiAIbUREvCupqmouqtdcQwtwwgSWlsXFMblp+3aKct++dLsWF1MA/H4KyYoVFBXj6jUE3vzb\n6m4/EwlsmVtT03wSZF8nfP58Tp4cDiatVVUx6TAxkdeqvJyP+3wU+V27eB2OHmV4ZN8+bhPMsm5P\ne1dBEIRWEBHvKtxuJkJVVgZf+MLpZKOX117jzd7vB265BfjLXygOx45RRAAmUWVnMzM6mJvcxMDb\n4m4/U7EvcFJcTLe5vYueOXdOJwVaa1rfcXG8HjNnAt//PgX6D3+wmvjs28eysocf5r4yMuhqF8ta\nEIRuIDramfZkQjXsyM4GNm5kVrp94Qv7UpdvvkkhSEjg7zVrKPyjR7MVa1qa1dZz0SJmTNuz0quq\nrGzrPXtaX0qzJxHuRiheLy3gYcPYVa2sjBUASjW30o8c4WNaU5z9flYaHDtGYb78cor43LkMiYwe\nTdf5lVdS6IcPl45sgiB0G2KJd4ZQSWRuN/Dpp7yRFxZSfOPjeXN/6CGKwYEDwJIltPROnKD198or\nXLr0xRfZf/uNN4DbbuN+Xn+dAmHc5ADfe/hwuutN+drpEGs15/WBB7jaV7j2N2sW/w8MOQwYwHNX\nWclrUlLChUtSUzn5uvhiLkjjclnu8Lw8lp1deSVDI0VFEroQBKHbEUu8M4Sq2c7OpihfdhlLxiZN\nYkb6889TPIYNY2w1LY1ZyykpVsLUxx9bCXG1tRQHt5tiv3KllWiVnc0M9rff5j5Xr6aL1/Tntvfo\nbotVG00tQM2x3XlneGqo7dcpMOSwaBGtdKeTjXg2bqRFvW8fFzWZMSP4gjRz5/J1hw5ZoQtBEIRu\nRkS8o4Rq2GFcs42Nlqt8/34KthFVj4eW3NSpLB1LT+f2Z58NbNrE55Yv574//ZR/Hz7M9zh8mP8v\nW8bX7N5NSz5QSIwot9TcxH4srW3TXZjz6nTSg5GV1fbXBpuI2K/TsmU8dybkUFEBvPQSm7ZkZTUP\nfxQWWn8bsTfs2cMFbVwunv+Kip4duhAEocci7vSOEiqJzJ5AZQh0a7tcVplRcTETrEaMYOJbfT1L\nnPLy6J6NjaXLvLYWmDyZlvmoURTzffu4/Sef0OVrsq1raiz3caiSM3tDmGgqS8vOprfh2DEmli1a\nRFd2a67qUC54+3VKTARGjgS++10+t3AhPSKbN1OYTfhj+3b+Vophj7o64I9/BK64Ahg7lpOCadPo\nhne7WVL27W/3zNCFIAg9GrHEO0JguZI9iczETIO5tQ1mm969mcxmGr7U1FA0li1judKnnwIbNrDB\nSGKi1ao1J4fCYpa3bGhg7PyJJygkRpSzsiwrdPlyCo49Gc7tbm6pmm0ihTmvhw8zIxxgAtq77/Lv\nllz+wVzwgdepshL4xz9Yfx8XR8tbKXoySkroOp82jYvXTJ4M/O53bNozbRprwFetsvYZH8/9JSRw\nMpWSIslsgiB0O2KJd4S2WNut4XYDs2dTCMaMoQCNHcvypMpKNg85cYJi39DA/RcU8HdGBpvDKMW/\ni4oo/pdddupSpyNG0IrfupUlbSdPcvJgj+WbVdW2bqXwP/RQ244hsL1rZ9u9ulxcvW3OHC5A4vfz\neHNzaSm/+mrwEjtzzFpzO3MMgdfp1Ve53X33sf1tfj4b73i9DHfs3Mls8xUruNiJ282Qx86drBNf\ntYptVk+XBEJBEHo8IuIdIRwNO7Kzrc5tWtPyvOQSCvjOnVyOdNcuikqfPhSe/v3pfn/xRcaLExK4\nfXw8sH49hcm4jxsbacUCLJuqqKAV2qsXs6m//W1a/ErR1fz557QyFy8Gbr+99RaggZn54Wj3qhQn\nJ2bt7VdfZbw6I4MLi4Ry+WdnMxSxZQvPkd0Fb65TXh5L+mpqmHfg9fI9vF6ef4Dn+bbb6DofPbp5\nbb/W/P3BB5EPOQiCIDQh7vRIYCzHCRPoLt+4ka7crVut3tyFhfy9fz/FOjfXqnGuqGDtsn3VtCee\noNAY93FJCZPm+venOF16KV3w+fkUsjVrrD7fN93E90tLo0VpXNktEZiZH67V1cwEydRy5+ZSPFev\nDr7ql3Fv5+Vx3JWVfN077zTf75w5FOTqak5wioqYSDhoEKsBzjmH52PzZp6DuDirtr+yEnjvPf6W\nBDZBEKIIscQjgT3Zyoj1uHF0y2pNa3TbNrq9Y2KsmPvFF1viv3MnhcZu9Wrd3NXr9fK9tmzhilyl\npRS6uDgu7DFkCJfb3LiREwOfj3H3YNam3VUemJlvXM3havdq9j9mTPBOd3Zr3OVip7tPPuHx1Nby\ndXl5FNv0dLrYly/n+amr4/GXlfHc1tdbCWrl5UyoO+ssK3QxZAgFvqyMCWymXlwQBCEKEBHvbuzJ\nVgcPWlblgQMUlbPOoku6utqKCZtWnh991Ny1G+hatrv53W7g17+m+B44QMuzro7POZ3cX3ExBWnl\nSqtP+9GjFLxvfIPbmUVZnn6aE4SMjFMz8+fO5d92kb3pprbHxwNj6SZDfcUKeh8WL7aENXDhF6+X\n3oqpU3ns9mzxmBju75136H0w5xPgOSwqYiiisJDvN3w4J0733ksPBsCJz0svha4XFwRBiCAi4t2N\nPdlKa0vEMzIoDg4Hk7oChcLjYdy7ooLx6/HjW17C0sTcJ03ia/v25f8OB9/b5eIkYupUbt+nDxPp\n0tPpqvf5gGef5YQiK4sTiKFDgbvvpnUMUFR9PsaYp0yxRHb5coYJZs9ue2mYiaXbM9Tdborm4MFW\nohpgJZKZ5MCSEgpsbKyVLe71Ar/5DWPqH37I5juxsfytFN3oR44wD2HnTjbdOfdcusxzc63J0ccf\nnzpBkZi4IAhRgoh4dxOYFDd8eNteZ8T/rbcottOmha5NtsfcP/2UwhoTw5h3bCy3GTeOVuixY7RC\ni4u53fHjrJNetIgZ81lZ/Ftr4OWXaZEqRXHs35+PFxfzb6UonkuW0Lpvi+AtWtQ8Yc3lYt38M8+w\nzOvwYY69b18KrR0zUYmPp9BPmgTcfDNF3iTCvfUWx3fVVRT7u+7icqGffcYchKFD+buqigJut/SB\nti3/KgiCECFExHsKStES3LmTQrpzZ2jXrj1DvbiYsd7aWgpuVRVFbvt2Ni9JS6Oo7dnDmHtFBXDD\nDcDf/sZY+rFjdO07nRTBxx6jFWu3Vs1ExO3mRMPn4wQiWHzc7jrPy+NiIl/+cvNtt2yhSPbty20K\nCqw4vXm9maiMHMnnrr6a1nhcHPdtEuHmz6crvaiIQl9UxOOcN4/iX1rKBECnk+VtLlfzkjEpJxME\nIYqJmIgrpW4EMBvAOADTtdabQ2z3FQAvgpn087TWz3XbIKOFwKVGQ8XEgeYx95ISWqe1tYxR19ay\nzGzIECZqPfggk7oWLGDp2ZgxjC/PmkWr9ORJTgBSU6333L6drvPly08V6Kwsjumss2jpB8bHA13n\nc+dygnDoEGPR2dm0cs349+5lvDolhR6F6dMpvqYTndPJ1zoc/D1gAC37hAQ+V17OSUxyMkMQF13E\nfX/968HFOVgYQ9b+FgQhilHa1Mh29xsrNRaAH8CfATwSTMSVUg4AewFcDuA4gA0AbtZa7w6xTx2p\n4+kyjPDdcw8X6Cgvp5COH0+L8Pnnm7t2tab1HEyg/vpXZqMPHsxtLriAonnffcxQnzKFSXC5uXSx\nx8RwP6mpfI+6Ok4opk2jRfvd79IyN+P82tdoDcfH08qPj2f2d0oKY9eLFrGE7vrraQ1fdx3Luior\nKbozZvBYleL7LlhAq3zgQHoIGho4sbjiCmbve70ct0lYO/dchgAmTKBw79/P46ypoVciLY2tVidP\nPiOT05RS0FpH5MBPy++mIISJznw3I2aJa633AIBSLd5NZwDYp7XOb9p2AYCvAggq4qclpv561aq2\nxcRDNaIJbEFq4rtf/zp7sa9YQUu2ro7iV1vLJLD6ev4+/3xOHuLi6MpXijHyG25gp7msLI5r7Fh6\nAEaPBn7wA66ytmIF8Oc/U5SN69zjsfqPr15NkR41CnjhBVraCQmcEJi11isrKejXXcdEugcesJrd\n+P0U6g0bOMmZPh34ylc4IUhI4HEmJTF+/uGHnKwIgiCcBkR7THwwgKO2/wtAYT8zCFaPHRgT93rb\nVsoVqlVsTQ1d1fHxwL//TVd4ebmVpJaYSCH/yU+YFFdSwvatXi/j6EuW0OpdvJj7bGjgdjk5rN/e\nsYOW8d//zvfat4+x7vfe43sVFXGfVVV8rF8/TlwuvZTju/tuJs0tXEjPQFyctf/8fGuN8Mcf534q\nKmid33orvRQ//jEF3OFg7N7E1mXtb0EQTgO6VMSVUh8DGGB/CIAG8HOt9b+78r1PC1qrx87KsoSs\nNVEKZaHPnUvx69uXgltbS0GPiaG1PmwYO5udey7j1vPmcUJQUEBxXbCA7vc+fTgGU8LmdNJ1bo9N\np6QwNn3ppRzLQw9RuPfv50Rh717G6t9/H3j9dYpvbi5d/vv2cTzvv89JzeLFnDyYDnEbNzK+blYi\n++ADuuxzc3ksVVUcv+nmdv/9Yb9cgiAI3U2XirjW+spO7uIYgGG2/4c0PRaS2bNn//fvzMxMZGZm\ndnIIESLQ/V1dzZagU6da7vDFi62Et47ULpte6QCt5F69+D4XXcTY+r59FPA5c/hc4CpjiYlsDlNT\nQ7f6D35g7buykj3eGxroFu/blxOExEROQp5/nsI6fz73VV3N50tLKbzl5cAXvtB80RETShg7luMb\nPZoThbo6vo/bzZKxwkIm3lVXM/N8zx5a8ElJXBDG3s3tNCYnJwc5OTmRHoYgCF1IxBLb/jsApZaD\niW2bgjwXA2APmNhWCGA9gG9rrXeF2NfpkzwTmKAWWI9dXEwhHD2aovXMM6eWcgGhXe1VVbR+772X\nv01714YGdmd77z3Gsr/8ZeCRR/ieWtONP2cOtzMrnyUkcDyLFgFf+pI13r17KbDPPEM3944dFPGG\nBrruV63iMZSWcl/V1RRbcw1HjWL8+ktfYib8rFksb8vJoRiffTYXcdGaYzhwgK/p14/Z8UeP8r1M\nYpvTyX306hU8E/00RxLbBCE66ZGJbUqprwF4GUBfAEuUUlu11lcppQYCeE1rfa3WulEpdR+ApbBK\nzIIK+GlHMPe3vTHMxx9bC3UElpu53YwRKwX88pfBl+585hlmlj///Klx8rIyWr1XXknRLiqyOsqZ\nVcb8fuC115gNrjWF8he/sES8qIirkN1/P7d/6y2OMz+flnR2NhPUfD4KvMPBn8ZGq5ztxAla/evW\nWbXq9tXZYmJ4LGb8MTEU7v79+fvBB5lZbz+2M1C8BUE4fYlkdvpiAIuDPF4I4Frb/x8BGNuNQ4t+\nQmWam05i2dmMEQOhl+48fDj0spqPP87ENVN7bd+HmVx4POx6Vl5u1ZJv20br+uKL+Zrdu9kh7ZVX\nOBkoKaEwJyXRjT9gAP9OSKBIJyVZK6jFx/Onf3/g+99neZx9dTank8l21dWW5a51817zItiCIJzm\nRHt2uhCMUJnmpp/40qXWc0uXNm/KEpjxHtiwZc8eJp+5XBThxMTgrUZ9Pr6uuJiu+aFDWcP92mvW\nWtxOJ+Phb73F7Xv3Zo12QQHF9ehRCq9pJnPeebTKAeDCCzmRmDoVmDmT+29LcxZBEIQzCBHxnkio\nTHOAFnBhIQUU4N92Szow4z3QUl+1yqrftq8IFliP/sEHFNLSUv4uKGAzlXXrgDfeYCz82DEK9/z5\ntKr79GGCW00NH9+5kzHsvXsZFigtpZibJUITE5lcV1EhndMEQRCCICJ+OuHxMBnNrIxmeqWvWNG2\nBT2Mmz4+ntnlZkWwlJTmFq99u4su4v6cTibJxcTQ8jYZ7LGxtNbT0ijse/fydWvWMEktM5Pd3Px+\n6z2Uar6qm/QqFwRBCErEs9PDyRmfAas1xfn4ccv17HBQLI0lG6olq8k+37uXFnCw5+3vE2o/QPMM\n9kOHmIiWnMze7DNnMvmtpcx6oUuQ7HRBiE46890UERcsAhco6ShG5E+e5P7q62mpx8fTbT5xImvB\n7T3cZY3uLkdEXBCiExHxJuRG0UnmzWNHtOuvD4+oBrPY7U1gTFc40/zlNG++EmlExAUhOhERb0Ju\nFJ3A7baaqRw/3nUu7pZc8ZJp3qWIiAtCdNIjm70IUUZrWevhoqXMekEQBKFdOCI9ACEKCGwe09DA\n/z2eSI9MEARBaAFxpwvi4j5DEHe6IEQnEhNvQm4UghAaEXFBiE46890Ud7ogCIIg9FBExAVBEASh\nhyIiLgiCIAg9FBFxQRAEQeihiIgLgiAIQg9FRFwQBEEQeigi4oIgCILQQ4mYiCulblRKbVdKNSql\nprSw3WGlVK5SaotSan13jlEQBEEQoplIWuLbANwA4LNWtvMDyNRaT9Zaz+j6YXWOnJycSA8hKsYA\nRMc4omEMQPSM40wmWq5BNIwjGsYARMc4omEMnSFiIq613qO13gegtS41Cj3I7R8NH4hoGAMQHeOI\nhjEA0TOOM5louQbRMI5oGAMQHeOIhjF0hp4gjhrAx0qpDUqpH0Z6MIIgCIIQLXTpUqRKqY8BDLA/\nBIryz7XW/27jbi7SWhcqpfqBYr5La70q3GMVBEEQhJ5GxBdAUUotB/Cw1npzG7Z9EkCl1npuiOdl\nhQVBaIFILoASifcVhJ5CR7+bXWqJt4Ogg1dKJQFwaK2rlFLJAL4M4KlQO4nUDUoQhJaR76YgdA2R\nLDH7mlLqKIALACxRSn3Y9PhApdSSps0GAFillNoCYC2Af2utl0ZmxIIgCIIQXUTcnS4IgiAIQsfo\nCdnpQYmWZjHtGMdXlFK7lVJ7lVI/DfMYeimlliql9iil/qOUcoXYLuznoi3HpZR6SSm1Tym1VSk1\nKRzv295xKKUuVUp5lFKbm34e74IxzFNKFSml8lrYpkvPRWtj6I7z0PQ+Ef9+RsN3s2n/Z/T3U76b\nbR9Hh86F1rpH/gAYC+BsAMsATGlhu4MAekVyHOBkaT+A4QBiAWwFcE4Yx/AcgEeb/v4pgGe741y0\n5bgAXAUgu+nvmQDWdsE1aMs4LgXwfhd/Ji8GMAlAXojnu+NctDaGLj8PTe8T8e9nNHw3m97jjP1+\nynez3eNo97nosZa4jpJmMW0cxwwA+7TW+VrregALAHw1jMP4KoA3mv5+A8DXQmwX7nPRluP6KoA3\nAUBrvQ6ASyk1AOGlree3S5OrNEsfT7awSZefizaMAeji89A0joh/P6Pkuwmc2d9P+W62bxxAO89F\njxXxdhANzWIGAzhq+7+g6bFw0V9rXQQAWms3gP4htgv3uWjLcQVucyzINt0xDgC4sMlVlq2UOjfM\nY2gL3XEu2kKkz4OdSH8/u/q7CZzZ30/5brafdp2LaCkxC4qKkmYxYRpHp2hhDMFiJqGyFc/kxjmb\nAAzTWlcrpa4CsBjAmAiPKRKE7TxEw/czGr6brYxDvp+tI99Ni3afi6gWca31lWHYx/9v7/5d5KjD\nOI6/PyBBwULSRMEfCLEzTcAfYKUQ0FKwsBB/gKjgP6D/gIW12Iitkip4BA5EElC0MJAgp4VoIZEY\nf4BaREUtHouZM8sle3s3mZ3duXm/4LjZ2bmZZx/u2Yed+973e7n9/kuSUzS3d/ZVGD3EcQm4e+bx\nne2+XmJoB0ocqaqfktwO/DznHDecix328rouAXctOOZGLYyjqq7MbG8meTvJ4ar6tedYdjNELnbV\nZx7WoT7XoTYXxTHx+rQ296FLLg7K7fS5k8UkubXd3p4s5suh4wDOAUeT3JPkEPA0sNHjdTeA59vt\n54APrglsObnYy+vaAJ5tr/sw8Pv2rcUeLYxj9u9bSR6k+ffKZbxJhPm/B0PkYtcYBszDzniuF8uQ\n9bmq2oRp16e1uY84OuViGSPwhviiGRzyPfAXcBnYbPffAZxut++lGQ15gWbp09dWEUf7+HHga+Cb\nvuMADgMftef/ELhtqFxc73UBLwMvzRzzFs0I1S/YZaTyMuMAXqV5U7wAfAY8tIQY3gN+AP4GLgIv\nDJ2LRTEMkYf2Oiuvz3Wozfb8k65Pa3PvcXTJhZO9SJI0UgfldrokSZNjE5ckaaRs4pIkjZRNXJKk\nkbKJS5I0UjZxSZJGyiauTtIs73g+yVaSk0lubvcfSfJ+u6TfuSSnkxxtn9tM8luSvifTkDTD+pwO\nm7i6+qOqjlfVMeBf4JV2/yngTFXdV1UPAK9zdU7pN4Fnhg9VmhzrcyJs4urDJzRTKz4K/FNV72w/\nUVVbVfVpu30WuDLnHJKWw/o8wGzi6ioASW4CnqCZKvJ+mlV4JK2W9TkRNnF1dUuS88DnwHfAu6sN\nR9IM63Mi1nopUq21P6vq+OyOJF8BT60oHklXWZ8T4SdxdXXNUnpVdQY4lOTF/w9KjiV5ZMfPzVsO\nUFI/rM+JsImrq3nL3z0JnEjybZIt4A3gR4AkHwMngceSXExyYphQpcmxPifCpUglSRopP4lLkjRS\nNnFJkkbKJi5J0kjZxCVJGimbuCRJI2UTlyRppGzikiSNlE1ckqSR+g+BaZi3HdOajQAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129f64e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scikit_pca = PCA(n_components=2)\n",
    "X_spca = scikit_pca.fit_transform(X)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))\n",
    "\n",
    "ax[0].scatter(X_spca[y == 0, 0], X_spca[y == 0, 1],\n",
    "              color='red', marker='^', alpha=0.5)\n",
    "ax[0].scatter(X_spca[y == 1, 0], X_spca[y == 1, 1],\n",
    "              color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[1].scatter(X_spca[y == 0, 0], np.zeros((500, 1)) + 0.02,\n",
    "              color='red', marker='^', alpha=0.5)\n",
    "ax[1].scatter(X_spca[y == 1, 0], np.zeros((500, 1)) - 0.02,\n",
    "              color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[0].set_xlabel('PC1')\n",
    "ax[0].set_ylabel('PC2')\n",
    "ax[1].set_ylim([-1, 1])\n",
    "ax[1].set_yticks([])\n",
    "ax[1].set_xlabel('PC1')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/circles_2.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ON4rIdgClYdcqMcJaok1N0a1QoH0++urVzEefObN90ZQ1a9ju0x3MZkubugvH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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e27470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_kpca = rbf_kernel_pca(X, gamma=15, n_components=2)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))\n",
    "ax[0].scatter(X_kpca[y == 0, 0], X_kpca[y == 0, 1],\n",
    "              color='red', marker='^', alpha=0.5)\n",
    "ax[0].scatter(X_kpca[y == 1, 0], X_kpca[y == 1, 1],\n",
    "              color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[1].scatter(X_kpca[y == 0, 0], np.zeros((500, 1)) + 0.02,\n",
    "              color='red', marker='^', alpha=0.5)\n",
    "ax[1].scatter(X_kpca[y == 1, 0], np.zeros((500, 1)) - 0.02,\n",
    "              color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "ax[0].set_xlabel('PC1')\n",
    "ax[0].set_ylabel('PC2')\n",
    "ax[1].set_ylim([-1, 1])\n",
    "ax[1].set_yticks([])\n",
    "ax[1].set_xlabel('PC1')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/circles_3.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Projecting new data points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import pdist, squareform\n",
    "from scipy import exp\n",
    "from scipy.linalg import eigh\n",
    "import numpy as np\n",
    "\n",
    "def rbf_kernel_pca(X, gamma, n_components):\n",
    "    \"\"\"\n",
    "    RBF kernel PCA implementation.\n",
    "\n",
    "    Parameters\n",
    "    ------------\n",
    "    X: {NumPy ndarray}, shape = [n_samples, n_features]\n",
    "        \n",
    "    gamma: float\n",
    "      Tuning parameter of the RBF kernel\n",
    "        \n",
    "    n_components: int\n",
    "      Number of principal components to return\n",
    "\n",
    "    Returns\n",
    "    ------------\n",
    "     X_pc: {NumPy ndarray}, shape = [n_samples, k_features]\n",
    "       Projected dataset   \n",
    "     \n",
    "     lambdas: list\n",
    "       Eigenvalues\n",
    "\n",
    "    \"\"\"\n",
    "    # Calculate pairwise squared Euclidean distances\n",
    "    # in the MxN dimensional dataset.\n",
    "    sq_dists = pdist(X, 'sqeuclidean')\n",
    "\n",
    "    # Convert pairwise distances into a square matrix.\n",
    "    mat_sq_dists = squareform(sq_dists)\n",
    "\n",
    "    # Compute the symmetric kernel matrix.\n",
    "    K = exp(-gamma * mat_sq_dists)\n",
    "\n",
    "    # Center the kernel matrix.\n",
    "    N = K.shape[0]\n",
    "    one_n = np.ones((N, N)) / N\n",
    "    K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)\n",
    "\n",
    "    # Obtaining eigenpairs from the centered kernel matrix\n",
    "    # numpy.eigh returns them in sorted order\n",
    "    eigvals, eigvecs = eigh(K)\n",
    "\n",
    "    # Collect the top k eigenvectors (projected samples)\n",
    "    alphas = np.column_stack((eigvecs[:, -i]\n",
    "                              for i in range(1, n_components + 1)))\n",
    "\n",
    "    # Collect the corresponding eigenvalues\n",
    "    lambdas = [eigvals[-i] for i in range(1, n_components + 1)]\n",
    "\n",
    "    return alphas, lambdas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = make_moons(n_samples=100, random_state=123)\n",
    "alphas, lambdas = rbf_kernel_pca(X, gamma=15, n_components=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.4816, -0.3551])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_new = X[-1]\n",
    "x_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.1192])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_proj = alphas[-1] # original projection\n",
    "x_proj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.1192])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def project_x(x_new, X, gamma, alphas, lambdas):\n",
    "    pair_dist = np.array([np.sum((x_new - row)**2) for row in X])\n",
    "    k = np.exp(-gamma * pair_dist)\n",
    "    return k.dot(alphas / lambdas)\n",
    "\n",
    "# projection of the \"new\" datapoint\n",
    "x_reproj = project_x(x_new, X, gamma=15, alphas=alphas, lambdas=lambdas)\n",
    "x_reproj "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7RKRXbX1FJFZE1ovIXhH5RESizaj1QuYtpGbOnImsrCzMnDkTAMOJiIKHBPqd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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129d95828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(alphas[y == 0, 0], np.zeros((50)),\n",
    "            color='red', marker='^', alpha=0.5)\n",
    "plt.scatter(alphas[y == 1, 0], np.zeros((50)),\n",
    "            color='blue', marker='o', alpha=0.5)\n",
    "plt.scatter(x_proj, 0, color='black',\n",
    "            label='original projection of point X[25]', marker='^', s=100)\n",
    "plt.scatter(x_reproj, 0, color='green',\n",
    "            label='remapped point X[25]', marker='x', s=500)\n",
    "plt.legend(scatterpoints=1)\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/reproject.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Sebastian/miniconda3/lib/python3.5/site-packages/ipykernel/__main__.py:15: VisibleDeprecationWarning: boolean index did not match indexed array along dimension 0; dimension is 99 but corresponding boolean dimension is 100\n",
      "/Users/Sebastian/miniconda3/lib/python3.5/site-packages/ipykernel/__main__.py:17: VisibleDeprecationWarning: boolean index did not match indexed array along dimension 0; dimension is 99 but corresponding boolean dimension is 100\n"
     ]
    },
    {
     "ename": "IndexError",
     "evalue": "index 99 is out of bounds for axis 0 with size 99",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-69-58b4f4f12849>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     15\u001b[0m plt.scatter(alphas[y == 0, 0], np.zeros((50)),\n\u001b[1;32m     16\u001b[0m             color='red', marker='^', alpha=0.5)\n\u001b[0;32m---> 17\u001b[0;31m plt.scatter(alphas[y == 1, 0], np.zeros((50)),\n\u001b[0m\u001b[1;32m     18\u001b[0m             color='blue', marker='o', alpha=0.5)\n\u001b[1;32m     19\u001b[0m plt.scatter(x_reproj, 0, color='green',\n",
      "\u001b[0;31mIndexError\u001b[0m: index 99 is out of bounds for axis 0 with size 99"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x129e1e320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = make_moons(n_samples=100, random_state=123)\n",
    "alphas, lambdas = rbf_kernel_pca(X[:-1, :], gamma=15, n_components=1)\n",
    "\n",
    "def project_x(x_new, X, gamma, alphas, lambdas):\n",
    "    pair_dist = np.array([np.sum((x_new - row)**2) for row in X])\n",
    "    k = np.exp(-gamma * pair_dist)\n",
    "    return k.dot(alphas / lambdas)\n",
    "\n",
    "# projection of the \"new\" datapoint\n",
    "x_new = X[-1]\n",
    "\n",
    "x_reproj = project_x(x_new, X[:-1], gamma=15, alphas=alphas, lambdas=lambdas)\n",
    "\n",
    "\n",
    "plt.scatter(alphas[y == 0, 0], np.zeros((50)),\n",
    "            color='red', marker='^', alpha=0.5)\n",
    "plt.scatter(alphas[y == 1, 0], np.zeros((50)),\n",
    "            color='blue', marker='o', alpha=0.5)\n",
    "plt.scatter(x_reproj, 0, color='green',\n",
    "            label='new point [ 100.0,  100.0]', marker='x', s=500)\n",
    "plt.legend(scatterpoints=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Sebastian/miniconda3/lib/python3.5/site-packages/ipykernel/__main__.py:1: VisibleDeprecationWarning: boolean index did not match indexed array along dimension 0; dimension is 99 but corresponding boolean dimension is 100\n",
      "  if __name__ == '__main__':\n",
      "/Users/Sebastian/miniconda3/lib/python3.5/site-packages/ipykernel/__main__.py:3: VisibleDeprecationWarning: boolean index did not match indexed array along dimension 0; dimension is 99 but corresponding boolean dimension is 100\n",
      "  app.launch_new_instance()\n"
     ]
    },
    {
     "ename": "IndexError",
     "evalue": "index 99 is out of bounds for axis 0 with size 99",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-66-2d1e9e70058f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m plt.scatter(alphas[y == 0, 0], np.zeros((50)),\n\u001b[1;32m      2\u001b[0m             color='red', marker='^', alpha=0.5)\n\u001b[0;32m----> 3\u001b[0;31m plt.scatter(alphas[y == 1, 0], np.zeros((50)),\n\u001b[0m\u001b[1;32m      4\u001b[0m             color='blue', marker='o', alpha=0.5)\n\u001b[1;32m      5\u001b[0m plt.scatter(x_proj, 0, color='black',\n",
      "\u001b[0;31mIndexError\u001b[0m: index 99 is out of bounds for axis 0 with size 99"
     ]
    },
    {
     "data": {
      "image/png": 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vto15K/Bh4K3AecCNERED9jqjxsfHR93CYeypP/bUv9nYlz3NrEFDZDlwSz1/C3B+h5qz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\nxKsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129f0a208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(alphas[y == 0, 0], np.zeros((50)),\n",
    "            color='red', marker='^', alpha=0.5)\n",
    "plt.scatter(alphas[y == 1, 0], np.zeros((50)),\n",
    "            color='blue', marker='o', alpha=0.5)\n",
    "plt.scatter(x_proj, 0, color='black',\n",
    "            label='some point [1.8713,  0.0093]', marker='^', s=100)\n",
    "plt.scatter(x_reproj, 0, color='green',\n",
    "            label='new point [ 100.0,  100.0]', marker='x', s=500)\n",
    "plt.legend(scatterpoints=1)\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/reproject.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kernel principal component analysis in scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dA6w3s/cDxwLHm9k97v6hrMcdGho6crtSqVCpVObafRER6YFqtUq1Wm2rbW77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\nhDe6VoBeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1147b2978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import KernelPCA\n",
    "\n",
    "X, y = make_moons(n_samples=100, random_state=123)\n",
    "scikit_kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)\n",
    "X_skernpca = scikit_kpca.fit_transform(X)\n",
    "\n",
    "plt.scatter(X_skernpca[y == 0, 0], X_skernpca[y == 0, 1],\n",
    "            color='red', marker='^', alpha=0.5)\n",
    "plt.scatter(X_skernpca[y == 1, 0], X_skernpca[y == 1, 1],\n",
    "            color='blue', marker='o', alpha=0.5)\n",
    "\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/scikit_kpca.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "..."
   ]
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}