week 7.ipynb

{
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   "source": [
    "**<h1> Week 7**\n",
    "   \n",
    "We'll be covering the following topics in this week:\n",
    "\n",
    "1) Dimensionality Reduction:\n",
    "* PCA\n",
    "* LDA\n",
    "* Kernel PCA\n",
    "\n",
    "2) Model Selection\n",
    "* K fold cross validation\n",
    "* Grid Search CV\n",
    "* Stacking"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "**<h2> Introduction to Dimensionality Reduction**\n",
    "    \n",
    "Dimensionality Reduction means reducing the number of features(columns) in a given dataset.\n",
    "Imagine working with a dataset with nearly 20000 features. Having so many features makes it problematic to\n",
    "draw insights from the data. It’s not feasible to analyze each and every variable at a microscopic level. \n",
    "\n",
    "**<h2> Why is Dimensionality Reduction important?**\n",
    "    \n",
    "* It helps reduce the amount of space required to store the data.\n",
    "* Less dimensions result into less computation time.\n",
    "* It helps improve the performance of the ML models by removing redundant features/columns.\n",
    "\n",
    "**<h2> How is Dimensionality Reduction implemented?**\n",
    "    \n",
    "It can be done in two different ways:\n",
    "\n",
    "* By removing the irrelevant features from the dataset. This is also known as feature selection.\n",
    "* By finding new input variables which are derived by combining the earlier inputted variables.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xe3jK0fmI8rz"
   },
   "source": [
    "In this week, we'll be covering the following Dimensionality Reduction techniques:\n",
    "* PCA\n",
    "* Kernel PCA \n",
    "* LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FliLt2mycxU0"
   },
   "source": [
    "**<h2>Principal Component Analysis**\n",
    "    \n",
    "Principal Analysis combines existing variables to form new variables. These newly extracted variables are addressed as Principal Components.A principal component is a linear combination of the original variables.Principal components are extracted in such a way that the first principal component explains maximum variance in the dataset.Second principal component tries to explain the remaining variance in the dataset and is uncorrelated to the first principal component.Third principal component tries to explain the variance which is not explained by the first two principal components and so on.\n",
    "\n",
    "Check out this link [article](https://www.analyticsvidhya.com/blog/2016/03/pca-practical-guide-principal-component-analysis-python/) to know more about **PCA** ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Nz_Q7PKmcxU2"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "IdP5-zRXI8sD"
   },
   "outputs": [],
   "source": [
    "def report_classification(test,pred):\n",
    "    from sklearn.metrics import classification_report\n",
    "    return (classification_report(test,pred))    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 226
    },
    "colab_type": "code",
    "id": "poa8KkyPcxVD",
    "outputId": "ed704d4b-91f1-403c-e5f6-3b29823d2290"
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    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic_Acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Ash_Alcanity</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</th>\n",
       "      <th>Proline</th>\n",
       "      <th>Customer_Segment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\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",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\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",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\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",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\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",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\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",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Alcohol  Malic_Acid   Ash  Ash_Alcanity  Magnesium  Total_Phenols  \\\n",
       "0    14.23        1.71  2.43          15.6        127           2.80   \n",
       "1    13.20        1.78  2.14          11.2        100           2.65   \n",
       "2    13.16        2.36  2.67          18.6        101           2.80   \n",
       "3    14.37        1.95  2.50          16.8        113           3.85   \n",
       "4    13.24        2.59  2.87          21.0        118           2.80   \n",
       "\n",
       "   Flavanoids  Nonflavanoid_Phenols  Proanthocyanins  Color_Intensity   Hue  \\\n",
       "0        3.06                  0.28             2.29             5.64  1.04   \n",
       "1        2.76                  0.26             1.28             4.38  1.05   \n",
       "2        3.24                  0.30             2.81             5.68  1.03   \n",
       "3        3.49                  0.24             2.18             7.80  0.86   \n",
       "4        2.69                  0.39             1.82             4.32  1.04   \n",
       "\n",
       "   OD280  Proline  Customer_Segment  \n",
       "0   3.92     1065                 1  \n",
       "1   3.40     1050                 1  \n",
       "2   3.17     1185                 1  \n",
       "3   3.45     1480                 1  \n",
       "4   2.93      735                 1  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url=('data/wine-clustering.csv')\n",
    "dataset = pd.read_csv(url)\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Dqdxh6xmcxVJ"
   },
   "outputs": [],
   "source": [
    "X = dataset.iloc[:, 0:-1].values\n",
    "y = dataset.iloc[:, -1].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "B7wYzNOpcxVT"
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aCwtaEGCcxVY"
   },
   "outputs": [],
   "source": [
    "sc = StandardScaler()\n",
    "X_train = sc.fit_transform(X_train)\n",
    "X_test = sc.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KNHsoW11cxVh"
   },
   "source": [
    "The maximum number of columns we can use is equal to total number of columns.  \n",
    "Let's observe variance along all the columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "colab_type": "code",
    "id": "oorEFOnqcxVi",
    "outputId": "8fe45670-6979-49b2-a840-19fdfef0e2d9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[14,  0,  0],\n",
       "       [ 0, 16,  0],\n",
       "       [ 0,  0,  6]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = LogisticRegression()\n",
    "classifier.fit(X_train, y_train)\n",
    "\n",
    "\n",
    "y_pred = classifier.predict(X_test)\n",
    "\n",
    "\n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "colab_type": "code",
    "id": "gKqOLRuFcxVn",
    "outputId": "a1169569-df2b-4490-bdbd-608fa75cd3cd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.36884109, 0.19318394, 0.10752862, 0.07421996, 0.06245904,\n",
       "       0.04909   , 0.04117287, 0.02495984, 0.02308855, 0.01864124,\n",
       "       0.01731766, 0.01252785, 0.00696933])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components = None)\n",
    "X_train = pca.fit_transform(X_train)\n",
    "X_test = pca.transform(X_test)\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JgnbL80_cxVs"
   },
   "source": [
    "Let's try using only two of these columns.  \n",
    "Hence, we reduced the number of columns to 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3CROYjq-cxVt"
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components = 2)\n",
    "X_train = pca.fit_transform(X_train)\n",
    "X_test = pca.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 199
    },
    "colab_type": "code",
    "id": "hYxZG62XcxVy",
    "outputId": "00a249ea-8e97-4e60-9e6d-817ea53b4952",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.17884511, -1.07218467],\n",
       "       [-1.80819239,  1.57822344],\n",
       "       [ 1.09829474,  2.22124345],\n",
       "       [-2.55584748, -1.66210369],\n",
       "       [ 1.85698063,  0.24157317],\n",
       "       [ 2.58288576, -1.3766817 ],\n",
       "       [ 0.87287612,  2.25618512],\n",
       "       [-0.41838403,  2.35415681],\n",
       "       [-0.30497725,  2.27659433],\n",
       "       [ 2.14082532, -1.10052871]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "O2tRMPBscxV3"
   },
   "source": [
    "From the above data, you can clearly make out the difference between this data and the one we were using before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "colab_type": "code",
    "id": "KbjRRaOXcxV4",
    "outputId": "1d6f7846-57d0-475d-b54a-1ce6ba8ad286"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[14,  0,  0],\n",
       "       [ 1, 15,  0],\n",
       "       [ 0,  0,  6]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = LogisticRegression()\n",
    "classifier.fit(X_train, y_train)\n",
    "\n",
    "\n",
    "y_pred = classifier.predict(X_test)\n",
    "\n",
    "\n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 199
    },
    "colab_type": "code",
    "id": "2A34AV9mJcIU",
    "outputId": "e61eb057-3f19-4c84-c249-83daf68016f9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           1       0.93      1.00      0.97        14\n",
      "           2       1.00      0.94      0.97        16\n",
      "           3       1.00      1.00      1.00         6\n",
      "\n",
      "    accuracy                           0.97        36\n",
      "   macro avg       0.98      0.98      0.98        36\n",
      "weighted avg       0.97      0.97      0.97        36\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(report_classification(y_test,y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "o7QvnANPcxV-"
   },
   "source": [
    "**<h2> Linear Discriminant Analysis**\n",
    "\n",
    "Linear Discriminant Analysis, like PCA , is a Dimensionality Reduction Technique.It focuses upon maximizing seperatibility among known categories.More formally, given a number of independent features relative to which the data is described,LDA creates a linear combination of those which yield the largest mean difference between the desired classes.\n",
    "\n",
    "\n",
    "Consider a 2D graph with variables X and Y. Using LDA one can transform this graph into a 1D graph. This is done by creating an axis with an intend to increase separatibility between the variables and plotting it on the 2D graph. Then, the given distribution is projected on this axis, thereby converting it into a 1D graph.\n",
    "\n",
    "Check out this [tutorial](https://www.youtube.com/watch?v=azXCzI57Yfc) or [article](https://www.geeksforgeeks.org/ml-principal-component-analysispca/) to know more about **LDA** .\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "R_q9w99-cxWC"
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0iT9HVDCcxWG"
   },
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "lda = LDA(n_components = 2)\n",
    "X_train = lda.fit_transform(X_train, y_train)\n",
    "X_test = lda.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 199
    },
    "colab_type": "code",
    "id": "-tiy2bsQcxWL",
    "outputId": "15237050-e2b3-43b9-c12c-369a9b006dcc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.57315552,  1.94018924],\n",
       "       [ 0.85475898, -2.08182977],\n",
       "       [ 0.62173655, -3.06234453],\n",
       "       [ 4.80786412,  2.00638739],\n",
       "       [-3.8579759 ,  0.14987256],\n",
       "       [-3.59455458,  1.24961706],\n",
       "       [-0.53772906, -3.0852704 ],\n",
       "       [ 0.04058577, -2.47312446],\n",
       "       [ 0.99835348, -3.36989668],\n",
       "       [-3.74095658,  1.94844242]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train[:10,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "colab_type": "code",
    "id": "g6npX0rpcxWT",
    "outputId": "a322fa6b-0f44-42fd-fe1d-a76d79c50aef"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[14,  0,  0],\n",
       "       [ 0, 16,  0],\n",
       "       [ 0,  0,  6]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = LogisticRegression()\n",
    "classifier.fit(X_train, y_train)\n",
    "\n",
    "\n",
    "y_pred = classifier.predict(X_test)\n",
    "\n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RndFeu4ZcxWY"
   },
   "source": [
    "**<h2> Kernel PCA**\n",
    "\n",
    "PCA is can only applied on data which is linearly separable.It cannot be used on non linear data.Here, Kernel PCA steps in. For a non linear dataset , the Kernel PCA uses a kernel function to project dataset into higher dimension feature space, from where it becomes linearly separable.\n",
    "\n",
    "Check out this [article](https://www.geeksforgeeks.org/ml-introduction-to-kernel-pca/) to know more."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "isK_6uejNR1Q"
   },
   "source": [
    "**<h3> KernelPCA with a linear PCA**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "colab_type": "code",
    "id": "6nZ-NBL_cxWZ",
    "outputId": "2d7b10fb-7525-4d67-e189-fff643b0de97"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>User ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age</th>\n",
       "      <th>EstimatedSalary</th>\n",
       "      <th>Purchased</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15624510</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>19000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15810944</td>\n",
       "      <td>Male</td>\n",
       "      <td>35</td>\n",
       "      <td>20000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15668575</td>\n",
       "      <td>Female</td>\n",
       "      <td>26</td>\n",
       "      <td>43000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15603246</td>\n",
       "      <td>Female</td>\n",
       "      <td>27</td>\n",
       "      <td>57000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>15804002</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>76000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    User ID  Gender  Age  EstimatedSalary  Purchased\n",
       "0  15624510    Male   19            19000          0\n",
       "1  15810944    Male   35            20000          0\n",
       "2  15668575  Female   26            43000          0\n",
       "3  15603246  Female   27            57000          0\n",
       "4  15804002    Male   19            76000          0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url=('data/Social_Network_Ads.csv')\n",
    "dataset = pd.read_csv(url)\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "DzEf0bqwcxWc"
   },
   "outputs": [],
   "source": [
    "X = dataset.iloc[:, [2, 3]].values\n",
    "y = dataset.iloc[:, 4].values\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, random_state = 0)\n",
    "\n",
    "\n",
    "sc = StandardScaler()\n",
    "X_train = sc.fit_transform(X_train)\n",
    "X_test = sc.transform(X_test)\n",
    "\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "efnrpXQZcxWi"
   },
   "source": [
    "Let's observe what will we get if we apply Logistic regression directly?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 53
    },
    "colab_type": "code",
    "id": "DI6MZuXwcxWl",
    "outputId": "d68f7ae3-ee76-4e09-c0fb-aad871acc8bf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[58,  0],\n",
       "       [22,  0]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = LogisticRegression()\n",
    "classifier.fit(X_train, y_train)\n",
    "\n",
    "\n",
    "y_pred = classifier.predict(X_test)\n",
    "\n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "itBgUMcXcxWq"
   },
   "source": [
    "That is a pretty bad performance.Let's try kernel PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Ozi3sJLocxWq"
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import KernelPCA\n",
    "\n",
    "kpca = KernelPCA(n_components = 2, kernel = 'linear')\n",
    "X_train = kpca.fit_transform(X_train)\n",
    "X_test = kpca.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 53
    },
    "colab_type": "code",
    "id": "ZdfvwkiKcxWt",
    "outputId": "77f8e1e8-9103-43f3-f728-7ff17fdcec88"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[50,  8],\n",
       "       [ 1, 21]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = LogisticRegression()\n",
    "classifier.fit(X_train, y_train)\n",
    "\n",
    "\n",
    "y_pred = classifier.predict(X_test)\n",
    "\n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xQ2zd2UuI8uA"
   },
   "source": [
    "This was a big improvement. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DxOFPFaGNdGX"
   },
   "source": [
    "**<h3> Non-linear PCA**\n",
    "\n",
    "The above was an example of a linear kernel PCA. Let's try another example without using the linear kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "colab_type": "code",
    "id": "HtDm03EzI8uB",
    "outputId": "cf1ef011-3eea-4679-ca15-e6f9ab171554"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons \n",
    "\n",
    "X, y = make_moons(n_samples = 500, noise = 0.02, random_state = 417) \n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c = y) \n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "id": "LHODUNyeI8uF",
    "outputId": "146dc549-031c-4ff2-c8e5-a32debdd31e9"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_pca = kpca.fit_transform(X) \n",
    "\n",
    "plt.title(\"PCA\") \n",
    "plt.scatter(X_pca[:, 0], X_pca[:, 1], c = y) \n",
    "plt.xlabel(\"Component 1\") \n",
    "plt.ylabel(\"Component 2\") \n",
    "\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ANho17C4I8uH"
   },
   "source": [
    "From the above graph we can see that PCA fails to distinguish between the two classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 281
    },
    "colab_type": "code",
    "id": "UFr_3QK-I8uJ",
    "outputId": "bad65af9-20c3-49e6-9dc2-cbcca70cb62f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IX1vA+Ad3nk7hdDuZ8eVMzm5/Gd2P2pcht5xM41a1f8KZUulKW/jA5g0FXLT3NRSsL4w7/t7pcpBZL4OMbC+NWzVi9KTbcHtcSYy0ZgwbfTZD7zgNscJDTsUSHE4HxrZZ/OdSVi1aw+djv+KSbv/H+pUbazhapVQs2sIHnv7vyxSUs+69WMLgESfQ45huuDxOOuxfdydY7Yqzbj2Vo845jG/HT6W4sIS3R31AwLftzTEUDFFcUMz4BydwyUNDazBSpVQs2sIHvn33p3LrGNsw+8d57HVQJzp2r9sTrHZV0zaNOfW6gfQ6bn9cUT7ZBP0h/vfIJzw87Jmoq4gqpWqWJnyoUHKyHFa5+8Kmi0bNGxD0R5+rYIzh0xcmc36Xq3VillK1TNon/F8+/61CrXWXx8WJV/ZPQkS1X5PWjdnr4E5xl6BYsWAVT17xYhKjUkqVJ60T/pyf5nHLf+6L2lq1HLJ1V6tGLXK57d1radNltyhnSU8jx19Ht377xK3z4VNfcPvJDyQpIqVUedI64d89eEzMceQujwuX28kNr13JG0ueoeex3ZIcXe2W3SCLez6+iX0O2TNuvR/e/4U5P89LUlRKqXjSNuGvX7mBtUtib9/nK/ZTUljKoxc/q33RcQx/+Nxy64y98Y3qD0QpVa60TfifPD+5QvUC/iB/TdUWaix7dGvHxQ+eE7dO/vqCJEWjlIonbRP+wt8XV7huIMaIFBV2yjUD6D/syJjl3Y7Ym79+nk9JUWkSo1JK7ShtEz4VHUdvYK+DO1dvLCng6qcvJrdp/Z2OW06Lj5/9khHH3MWpTS/kf49+XAPRKaUgTRP+B49/xg/v/xy1bMv7gMvjxJPpZsRrV6bF8glVJSK8tfw5zrjxROo1yiGrQSa5TesjQKA0QPHmEnzFPsbe/BbTPv+tpsNVKi2l5Z62/TPPJFAa2Om4WMLt7/0fs76dTb28evQ76xCa7JZXLTGkujVL1nJe56vwR/k5dztyH0Z/ObIGolIq9cXb0zbt1tIpyi+KmuwhvHyCO9PFJQ+dm9ygUlD+ugKcbmfUhP/Hd3/x0i1vcsq1A8jJza6B6JRKT2nXpfNPOTdrbzvhAT565ovkBJPC2nRphR1jjkPQH+SdBycwvMcNFBdUfDlqpVTVpF3Cf/uBndd1L8tf4ueJK8byxctfEwzo6Jxd5fa6ueShc/BkeqKWB/1BVi1aw92nj9F5DkolSdol/MV/Lim3jh2yeWz481x3xB0E/NG7f1T5jr/oKO75+EY6dG+3dS39Hc2YOJN3HvgwyZEplZ7SLuE3aFyvQvX8pX7++X0RU978oZojSm37HrYXVzxxId4YLX3bNrx+z3uEQrqcslLVLe0SfmXG1JcW+fj6bU34VdW51x7ktWoYs7ykoJQTc89l5jdzkhiVUukn7RJ+z+O64fJWfFx9Zv3MaowmPYgIoyaOxJPhjlmnpLCU/zvydtat2JDEyJRKL2mV8OfN+IcxFz1N0Lf9zVinyxG1j9mT6WHAxUcnK7yU1rhVI+76aETcSWzGNoy56JkkRqVUekmbhF9SWML1/e5k3bINO40K6XPSgdz54Q14Mt2IJViWhcPl4PTrB7LvYXvVUMSpp9sR+3DfF7eQFedT07TPfuP+sx9LYlRKpY+0Sfjfv/8LdsiOWvbDBz/z0IVPY4dsjG2wbRuny0HAp8MyE63rIV045/bT4taZ/Pp3PHf9q0mKSKn0kZCELyLHishcEVkgIiOilF8jInNEZJaITBaRNom4bmVsWp1PwBd9iGXAF4yUb0vwvmI/7z38MRvX5CcrxLQx4NKjycjJiFvnfw9/jL/Un6SIlEoPVU74IuIAngSOA7oAZ4hIlx2q/Qb0MMZ0Bd4FRlf1upXV9dAuOFyVW0nC5XYyb9qCaooofbncLl766xEaNs+NWccILJz1bxKjUir1JaKF3wtYYIxZaIzxA28Bg8pWMMZMMcYUR57+BLRKwHUrpVPPPehxzL5QwVWRAUIhm9xmDaovqDTWqEVDXvr70Zi/DxFh/cqNlBb7khuYUiksEQm/JbC0zPNlkWOxXAB8loDrVtqt71zDwYN6xZz1WZblsGjSujEd9m+XhMjSU2ZOBqdeNyhqmR20GT30CU5tegHvPaJr6CuVCEm9aSsiZwE9gAdilA8TkekiMn3t2rUJv77D4eCmN69mn7574s2KPvMTwssk79Ftd0ZNvAWp6EYpapcMG3UWp143AMth4XQ7wz9vAWMMxZtLKC3y8eKNr/PDh7/UdKhK1XlVXg9fRHoDtxtjjok8vxHAGHPfDvX6AY8Dhxpj1pR33upcD98Yw+wf/ubTFyYz5a0fCJbZwtDldXHzm1dz8KBe1XJtFV3hpiJmfDmL+89+bLvfxxYOl4OnZ4xm971b10B0StUd8dbDT0QLfxrQQUR2FxE3MBjYbklKEekGPAsMrEiyry62bW/tE967z55c//Ll3PvpTexzSBfyWjbkwAE9eOzHezTZ14DsBlm03rMlLk/0G+uhQIib/3OfrqypVBVUeQMUY0xQRC4HvgAcwFhjzGwRuROYboyZQLgLJxsYH+kiWWKMGVjVa1dUKBji5Vvf4oMnPsNfGiCvZUMue/R8DhrUk25H7EO3I/ZJVigqjpYdmsftQlu7ZB3n7HE5L819FKcz7fbuUarK0mKLw4cvfpYvXp5CKLBtRUZPhpt7P7uZrofsOIJU1aTPXpzMwxc/i4mxeQpAs3ZNeHXBk0mMSqm6o7q7dGq1lQtX8enzk7ZL9gC+Ej+v3jG+hqJSsRx3wZEMvPTouCOpVi1cw79/LY1ZrpSKLuUT/qt3vRuzbNn8FUmMRFXUsAfOoVOP9nHrXNbrRlYuXJ2kiJRKDSmf8GdMnBmzLK9loyRGoirK7XXzyPd3x23l+4p8PHzxs0mMSqm6L+UTfqwF0yC8MYeqnRxOBydddXzcOr9N/oPnR7yWpIiUqvtSPuE3ahF7p6XGu2kLvza75KGhHHPuYXHrvDfmI7589ZvkBKRUHZfyCb9p67yYZVn1s5IYidoV1429jCOH9MVyRu/eCQVtHrrgKeb/ujDJkSlV96R8wm/RoXnMssWzlyQxErWrrnjyQlp1jL08Uyho8+SVY5MYkVJ1U0on/FnfzuHdMR/FLP/k2S9ZsyTxa/aoxMqql8njU+/FGWMWLsDfv8xPYkRK1U0pm/CNMdx56kMQZ16ZiPDjh9WzXo9KrMycDP5v7PCY5RnZ8TdUUUqlcMLftCafzes2x68UWZlR1Q1HnNGX4y48Eodz+z9bT4abgcOPqaGolKo7UnZBEpfHRTibx27iG9umz4m6UFpdcsUTF1BSWMoP7/+C2+vC7wvQ56QDOPu2U2s6NKVqvZRN+NkNsti9a2sWzoy9Td4JV/bXyVd1jMvt4uY3rmbd8vUsX7CKlh2akxdn6K1KHmNsTGglBBaAyQcrG0LrILQQggsh+C/YpeDMBcfugBvc3cBzNBSOBv9UsHLBcwLYCyDwDzjqg+doJKM/Il6MMbpHRRWkbMIHuPfTmzhnj8vxl+y8eblYQrYOy6yz8lo20jfrGmTsQgj+hcELJR9AyXigtGIvDq6E4JzwY9/7UDByW5ldpgwgCPi+wmy+HeNoAaFFGCzCvdEZIF5wtgDvWeDeB3HkIpZuSxpLSid8l9tF686tWPDbop3KPBlucpvWr4GolKq97OBaKPkQcIH9DwSXQGAOUAhSD7KGATYUPkZ4NfRi4o6MSJjS8CcFAEKRrwCYzRBYA4HfIRKJwQFWY8i+EivzlCTEVnekbMI3xnDdEbez5K9lUcsth8Uhp/ZOclRK1Q7GGExwERKaB47dMI5OsPZQMHGGKZsN4a4XhHDCra1CYK+CzTdhb74pcswJzr3BexSSMQBxNKvRCGtKyib8P777i5WL1hAK7ryWTma9DEZ/OZKsepk1EJlSyWWHNkHR8xD4CyQTQoshNA8Ag5NtaaAiXTKx16aq3YIQ/B0KZ2IKH8U4uwNF4GwL2VdhOXer6QCTImUT/op/VhP07dx3D+EF1fJaaf+vSi3GGIy9AQJ/IKF/wNEa45sNJU/FeVUw8pUuDOCH4NTw0+AsKJ2AjQWZ5yA5IxBJ2dHqqZvw23VtTTAY/WNnaZGP8ztfxWNT76FNl/R4Z1epx9gbMb6pUPQmBP8AStjSn24QwEOFb6SmPRuKX8YUv4pxHwZZF2N59qvpoBIuZRN+x+7tcTgdO+10tUVJYQmPX/4iD351e3IDU2oX2b4foOR9wAGBvyH0N7FvmBqqL9k7CY+S8Zc5tuOcFwusZmC1AwohtBpMKZAJrvZgL4fQEpAc8A6CwGKw54OjGQRXgSlz7825H2SeB5uvB3zV9D1tEQL/ZPBPxnYdDrlPYFmuar5m8qRswgc4ckhfJo77Our/CWPC/fxK1UbGhDC+r6HkvXByt9ewfYKtIe4+UO8uKPkf+L4GR1Mk6zxw7gE4EKteQi5j7EKw14GjGSLe8DFvX0zxG1D6JZABjpzIz2Yt1fLmFpgCa/bClkaQcyuScVydnwOQ0puYb1yTzyXdrmPDyk1Ry71ZXj4qeLVK11AqEWz/b1DyLkg2ePrB5hshtIyk3SSVTHAfAb5P2NZCcoGzC2ScEL656eqGZdXOgQ4mtBrs9RhjQ+kE8P0AoUQvqOeE+o9iZRyV4PMmVrxNzFO2hZ+/bjOPXvpczGTv9ro49rzDkhuUUoAxpZjQBigYDf4fwBSx3Y3T4peSFElkvLr3GCTrPMTRAhiTpGsnljiahj9tALj3BsC2fVA6BfzfgHGBbzxVG04ahPzLsEsOQxo8gtTSN794UjLh27bNNYeOZNm8lTHrtOrYggtHnZXEqFS6sgN/Q2A2ONpB0cPg/4XktNydkT7yAVA6EfCBqytkD8dyd0vC9WuWZXkg89jwF2AXdYKC+4EAVfr5+7/GrB+EyX0Ny9k0IbEmS0om/N+/+pO1S9fH3M9WBA45tTeeDE+SI1OpzthFEFqCCS6GwqcgNLcGovCCqwd4j0Myjg+3ROvfUgNx1C5W1hCMpw+m9DMw/vD9iOBCKHkbgjMrd7LQv7DuEOzMcyNDOetG335KJvylc1fg90cfgw/gzfbSrmubJEakUpGxiwEfhgzYdB34J5HciUmZIBaQE+5rz+yPePshonsDxCLONkj2JdsOePaHrFOwSyZB/mVUbpkIA8UvYfwzod71iHv/RIebcCmZ8PNaNSTkj91X16hFQ3odl/ofaVXiGGPCXTHBPzDUA9+kcP87EE7y1bHUgItw98MWOeDICw93zB6O5TmgGq6ZnqyMftgFTcNLMlRW8FfMhrMwWZdg5VyZ+OASKCUT/q+TZsUsExFGTbwVh9ORxIhUXWDsQvBNBHsDuHqCqysigjE+zIZzIfgXGB/hBF/No9vch4P7YAgtCo9N9xyOODvUma6DOinzTCh8gl0b/hqEoiewA0uQBjchVu1csjslE/737/8Ss8yb5SGvZe38ZaiaYwJ/YDYMBWMT/g/vAs/B0OBxTOFzEPiTap/0YzUHRwvIugTLe2j1XkvtRDKHYEregdBadvl37Z+AWTMB4z0JqX9breteS8mE7y+O/Q494NJjsKzUXStDVZ4xBrPxcjCFZY4Gw2O5S96PzG5NYLKXLMAJroPB1RYcrcE7CMvST501SawcaPRheHKXb1J4yKqnLxQ8GBk6W4n7M6X/w5R+iMm6Fsm+oNZ8MkvJhC9WjB+uwLEXHJHcYFTtF5wb3qFpJyXhFl+i+uelETR4FMuj22rWVmLlINkXQ/bFW48Z7yBM6aeweTQQfV5PdCEoGo0pegST+yyW5+CEx1tZKdnUbdqmcdTjTpeTnFzd5UrtyCbmbvbGhoyBgDvO66O81tER6j8GDd+Bxj8iTf/GajpVk30dJFYmVuYpWM1+gdxxQGVziB82no9d9B4mGH1/jmRJSMIXkWNFZK6ILBCREVHKPSLydqT8ZxFpm4jrxnL00MNwuLb/eOx0OdjvsL1o0Fh3uVI7cHYOLy2wEy9knIxkXQLOdmXqeAEPWE1AcsNLD+RNQhq+Dg3HI03nYjX+GCvjWCz3fliOvJRecjedWJ7eSJOvwdq9kq80UHAzZt3R2JuuCy8BUQOq3I+5hsgAACAASURBVKUjIg7gSeAoYBkwTUQmGGPKbEzJBcBGY8weIjIYGAWcXtVrRzP/14U8f8OrO62S2Xbv1tz4+lXVcUlVx4lY0OAxzMYLIjdtS8PJ3bUvknkKIi5oFF4szARmhZcg8P4HsbJ3OFPrWJ8TVAoRqz7S5Avs0p8g/9r4u4Rtxw5/lU7AhNZBw5eS3refiD78XsACY8xCABF5CxgElE34g4DbI4/fBZ4QETHVsHLbLQPuJ+DbeUOHhs0aUK9RTqIvp1KEuLtD4ylQ8jHGXo+4e4L7oK3/IUWc4O2HePthfD9iNl4Qnk3r3AOyr0AcLTCSi+XQv7F0YXkPBO8P2EVjwzd2K7ORTOBHzJo+GEcjyDgVyTwrKck/EQm/JbC0zPNlwI4zQrbWMcYERSQfaASsK1tJRIYBwwBat25d6UA2rdnEhpUbo5bNiDM2XykAsXIh6+y4rXRTOgWz6Sq2LscbmAYbz9k6Kt9GwLkvZA8H137h1mAtGaGhqoeVdT4m8zxM0RtQeEfFX2jWQnAtFNyFKRiNqf8A4j2mWv9ealXHojHmOWNMD2NMj8aNo994jWfhn0tin9uunctAq7rFFNxD/LXXTXjv1E3DYG0vzOpO2Ks6Ya8dhB3ckKwwVZKJCGJ52fWU6oP8KzHrT8eY6tv3IBEJfzlQdp/AVpFjUeuIiBOoD6xPwLW3k9ci9j61bm/q7FqjaoYxofAuTZV/JYT+gnUHYuffjb36YOzVfbA3P0pt3Y9CVZ7x/0SV11IK/o5ZfSi2f075dXdBIhL+NKCDiOwuIm5gMDBhhzoTgKGRx6cAX1VH/31u09gjcPQ/lqoqEQdIFUd5lbwS/ihv1kDxk5FPAL2wN92EXfwetv+vGhvBoarI0ZLw+kdVtR42nIBd+HwCzrW9KvfhR/rkLwe+ABzAWGPMbBG5E5hujJkAvAi8KiILgA2E3xQSzpvlweVxRr1p26h5bnVcUqWbrGGR9VZKEnjSTVD6LpS+BxgMYBx7gGsfsBqCpz+4uuhM3FpOMk/DFL3E9gvebeEEyYgswVRQsRMWPoDtPBDLu0/CYkzITFtjzKfApzscG1nmcSlwaiKuFY/L7eKYcw9n4ivf4C/Z1g/mzfRw2vWDqvvyKg1I1oUYSqHoRTBBErvPbJlPoaEF4S+A4hcBsB3tIeui8Pr27j5RhoWqmiSOFpD7HCb/OrA3A3Z4/kbOTYi7OyJOTHAxZt0AKrxUx6ZTME3/TtiN3JTb09bvCzDmwqf55t2pWJaFHbI5+erjueC+ITpaQiWMMX6wN2JCa2DDJUBFx2IngGSF32zcB0FwXvixaz/IvgRxdQ53PakaY4wJb5AiXsTRbLsye8Ow8JaLlVltNfNirHrXVrh6vD1tUy7h/zppFo9d9gLL56/EsgQswQ7Z1GuYw4BLjuLMm0/G7Y03TV6pyjPGhDfS9k8F39fgm0xiW/8VZYV3u3J2AM+R4OyMOLIR8dZALGpH9qquxB/lFYXVCqvJVxWunjYJf/Ib3zHmwqfxl0bf7crlcdHloI48MOk2be2ramcH18LmW8EugIyzoORVCFa+EZM4XnAdAJ6ekHE6lkOXGUkWY/xgSjFrjgSiLdQXh6MLVuMPKlw9LRK+bduc1vwi8tdujlvPk+nhgcm3secBHaoaolKVZvtmQOEYsDeBXQRmRQ1G4wDnXuDsGH7q7o54jwbJ1gZRghhTitl0fXhjnV0dstnwDSx31PwdVbyEnzLLI29ak09JQfkjJ4L+IAt+W6QJX9UIy9MdPK9vfW5MAGPnQ/EbUPoRhFYQfZRHdQhBcFb4C6D0XczmG8NxAbiPQ7x9McF/QbLBeziWq2OSYqv97MACKHkrPPom63xEGiAi2LYPCl+A4pepdGt+R9KyUsm+PCmT8LPqZxIKlr9uuW3bNNu9SRIiUqp8Ii7EkQc5V4a/CE/wMiXvQ9HzEFrMtht8QqVu9lWV/zOM/7Ntz4seirRRBXCAY3dw9wXLAmkM7t5Y7s7Jiy/JTHARpuBh8P1M+P5M0bbComfDw2mxSOhG9nmfJ+5cpFDCnzvtnwr9V3C5nezfL3HjWpVKNBEHknkKZJ6y9diWTdRN6YTwip7+mWAvqKEIDRCE0Hwomb9diW01htxXEHs1pujV8CgiguDqCjnXh4cuGh9IRp3pNrJDGyH/TvB/UpHaCbqqExqOx3J4EnS+rWdNDa/eOR47GP+HLSJc/czFOBw6bE3VLSICngMQz7Z1CW3fTCgcDYE5bJsIZgjP9qyJEUKAvRbWD4g0vspMgPStBN8XmDKfUgzO8P0Dx+5grwQrD7z9wdkV/F+Doy3iObhCbwzGLgb/d2AC4OmDWA12rhNcCIHZ4GgOru7hDertjRD4GyOZYOdD8TgI/BrZrD5EUj9RbZF5KZJzZbUMr02ZhL/in1Xl1smsn0G/sw9JQjRKVT/Ls+929wMAjF0EvimY0L9QMhlCf9ZAZPGWCS6bQIMQnBP+2sI3cYfaEpl7XFZOeEKT59DwfsAl70HgpzLntjDe0yAwF0KLCA+DDBBO4FtSXiOM+MFEX103+TIh6zwk60LEqr5d+VIm4XfquQdrl66PuypmKBBi2bwV7NapZRIjUyp5xMqCjP+El3jOvgyI3Fz0TwP/7xCYAfZGoJiE7dVbraL9fy6A4MzIzeZo5TaUvhXjfFvejFbXSON9G3f4043nMPD+B8vVLilXTZmEf85tp/HLp7/iK479UTboDzL+wQn06r8/vQf0wOHUrh2V+izXHuDaA7LO2HosPBzbhtAiTPHb4JsJoXmE3wjqito5pDwm515Q71Ys9/41FkLKjMM3xnDh3tew9O/lsVfGjHQfZmR7ad6+KY98dxcZ2RmJCVipFGHbNpZlRUalPAG+b9n2RlDekFGJfKXbip9ewvdNLMCA5IG7B7j2As8AxNk4afsap8U4/L9/WcCaJWvjL4McKSopLGXZ3BW8PeoDzr3rjNj1lUpDlhVOTOLcHcl9aLsy2y4B/6+R0TcG/L9FbnIWgJUDGUNA3FD4MMmbT1CTXJA1DMm+vE6sYZQyCX/ZvBXEbNgLO5X5SwNMfuN7TfhKVYJlZYD3YODguPVMxiBM6bfhG7KhVeBoBjjDE5USurR0MjlAGoDn8PCQWWcXLKturVGUMgm/Ses8fMU7Lzka3npMMKGdP2JqH75S1UMcjZGsk4GTty+ofyPG+MPDIY0PrKYQ+A18k8D2g6MxlH4Tvp8g7sgS1NHuK7gI34C1qPzNZ4tt3U5lW4K54TcmR3PwHg3e48DYiOVGJDV2zEuZhD9/xsJwYt9hlI4xhmZtmrBq0ZrtunvcGW6OPf+IZIepVNoTcSOOptsOeA4Mf22Rc8V29Y2xMaEV4J8FjgZgZSP2ZoxzTyS0EOOfGf4UEVgAlhu8x4IJQel4COaDlRV+83B2BGd7xHKFW+lWM0zgL7DcWM49kvTd16yUSfj/zFwcdUimJ8PNcRccwf8e/RRfiY+AL4jT5WDPAzty8n+Pr4FIlVKVIWIhzlbgbLX9cQBHI8TdM/oLs8rfc0ncXaoeYB2SMgm/Y/d2fPfezzt16wT8QV6/5380aFyP3gO607pLK/Y8oCNdenesM1O7VXSzp87l6f+Oo7SwhP4X9WPApUfjcqfGR2+lqkPKDMssyi9iaIcrKdhQgB1j8pUn08PA4UczbPQ5iQpT1ZDbT36AH97/Zbtj9RvX49WFT5KRVbdupCmVSPGGZSZnYGgSZNXP4tGpd9OyY7OYdXzFPj584nMKNxXFrKNqN2MMHz8zcadkD5C/djNjb3qjBqJSqm5ImYRvjOGGo+9i6d8r49ZzeVwsnx+/jqqdSopKuarPLTx62fMx63z5yjdJjEipuiVlEv7EcVNYvaj8jaQDvgBNWuclISKVaONue5sFvy6KP6Neb8soFVPK3LQd/9DH5dZxe930Htid3KY7L52qaq9Nazbx+dgpfPLslwR88WdvHjP0sOQEpVQdlDIJ33KU37TbrXNzrn/58iREoxLlseHP89EzE8uvCOQ0zObih4ZWc0RK1V0p06Vz5k0nlVtn+fxVzP5xbhKiUYnw44RpFUr2DpfF4BEn8N7asVvXgVFK7Sxl/ncceupBWI74305pkY/Px05JUkSqKowxvHL7O3HreDM95ORm8dzMMVxw7xCdV6FUOVKmS0dE2K1TC/6dsyxuvYCvhrZ+UxWycfUmHr/iRX78cBqhQOw1Utp0acWA4cfQb0hfsupX3w5BSqWSlEn4EO7WeXjYs5RGWUQNwJvl4fDBfZIclaqo4sISzu10JcWby19N8ZrnL6VL745JiEqp1JEyXToAh5/RhyG3now3y4PbG5liH/mU783ysH+/rhx8Yq+aC1DFNeLouyqU7Lv07qjJXqldkFItfBGhYfNcshtks27FevJaNmTP3h1p2CyX3gO6s3+/rtrPW0utWbKWedP/iVnuznCTk5vFCZcfx+k3nJDEyJRKHVVq4YtIQxH5UkTmR/7NjVJnPxGZKiKzRWSWiJxelWvG89mLk3ls+AusW74eDKxbvoGpH06j7V670f2ofTXZ11IlhSX8PW0BTnf09odYwvUvX85by55j8IgT9feo1C6q0uJpIjIa2GCMuV9ERgC5xpgbdqjTETDGmPki0gKYAexpjNkU79y7sqft6S0uYuPq/CiBwslXH8/FDw7VZFGLFOUX8eD5T/PzJzMwAkFfMGq9jBwv760dqythKlUB1bl42iBgXOTxOGCnz9rGmHnGmPmRxyuANUDjKl53J8FAMHqyBzDwyXOT+OWz3xJ9WVUFI08Yzc+fzCDgD8ZM9g6ngwcm36bJXqkEqGrCb2qM2bIS2SqgabzKItILcANRO2tFZJiITBeR6WvXlr8uTllOlxOXJ/YtidIiH58+P6lS51TV56ePpjNn6jwC/h0SvYQXuHO6nex3+F48NX0UnXqkx25ESlW3cm/aisgkINqawzeXfWKMMSISs39IRJoDrwJDjTE7bzAbPsdzwHMQ7tIpL7ay/KV+QsGop93KV6Jj8GtawaZC/tt3JEv/Xo4dZZ9hDHTs0Y5Hvrs7+cEpleLKTfjGmH6xykRktYg0N8asjCT0NTHq1QM+AW42xvy0y9HGUVrkw3JY0ZMI4WGZRw7pWx2XVhW04p9VXNDlaoJxJlS5PE72PXSvJEalVPqoapfOBGDLalVDgQ93rCAibuB94BVjzLtVvF5M9Rrl0LhVo6hllsNiz94dOeIMnXRVU5b+vZxzO14RN9lbDgtvtpcTrjguiZEplT6qmvDvB44SkflAv8hzRKSHiLwQqXMacAhwroj8Hvnar4rX3YmI0PfkA2MUwr2f3oTD6Uj0ZVUF3XbSaMobEHb4GX14evpoXb5aqWpSpYlXxpj1wJFRjk8HLow8fg14rSrXqajPXoh+U9YO2rww4nUueVCXzq0pS+euiFt+wPH7M+KVK5IUjVLpKaWWVijYGHuv2g8e/4xgIPrQP1X9JM5WVGIJlz16fhKjUSo9pdTSCi6PK+aOSJYl/DPzXzr1aJ/kqNKTr8THa3eOZ8rbP+LN9NCkdR6r/40+1Pbh7+6iebu4I3qVUgmQUgn/5P8ez1v3fxC9UARvlie5AaWpwvwizmo7nKL84q3HLIdgOS3sMkNnLYfFI9/fzZ4HdKiJMJVKOymV8M+/50x+nDCNJXOW71Tmcjtp3bllDUSVfkYOHLVdsgewQwan2+LU6wexZsk62u/XlhOuOA5Phr4JK5UsKdWHLyIcdvrBUfe3DfgCMbsUVOIUF5TE3EYy6A+R27QBN71xNadff4Ime6WSLKUSPsCcH+dih3Ye/+f2uFg4698aiCi9FOUXI1aMG7QCjVrstKCqUipJUi7ht+7cKmrCKSoo4e0HPuT3KX/WQFSpzRjDrG/n8PnYr1i3fD3ZDaJvOeh0OTloUM8kR6eU2iKl+vAB2u3bBmNHmeFjYM4Pc7nxuHvIzs3ChGz2O2Ifzr/nDFq0j7ZUkKqIpXOXc0XvmyjaFO6zdzgdNG/fhOLNJduNmBJLuPOD63F73TUVqlJpL+US/rRylkAO+oNsiiyj/N27U5kxcSbPzXoo5rIMKrblC1Zy/p5Xb3csFAyxfN4qDj39IPwlfpb8tZxOvdpz/t1n0KR1wlfFVkpVQsol/HhrtezItg0lRaW8cc97XPX0sGqMKvUsm7+S8zpdGbXMGMMvn/7Kh5teSXJUSql4Uq4P/8ghfSs13j4UCPHxc19yz5mP4CvxVWNkqeWaQ26NWx5rApxSquakXMI/+MRe9DhmP9wZldghycCPH/zCI5c+X32BpZDV/66NvbtYRKdeummJUrVNyiV8y7IYOf5a2nTZrVKv85cG+OadHykuKKmmyOq+4oISJjz1BY8Of544S+MAcIMuhKZUrZNyffhbLPh1UaVfY1lC4cZCMnMyqiGiuu3fv5Zyea8R+EsDUec5lPXoj/fQrE2TJEWmlKqolGvhA9i2jYmz+HrP/t2itlA9GR4atWxYjZHVTd++N5UL97qG0iJ/ucn+3k9vpMuBHZMUmVKqMlIy4TscDrLqZ0Yvczq45MFzyMjOwHJs+/Y9mW4ufXgoDoduklJWMBDknsGPxK3ToEk9+px0AG8seYaex+6fpMiUUpWVsl06Vz0zjHvP2DlRuTNc5DTM4ekZo3jtrneZ/cNcmrZtzBk3nsT+R+5TA5HWXqFQiEmvfRtzn2AAp8vBG0ueweWuxE1ypVSNSNmE37RN9Ek+/tIA4x/8kGGjz+GGcXpjMZbR5z7BpNe+jT5ruYwD/9NDk71SdURKdukAPHjBU1GPhwIhfv40/mzcdDf63Cf48pVvyk32GTkZXP2sTlhTqq5IyRa+3xdg2d87r4m/RcOm9ZMYTd0yZ+pcvnzlm3LreTLcvP7vU+Q0yE5CVEqpREjJhO9wWjjdTgK+6HvY9jhmvyRHVPsZY3j88heY+PLXcevtvk9reg/ozpCRp+LWrhyl6pSU7NJxOBwcevpBMcunvPVDEqOp/YwxTHjqcz5/8St8Jf6Y9RwuB8/NfIjz7j5Tk71SdVBKJnyAM248MWbZoj+WJDGS2m3OT/M4Oe88nrhyLAF/9E9EW5x09fFJikopVR1SNuFvXBV7rRc7ZDPxla+TF0wt9fboD7jqoJsp2FgEce7PiiWccu0Aho06O3nBKaUSLiX78AGatW2C5bBijiF/6PynWLt0PUNuPjnJkdW8YCDIyEGjmfZ5+aOV3Blu3lr2LDm5enNWqbouZVv4Tds0pscx+8bcX9W2DeNue5txt72d5Mhq1tpl6zljt0sqlOw9GW5ufO1KTfZKpYiUTfgAt7x9DT2O3jdmubENb436gPUrNyYxqpr10AVPsWlN/KWNAfY6uBNvLHmGPicekISolFLJkNIJPyPLy/79usatY2zDrG9mJymimuUr8fH7lPK/V2+2h5Hjr6Veo5wkRKWUSpaU7cMvy3Ja2MHoffmhYKhCLd66yu/z89jwF/juvZ8wxsRdFwcgq34Gry7SCVVKpaKUT/gHDerJS7e8hT8Ye3x5wYai7Z4vX7CSieO+pmhTEQcc353uR++LZdW9D0O2bXNW2+Hl7k61RddD9+S+z27B7XVXc2RKqZpQpYQvIg2Bt4G2wGLgNGNM1A5xEakHzAE+MMZcXpXrVkaL9s04flg/3n/s06jlDpeDnIbbWrNfvfkdYy58hlAwRDAQ4ouXv2bfw/bijg+ur1NLJxtj+PDJz2Mme6fLQTAQwuFykJHtZdTEW+nYvX2So1RKJVNVW/gjgMnGmPtFZETk+Q0x6t4FfFvF6+0Shyt2og4FQhx8Qk8ASgpLGHPRM9vNNi0t8jHz69l8/97PHHpa7Nm7tUVhfhE3HHUn86YvjFuvRftm9B7Ygz267c7BJ/bSFS+VSgNV7acYBIyLPB4HnBCtkoh0B5oCE6t4vV3iK/bFLb/yoJtZs2Qts76Zg8O585tDaZGPr978vrrCS5jl/6xkcMth5SZ7gD32b8eF95/FYacfrMleqTRR1YTf1BizMvJ4FeGkvh0RsYCHgOvKO5mIDBOR6SIyfe3atVUMbZuDT+wVt3zj6nwevOBpXJ7Yic+dUXv7tf2+ACMHjeLcDlfiK459r6Ks8+4eXM1RKaVqm3K7dERkEtAsStHNZZ8YY4yIRJugPxz41BizTCT6JKgy53gOeA6gR48e8Rdjr4TGrfIQS2Ku726HbH6f8if7HLJn1L1wvVkejrvgyESFk3BPXvEiP308o0J1RYQrnriAZm11k3Gl0k25Cd8Y0y9WmYisFpHmxpiVItIcWBOlWm+gr4gMB7IBt4gUGmNG7HLUldSgST2cLkfM5ZIhPB7/9bvexXI4cLgcuDxOjA3Gthl42bG1cvvDKW//wKu3v8PSuSvKrZvXqhHn3TWYw8/QLhyl0lVVb9pOAIYC90f+/XDHCsaYIVsei8i5QI9kJnuAeg1zOOD47vz8ya8EfIGY9UJBm1DQxpvlYcAlx9CqQ3O69duH5rvv1FNVY0KhEG/c+z9ev/s9QoFQhV930xtXsU+fPasxMqVUbVfVPvz7gaNEZD7QL/IcEekhIi9UNbhEuv7ly+h1XDecbmfM9XW2KC3ysXLhavpf1K9WJfvlC1ZyUqPzeOW2dyqc7J0uJze//V9N9kopJFqfdW3Qo0cPM3369ISfd9PafNYt38AXL03hi5enUFJQGrXe7vu04dnfH6C8+w7JYozhvM5Xsnz+qgq/ZveurXnsx3vxZnqqMTKlVG0iIjOMMT2ilaX8TNsdNWhcn1duf4ePno4/QnTZvOW8csc7DL399CRFtrPighJev+ddprz5A8YY1q+o2CJv7fdryxkjTuSQU3vXmjcspVTNS7uEX5RfVG6yBwj4gox/8CMG33ACnozkt5C/e28qd53+cMyRRdGIJRw++GBufO2qaoxMKVVXpV3C//bdnypcVyxh7bINtOrQvBoj2l4oFOKOkx5k6keV7876z8VHcenD5yY+KKVUSki7hJ/btEGF65YWlvLLJzNodfV/qjEiKNpczKJZ/9KweS6/TvqDnz/9tVKvz2qQyeNT72W3Ti2rKUKlVCpIu4R/wPH7gxB3D9eynr5mHIvnLOWa5y4FYNa3c3jq6pdY9McSchpmc+p1Azj12oEVWk3TX+rn10l/EPAH2f/Ivcmqn8UtA+/j54+3JXjLGXtbRgAEeh7bjfx1m8lr3pDTrh/IXgd1rtg3o5RKa2k3SgfgvUc/5pn/jiu/YoRYMGriSLLqZ3LNoSO3W77Ak+lh0GXHcNEOG3yHQiGmffY7i/9cQqtOLfBmebjrtDEY22AAE7Jp360tc36cV6nYXR4nH+a/opOnlFJRxRulk5YJH+DWgfdXeDkCgJYdm9OqYwt++WQGO/7IPBluxq95EbfXxS+f/sb0ib8z5c0fKCksJRQMYVlCKMYGLJX14JTb2ffQvRJyLqVU6tFhmVHc+s41nN3+Mjas3FSh+svnraRgXcFOyR5AHMLi2ct46qqx/Dt7KSWF24/tD1VipM0WlsvCDmx7k8hqkMU9H4/Q7hul1C5L2xY+QP76zQxpc2mFV5hMpuGPnseSv5bTZLdGHDX0MPJaNKzpkJRSdYC28GOo36geo78cyX/73oq9C63w6tK8XVNOvKJ/TYehlEoxdW+j1gTr0rsTj/10H94sD5Yz+T+O3Kb1t3u+R7fdeeHPMUmPQymV+tK6hb9Fpx7teXPps3z56jdMHPc1C35bVOFhm1X1/B8P4fa62bRmM3mtGuroG6VUtUn7Fv4W2Q2yOPGK/jw1bRRXPXURDZrUL/9FVeByOxn95Ujq59UnIzuD5u2aarJXSlWrtL5pW56XRr7Fe2M+xl/ij7oTVixOt4Ojzz2cTavz+WfmYgrWF1C/cX1OuXYg+/TphOV00LpzS13YTCmVcHrTdhedd+dgeh6zHxPHfU3QHySvZUPeeXBC3LXo23RpxTUvXEqXAzsmMVKllCqftvArKRQMMX3iTNYtW0+nnnvQsmNznC4HAEF/kIzsjBqOUCmVzrSFn0AOp4MD+u8ftUz74JVStZnetFVKqTShCV8ppdKEJnyllEoTmvCVUipNaMJXSqk0UWuHZYrIWuDfmo5jB3nAupoOIg6Nr+pqe4waX9WkQ3xtjDGNoxXU2oRfG4nI9FjjW2sDja/qanuMGl/VpHt82qWjlFJpQhO+UkqlCU34lfNcTQdQDo2v6mp7jBpf1aR1fNqHr5RSaUJb+EoplSY04SulVJrQhB+HiDQUkS9FZH7k39woddqIyK8i8ruIzBaRS2pZfPuJyNRIbLNE5PTaFF+k3ucisklEPk5SXMeKyFwRWSAiI6KUe0Tk7Uj5zyLSNhlxVSK+QyJ/c0EROSWZsVUixmtEZE7kb26yiLSpZfFdIiJ/RP7ffi8iXWpTfGXqnSwiRkQSM1TTGKNfMb6A0cCIyOMRwKgoddyAJ/I4G1gMtKhF8XUEOkQetwBWAg1qS3yRsiOBAcDHSYjJAfwDtIv87mYCXXaoMxx4JvJ4MPB2Ev/mKhJfW6Ar8ApwSrJiq2SMhwOZkceX1sKfYb0yjwcCn9em+CL1coBvgZ+AHom4trbw4xsEjIs8HgecsGMFY4zfGOOLPPWQ3E9NFYlvnjFmfuTxCmANEHUWXk3EF4lrMlCQpJh6AQuMMQuNMX7gLcJxllU27neBIyV5+1GWG58xZrExZhZgJymmHVUkxinGmOLI05+AVrUsvs1lnmYByRy9UpG/QYC7gFFAaaIurAk/vqbGmJWRx6uAptEqichuIjILWEq4FbuiNsW3hYj0Ityi+Ke6A4uoVHxJ0pLw72mLZZFjUesYY4JAPtAoKdFVLL6aVtkYLwA+q9aItleh+ETkMhH5h/An0SuTFBtUID4R2R/YzRjzSSIvnPY7XonIJKBZlKKbyz4xxhgRidoKMMYsQkP+BAAAAfBJREFUBbqKSAvgAxF51xizurbEFzlPc+BVYKgxJmEtw0TFp1KTiJwF9AAOrelYdmSMeRJ4UkTOBG4BhtZwSACIiAWMAc5N9LnTPuEbY/rFKhOR1SLS3BizMpIw15RzrhUi8ifQl3BXQK2IT0TqAZ8ANxtjfkpEXImML8mWA7uVed4qcixanWUi4gTqA+uTE16F4qtpFYpRRPoRfuM/tEy3ZzJU9mf4FvB0tUa0vfLiywH2Br6O9CQ2AyaIyEBjTJU2+tYunfgmsO1dfyjw4Y4VRKSViGREHucCfYC5tSg+N/A+8IoxJiFvQpVQbnw1YBrQQUR2j/xsBhOOs6yycZ8CfGUid9FqSXw1rdwYRaQb8Cww0BiT7Df6isTXoczT44H5tSU+Y0y+MSbPGNPWGNOW8D2QKif7LSfXr9h30xsBkwn/MUwCGkaO9wBeiDw+CphF+E77LGBYLYvvLCAA/F7ma7/aEl/k+XfAWqCEcH/mMdUcV39gHuF7GTdHjt0Z+U8F4AXGAwuAX4B2Sf67Ky++npGfUxHhTx6zkxlfBWOcBKwu8zc3oZbF9ygwOxLbFGCv2hTfDnW/JkGjdHRpBaWUShPapaOUUmlCE75SSqUJTfhKKZUmNOErpVSa0ISvlFJpQhO+UkqlCU34SimVJv4fmYvpM1/HRsQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kpca = KernelPCA(kernel ='rbf', gamma = 15) \n",
    "X_kpca = kpca.fit_transform(X) \n",
    "\n",
    "plt.title(\"Kernel PCA\") \n",
    "plt.scatter(X_kpca[:, 0], X_kpca[:, 1], c = y) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PPDKkpQqI8uM"
   },
   "source": [
    "Here, we see that Kernel PCA succesfully distinguish between the two curves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PCTwYptLI8uO"
   },
   "source": [
    "**<h3>Congratulations on covering the basic concepts of Dimensionality Reduction !**\n",
    "To know more techniques or to know more about this topic check out this [link](https://www.analyticsvidhya.com/blog/2018/08/dimensionality-reduction-techniques-python/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xnLkuC2GcxW0"
   },
   "source": [
    "**<h2> Model Selections**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "b4iD7PjTcxW1"
   },
   "source": [
    "**<h2> K Fold Cross Validation**\n",
    "\n",
    "The above implemented ML models are actually not accurate as we did not train on one the whole dataset.  \n",
    "There is a possibility that we got a high accuracy by chance as the data we splited wasn't distributed evenly.\n",
    "For this we use K fold cross validation.  \n",
    "\n",
    "<img src=\"images/okay.jpeg\">\n",
    "\n",
    "Learn more about it [here](https://scikit-learn.org/stable/modules/cross_validation.html). Check out why we use it [here](https://towardsdatascience.com/5-reasons-why-you-should-use-cross-validation-in-your-data-science-project-8163311a1e79)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "colab_type": "code",
    "id": "2ZSLmv85cxW2",
    "outputId": "100377d8-a520-405e-bb17-600d13a23433"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>User ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age</th>\n",
       "      <th>EstimatedSalary</th>\n",
       "      <th>Purchased</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15624510</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>19000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15810944</td>\n",
       "      <td>Male</td>\n",
       "      <td>35</td>\n",
       "      <td>20000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15668575</td>\n",
       "      <td>Female</td>\n",
       "      <td>26</td>\n",
       "      <td>43000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15603246</td>\n",
       "      <td>Female</td>\n",
       "      <td>27</td>\n",
       "      <td>57000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>15804002</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>76000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    User ID  Gender  Age  EstimatedSalary  Purchased\n",
       "0  15624510    Male   19            19000          0\n",
       "1  15810944    Male   35            20000          0\n",
       "2  15668575  Female   26            43000          0\n",
       "3  15603246  Female   27            57000          0\n",
       "4  15804002    Male   19            76000          0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = pd.read_csv(url)\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lwOBJr1acxW4"
   },
   "outputs": [],
   "source": [
    "X = dataset.iloc[:, [2, 3]].values\n",
    "y = dataset.iloc[:, 4].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UDCYmrrxcxW-"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "classifier = LogisticRegression()\n",
    "scores = cross_val_score(classifier,X,y,cv=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "poV-xrVwcxXB",
    "outputId": "673bed8b-5d00-491d-d39f-1fe0e6556079"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.65  , 0.65  , 0.6375, 0.8125, 0.625 ])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "561ffZtXcxXG"
   },
   "source": [
    "The dataset was divided in 5 equal parts and each time one of the part was used as test set and rest as training.  \n",
    "The final model was trained on whole dataset and the mean of the scores gives us the final accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "h0VLW_VYcxXH",
    "outputId": "84e29415-4d9f-42ca-966b-26f85a965942"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.675"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "1zR8n_obcxXM"
   },
   "outputs": [],
   "source": [
    "kpca = KernelPCA(n_components = 2, kernel = 'linear')\n",
    "X = kpca.fit_transform(X)\n",
    "classifier = LogisticRegression()\n",
    "scores = cross_val_score(classifier,X,y,cv=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "nd5c_l4UcxXO",
    "outputId": "caab7764-67ff-482b-d6a0-313c8440bdcd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.765"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8ncOGpIIcxXZ"
   },
   "source": [
    "**<h2> Grid Search**\n",
    "\n",
    "Grid Search is the best way to deal with hyperparameters.It helps in tuning hyperparameters, to give you the best result.In order to do so , you must provide it with the parameters you wish to change.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "1SCPxXLbcxXa"
   },
   "outputs": [],
   "source": [
    "dataset = pd.read_csv(url)\n",
    "X = dataset.iloc[:, [2, 3]].values\n",
    "y = dataset.iloc[:, 4].values\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 53
    },
    "colab_type": "code",
    "id": "lnYlTaJxcxXc",
    "outputId": "71c1a2a5-dd28-4189-e96c-dcdc74f5f59c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[48, 10],\n",
       "       [ 7, 15]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "\n",
    "classifier = KNeighborsClassifier()\n",
    "grid_values = {\n",
    "    'n_neighbors': [1,2,3,4,5,6,7,8,9,10],\n",
    "               'p':[1,2]\n",
    "    }\n",
    "grid_clf_acc = GridSearchCV(classifier, param_grid = grid_values)\n",
    "grid_clf_acc.fit(X_train, y_train)\n",
    "\n",
    "#Predict values based on new parameters\n",
    "y_pred = grid_clf_acc.predict(X_test)\n",
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "g1olkVnKcxXl",
    "outputId": "3f44d33f-2759-4ac4-a240-1825048c3837"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'n_neighbors': 3, 'p': 1}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_clf_acc.best_params_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5yp9e0TGcxXo"
   },
   "source": [
    "So we got the best paramters within a single line of code\n",
    "Once we get the best paramters we can can use cross val score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DBkkeSefI8u2"
   },
   "source": [
    "**<h2>Stacking**\n",
    "    \n",
    "* Ensemble Learning:\n",
    "\n",
    "Ensemble Learning is a technique which combines multiple models to give a better overall performance.This can be achieved in various ways, one of which is Stacking.\n",
    "\n",
    "* Stacking:\n",
    "\n",
    "It is an advance ensemble learning technique that uses predictions from multiple models to build a new model.This model is then used for making predictions on a test set. This is popular technique used in data science competitions.\n",
    "\n",
    "Read more about Ensemble Learning and Stacking [here](https://www.analyticsvidhya.com/blog/2018/06/comprehensive-guide-for-ensemble-models/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "colab_type": "code",
    "id": "em0JhomVI8u2",
    "outputId": "d0d5aa15-8d2f-420f-ec20-6036fb4476ad"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>User ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age</th>\n",
       "      <th>EstimatedSalary</th>\n",
       "      <th>Purchased</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15624510</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>19000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15810944</td>\n",
       "      <td>Male</td>\n",
       "      <td>35</td>\n",
       "      <td>20000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15668575</td>\n",
       "      <td>Female</td>\n",
       "      <td>26</td>\n",
       "      <td>43000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15603246</td>\n",
       "      <td>Female</td>\n",
       "      <td>27</td>\n",
       "      <td>57000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>15804002</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>76000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    User ID  Gender  Age  EstimatedSalary  Purchased\n",
       "0  15624510    Male   19            19000          0\n",
       "1  15810944    Male   35            20000          0\n",
       "2  15668575  Female   26            43000          0\n",
       "3  15603246  Female   27            57000          0\n",
       "4  15804002    Male   19            76000          0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "colab_type": "code",
    "id": "tuJC5zbaI8u4",
    "outputId": "7c3b9938-4ac2-4f97-f070-f52b8895a35d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    257\n",
       "1    143\n",
       "Name: Purchased, dtype: int64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset['Purchased'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fk66QJNsI8u-"
   },
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.ensemble import StackingClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "estimators = [('knn',KNeighborsClassifier()),('lr',LogisticRegression()),('rf',RandomForestClassifier())]\n",
    "clf = StackingClassifier(estimators=estimators, final_estimator=LogisticRegression())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OPSNOkfNI8vB"
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "cmlmVTlkI8vE"
   },
   "outputs": [],
   "source": [
    "clf.fit(X_train,y_train)\n",
    "y_pred=clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 181
    },
    "colab_type": "code",
    "id": "Z-TJ6Rc9I8vI",
    "outputId": "61f2f7cc-3ce8-4470-9ccd-0f2b8938c576"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.95      0.93      0.94        58\n",
      "           1       0.83      0.86      0.84        22\n",
      "\n",
      "    accuracy                           0.91        80\n",
      "   macro avg       0.89      0.90      0.89        80\n",
      "weighted avg       0.91      0.91      0.91        80\n",
      "\n"
     ]
    }
   ],
   "source": [
    "y_pred=clf.predict(X_test)\n",
    "print(report_classification(y_test,y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2qfIwjidOqLa"
   },
   "source": [
    "The F1 score dictates a good performance by the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PVjVp6ujO143"
   },
   "source": [
    "**<h2>Congratulations on completing this week's notebook!**"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "week_7.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "pygments_lexer": "ipython3",
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