Ch10 Unsupervised Learning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Murder  Assault  UrbanPop  Rape\n",
       "Alabama       13.2      236        58  21.2\n",
       "Alaska        10.0      263        48  44.5\n",
       "Arizona        8.1      294        80  31.0\n",
       "Arkansas       8.8      190        50  19.5\n",
       "California     9.0      276        91  40.6"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "usarrest= pd.read_csv('Dataset/USArrests.csv', index_col=0)\n",
    "usarrest.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/sklearn/preprocessing/data.py:645: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/sklearn/base.py:464: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, **fit_params).transform(X)\n"
     ]
    }
   ],
   "source": [
    "scaler= StandardScaler()\n",
    "scale_usarrest = scaler.fit_transform(usarrest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Murder</th>\n",
       "      <td>0.535899</td>\n",
       "      <td>0.418181</td>\n",
       "      <td>-0.341233</td>\n",
       "      <td>0.649228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Assault</th>\n",
       "      <td>0.583184</td>\n",
       "      <td>0.187986</td>\n",
       "      <td>-0.268148</td>\n",
       "      <td>-0.743407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UrbanPop</th>\n",
       "      <td>0.278191</td>\n",
       "      <td>-0.872806</td>\n",
       "      <td>-0.378016</td>\n",
       "      <td>0.133878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rape</th>\n",
       "      <td>0.543432</td>\n",
       "      <td>-0.167319</td>\n",
       "      <td>0.817778</td>\n",
       "      <td>0.089024</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                V1        V2        V3        V4\n",
       "Murder    0.535899  0.418181 -0.341233  0.649228\n",
       "Assault   0.583184  0.187986 -0.268148 -0.743407\n",
       "UrbanPop  0.278191 -0.872806 -0.378016  0.133878\n",
       "Rape      0.543432 -0.167319  0.817778  0.089024"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_loadings = pd.DataFrame(PCA().fit(scale_usarrest).components_.T, index=usarrest.columns, columns=['V1', 'V2', 'V3', 'V4'])\n",
    "pca_loadings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca= PCA()\n",
    "std_pca_df= pd.DataFrame(pca.fit_transform(scale_usarrest),index =usarrest.index, columns =['P1','P2','P3','P4'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>P1</th>\n",
       "      <th>P2</th>\n",
       "      <th>P3</th>\n",
       "      <th>P4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0.985566</td>\n",
       "      <td>1.133392</td>\n",
       "      <td>-0.444269</td>\n",
       "      <td>0.156267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>1.950138</td>\n",
       "      <td>1.073213</td>\n",
       "      <td>2.040003</td>\n",
       "      <td>-0.438583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>1.763164</td>\n",
       "      <td>-0.745957</td>\n",
       "      <td>0.054781</td>\n",
       "      <td>-0.834653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>-0.141420</td>\n",
       "      <td>1.119797</td>\n",
       "      <td>0.114574</td>\n",
       "      <td>-0.182811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>2.523980</td>\n",
       "      <td>-1.542934</td>\n",
       "      <td>0.598557</td>\n",
       "      <td>-0.341996</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  P1        P2        P3        P4\n",
       "Alabama     0.985566  1.133392 -0.444269  0.156267\n",
       "Alaska      1.950138  1.073213  2.040003 -0.438583\n",
       "Arizona     1.763164 -0.745957  0.054781 -0.834653\n",
       "Arkansas   -0.141420  1.119797  0.114574 -0.182811\n",
       "California  2.523980 -1.542934  0.598557 -0.341996"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_pca_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.53085875, 1.00996444, 0.36383998, 0.17696948])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We typically decide on the number of principal components required to visualize the data by examining a scree plot. This is done by eyeballing the scree plot, and looking for a point at which the proportion of variance explained by each subsequent principal component drops off. This is often referred to as an elbow in the scree plot.For example, one might conclude that a fair amount of variance is explained by the first two principal components, and that there is an elbow after the second component. After all, the third principal component explains less than ten percent of the variance in the data, and the fourth principal component explains less than half that and so is essentially worthless."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Prop.Variance Explained')"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([1,2,3,4],pca.explained_variance_ratio_, marker= 'o')\n",
    "plt.xticks([1,2,3,4])\n",
    "plt.title('Explained Variance Ratio vs Principal components')\n",
    "plt.xlabel('Principal Components')\n",
    "plt.ylabel('Prop.Variance Explained')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Cumulative Prop. Variance Explained')"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([1,2,3,4], np.cumsum(pca.explained_variance_ratio_), marker ='o')\n",
    "plt.xticks([1,2,3,4])\n",
    "plt.title('Cumulative explained variance ratio vs Principal Components')\n",
    "plt.xlabel('Principal Components')\n",
    "plt.ylabel('Cumulative Prop. Variance Explained')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>P1</th>\n",
       "      <th>P2</th>\n",
       "      <th>P3</th>\n",
       "      <th>P4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>64.802164</td>\n",
       "      <td>11.448007</td>\n",
       "      <td>-2.494933</td>\n",
       "      <td>2.407901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>92.827450</td>\n",
       "      <td>17.982943</td>\n",
       "      <td>20.126575</td>\n",
       "      <td>-4.094047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>124.068216</td>\n",
       "      <td>-8.830403</td>\n",
       "      <td>-1.687448</td>\n",
       "      <td>-4.353685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>18.340035</td>\n",
       "      <td>16.703911</td>\n",
       "      <td>0.210189</td>\n",
       "      <td>-0.520994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>107.422953</td>\n",
       "      <td>-22.520070</td>\n",
       "      <td>6.745873</td>\n",
       "      <td>-2.811826</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    P1         P2         P3        P4\n",
       "Alabama      64.802164  11.448007  -2.494933  2.407901\n",
       "Alaska       92.827450  17.982943  20.126575 -4.094047\n",
       "Arizona     124.068216  -8.830403  -1.687448 -4.353685\n",
       "Arkansas     18.340035  16.703911   0.210189 -0.520994\n",
       "California  107.422953 -22.520070   6.745873 -2.811826"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_df= pd.DataFrame(pca.fit_transform(usarrest),index =usarrest.index, columns =['P1','P2','P3','P4'])\n",
    "pca_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.65534221e-01, 2.78173366e-02, 5.79953492e-03, 8.48907879e-04])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([83.73240025, 14.21240185,  6.48942607,  2.48279   ])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig , ax1 = plt.subplots(figsize=(9,7))\n",
    "ax1.set_xlabel('Principal Component 1', fontsize=15)\n",
    "ax1.set_ylabel('Principal Component 2', fontsize =15)\n",
    "\n",
    "ax1.set_xlim(-3.5,3.5)\n",
    "ax1.set_ylim(-3.5,3.5)\n",
    "\n",
    "# Plot Principal Components 1 and 2\n",
    "for i in std_pca_df.index:\n",
    "    ax1.annotate(i, (std_pca_df.P1.loc[i], -std_pca_df.P2.loc[i]), ha='center')\n",
    "\n",
    "# Plot reference lines\n",
    "ax1.hlines(0,-3.5,3.5, linestyles='dotted', colors='grey')\n",
    "ax1.vlines(0,-3.5,3.5, linestyles='dotted', colors='grey')\n",
    "\n",
    "ax1.set_xlabel('First Principal Component')\n",
    "ax1.set_ylabel('Second Principal Component')\n",
    "\n",
    "# Plot Principal Component loading vectors, using a second y-axis.\n",
    "ax2 = ax1.twinx().twiny() \n",
    "\n",
    "ax2.set_ylim(-1,1)\n",
    "ax2.set_xlim(-1,1)\n",
    "ax2.tick_params(axis='y', colors='orange')\n",
    "ax2.set_xlabel('Principal Component loading vectors', color='orange')\n",
    "\n",
    "# Plot labels for vectors. Variable 'a' is a small offset parameter to separate arrow tip and text.\n",
    "a = 1.07  \n",
    "for i in pca_loadings[['V1', 'V2']].index:\n",
    "    ax2.annotate(i, (pca_loadings.V1.loc[i]*a, -pca_loadings.V2.loc[i]*a), color='orange')\n",
    "\n",
    "# Plot vectors\n",
    "ax2.arrow(0,0,pca_loadings.V1[0], -pca_loadings.V2[0])\n",
    "ax2.arrow(0,0,pca_loadings.V1[1], -pca_loadings.V2[1])\n",
    "ax2.arrow(0,0,pca_loadings.V1[2], -pca_loadings.V2[2])\n",
    "ax2.arrow(0,0,pca_loadings.V1[3], -pca_loadings.V2[3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unscaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig , ax3 = plt.subplots(figsize=(9,7))\n",
    "ax3.set_xlabel('Principal Component 1', fontsize=15)\n",
    "ax3.set_ylabel('Principal Component 2', fontsize =15)\n",
    "\n",
    "ax3.set_xlim(-150,150)\n",
    "ax3.set_ylim(-150,150)\n",
    "\n",
    "# Plot Principal Components 1 and 2\n",
    "for i in pca_df.index:\n",
    "    ax3.annotate(i, (pca_df.P1.loc[i], -pca_df.P2.loc[i]), ha='center')\n",
    "\n",
    "# Plot reference lines\n",
    "ax3.hlines(0,-150,150, linestyles='dotted', colors='grey')\n",
    "ax3.vlines(0,-150,150, linestyles='dotted', colors='grey')\n",
    "\n",
    "ax3.set_xlabel('First Principal Component')\n",
    "ax3.set_ylabel('Second Principal Component')\n",
    "\n",
    "# Plot Principal Component loading vectors, using a second y-axis.\n",
    "ax4 = ax3.twinx().twiny() \n",
    "\n",
    "ax4.set_ylim(-1,1)\n",
    "ax4.set_xlim(-1,1)\n",
    "ax4.tick_params(axis='y', colors='orange')\n",
    "ax4.set_xlabel('Principal Component loading vectors', color='orange')\n",
    "\n",
    "# Plot labels for vectors. Variable 'a' is a small offset parameter to separate arrow tip and text.\n",
    "a = 1.07  \n",
    "for i in pca_loadings[['V1', 'V2']].index:\n",
    "    ax4.annotate(i, (pca_loadings.V1.loc[i]*a, -pca_loadings.V2.loc[i]*a), color='orange')\n",
    "\n",
    "# Plot vectors\n",
    "ax4.arrow(0,0,pca_loadings.V1[0], -pca_loadings.V2[0])\n",
    "ax4.arrow(0,0,pca_loadings.V1[1], -pca_loadings.V2[1])\n",
    "ax4.arrow(0,0,pca_loadings.V1[2], -pca_loadings.V2[2])\n",
    "ax4.arrow(0,0,pca_loadings.V1[3], -pca_loadings.V2[3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering Methods\n",
    "### Kmeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate data\n",
    "np.random.seed(2)\n",
    "X = np.random.standard_normal((50,2))\n",
    "X[:25,0] = X[:25,0]+3\n",
    "X[:25,1] = X[:25,1]-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.58324215, -4.05626683],\n",
       "       [ 0.8638039 , -2.35972919],\n",
       "       [ 1.20656441, -4.84174737],\n",
       "       [ 3.50288142, -5.24528809],\n",
       "       [ 1.94204778, -4.90900761],\n",
       "       [ 3.55145404, -1.70779199],\n",
       "       [ 3.04153939, -5.11792545],\n",
       "       [ 3.53905832, -4.5961597 ],\n",
       "       [ 2.9808695 , -2.82499878],\n",
       "       [ 2.25212905, -3.99097475],\n",
       "       [ 2.12189211, -4.15643417],\n",
       "       [ 3.25657045, -4.98877905],\n",
       "       [ 2.66117803, -4.23618403],\n",
       "       [ 2.36234499, -5.18761229],\n",
       "       [ 1.57878277, -4.1534952 ],\n",
       "       [ 2.73094304, -1.76863321],\n",
       "       [ 0.56523242, -3.8872735 ],\n",
       "       [ 3.37044454, -2.64036614],\n",
       "       [ 3.50185721, -4.8442137 ],\n",
       "       [ 3.00000976, -3.45764743],\n",
       "       [ 2.6864918 , -3.22898826],\n",
       "       [ 1.13190935, -2.26881533],\n",
       "       [ 4.46767801, -4.33567734],\n",
       "       [ 3.61134078, -3.95202941],\n",
       "       [ 2.17086471, -3.91228978],\n",
       "       [ 1.00036589, -0.38109252],\n",
       "       [-0.37566942, -0.07447076],\n",
       "       [ 0.43349633,  1.27837923],\n",
       "       [-0.63467931,  0.50839624],\n",
       "       [ 0.21611601, -1.85861239],\n",
       "       [-0.41931648, -0.1323289 ],\n",
       "       [-0.03957024,  0.32600343],\n",
       "       [-2.04032305,  0.04625552],\n",
       "       [-0.67767558, -1.43943903],\n",
       "       [ 0.52429643,  0.73527958],\n",
       "       [-0.65325027,  0.84245628],\n",
       "       [-0.38151648,  0.06648901],\n",
       "       [-1.09873895,  1.58448706],\n",
       "       [-2.65944946, -0.09145262],\n",
       "       [ 0.69511961, -2.03346655],\n",
       "       [-0.18946926, -0.07721867],\n",
       "       [ 0.82470301,  1.24821292],\n",
       "       [-0.40389227, -1.38451867],\n",
       "       [ 1.36723542,  1.21788563],\n",
       "       [-0.46200535,  0.35088849],\n",
       "       [ 0.38186623,  0.56627544],\n",
       "       [ 0.20420798,  1.40669624],\n",
       "       [-1.7379595 ,  1.04082395],\n",
       "       [ 0.38047197, -0.21713527],\n",
       "       [ 1.1735315 , -2.34360319]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Number of cluster is 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=2, n_init=20, n_jobs=None, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "k2 =KMeans(n_clusters=2, n_init= 20)\n",
    "k2.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.23940153,  0.14703307],\n",
       "       [ 2.53287159, -3.80815122]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k2.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1271c1e48>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], s=40, c=k2.labels_, cmap=plt.cm.prism)\n",
    "plt.scatter(k2.cluster_centers_[:,0],k2.cluster_centers_[:,1], marker ='+')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Number of cluster is 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=3, n_init=20, n_jobs=None, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k3= KMeans(n_clusters=3, n_init=20)\n",
    "k3.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.82805911, -4.11351797],\n",
       "       [-0.27876523,  0.51224152],\n",
       "       [ 0.69945422, -2.14934345]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k3.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x127528e10>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], s=40, c=k3.labels_, cmap=plt.cm.prism)\n",
    "plt.scatter(k3.cluster_centers_[:,0],k3.cluster_centers_[:,1], marker ='+')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "hc_complete= AgglomerativeClustering(linkage='complete')\n",
    "hc_average=AgglomerativeClustering(linkage='average')\n",
    "hc_single = AgglomerativeClustering(linkage='single')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AgglomerativeClustering(affinity='euclidean', compute_full_tree='auto',\n",
       "            connectivity=None, linkage='complete', memory=None,\n",
       "            n_clusters=2, pooling_func='deprecated')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hc_complete.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,\n",
       "       1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hc_complete.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "l_c= linkage(X, method ='complete')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1, figsize=(15, 8))\n",
    "dendrogram(l_c, ax=axes, color_threshold=0)\n",
    "plt.title('Complete Linkage')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_s= linkage(X, method ='single')\n",
    "fig, axes = plt.subplots(1, 1, figsize=(15, 8))\n",
    "dendrogram(l_s, ax=axes, color_threshold=0)\n",
    "plt.title('Single Linkage')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_a= linkage(X, method ='average')\n",
    "fig, axes = plt.subplots(1, 1, figsize=(15, 8))\n",
    "dendrogram(l_a, ax=axes, color_threshold=0)\n",
    "plt.title('Average Linkage')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lab 3: NCI60 Data Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "X= pd.read_csv('Dataset/NCI60_X.csv').drop('Unnamed: 0', axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>...</th>\n",
       "      <th>6821</th>\n",
       "      <th>6822</th>\n",
       "      <th>6823</th>\n",
       "      <th>6824</th>\n",
       "      <th>6825</th>\n",
       "      <th>6826</th>\n",
       "      <th>6827</th>\n",
       "      <th>6828</th>\n",
       "      <th>6829</th>\n",
       "      <th>6830</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.300000</td>\n",
       "      <td>1.180000</td>\n",
       "      <td>0.550000</td>\n",
       "      <td>1.140000</td>\n",
       "      <td>-0.265000</td>\n",
       "      <td>-7.000000e-02</td>\n",
       "      <td>0.350000</td>\n",
       "      <td>-0.315000</td>\n",
       "      <td>-0.450000</td>\n",
       "      <td>-0.654981</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.990019</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.030000</td>\n",
       "      <td>-0.175000</td>\n",
       "      <td>0.629981</td>\n",
       "      <td>-0.030000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.280000</td>\n",
       "      <td>-0.340000</td>\n",
       "      <td>-1.930000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.679961</td>\n",
       "      <td>1.289961</td>\n",
       "      <td>0.169961</td>\n",
       "      <td>0.379961</td>\n",
       "      <td>0.464961</td>\n",
       "      <td>5.799610e-01</td>\n",
       "      <td>0.699961</td>\n",
       "      <td>0.724961</td>\n",
       "      <td>-0.040039</td>\n",
       "      <td>-0.285020</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.270058</td>\n",
       "      <td>-0.300039</td>\n",
       "      <td>-0.250039</td>\n",
       "      <td>-0.535039</td>\n",
       "      <td>0.109941</td>\n",
       "      <td>-0.860039</td>\n",
       "      <td>-1.250049</td>\n",
       "      <td>-0.770039</td>\n",
       "      <td>-0.390039</td>\n",
       "      <td>-2.000039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.940000</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>-0.170000</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>-0.605000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.090000</td>\n",
       "      <td>0.645000</td>\n",
       "      <td>0.430000</td>\n",
       "      <td>0.475019</td>\n",
       "      <td>...</td>\n",
       "      <td>0.319981</td>\n",
       "      <td>0.120000</td>\n",
       "      <td>-0.740000</td>\n",
       "      <td>-0.595000</td>\n",
       "      <td>-0.270020</td>\n",
       "      <td>-0.150000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.120000</td>\n",
       "      <td>-0.410000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.280000</td>\n",
       "      <td>-0.310000</td>\n",
       "      <td>0.680000</td>\n",
       "      <td>-0.810000</td>\n",
       "      <td>0.625000</td>\n",
       "      <td>-1.387779e-17</td>\n",
       "      <td>0.170000</td>\n",
       "      <td>0.245000</td>\n",
       "      <td>0.020000</td>\n",
       "      <td>0.095019</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.240020</td>\n",
       "      <td>-0.110000</td>\n",
       "      <td>-0.160000</td>\n",
       "      <td>0.095000</td>\n",
       "      <td>-0.350020</td>\n",
       "      <td>-0.300000</td>\n",
       "      <td>-1.150010</td>\n",
       "      <td>1.090000</td>\n",
       "      <td>-0.260000</td>\n",
       "      <td>-1.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.485000</td>\n",
       "      <td>-0.465000</td>\n",
       "      <td>0.395000</td>\n",
       "      <td>0.905000</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>-5.000000e-03</td>\n",
       "      <td>0.085000</td>\n",
       "      <td>0.110000</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>1.490019</td>\n",
       "      <td>...</td>\n",
       "      <td>0.554980</td>\n",
       "      <td>-0.775000</td>\n",
       "      <td>-0.515000</td>\n",
       "      <td>-0.320000</td>\n",
       "      <td>0.634980</td>\n",
       "      <td>0.605000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.745000</td>\n",
       "      <td>0.425000</td>\n",
       "      <td>0.145000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 6830 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          1         2         3         4         5             6         7  \\\n",
       "0  0.300000  1.180000  0.550000  1.140000 -0.265000 -7.000000e-02  0.350000   \n",
       "1  0.679961  1.289961  0.169961  0.379961  0.464961  5.799610e-01  0.699961   \n",
       "2  0.940000 -0.040000 -0.170000 -0.040000 -0.605000  0.000000e+00  0.090000   \n",
       "3  0.280000 -0.310000  0.680000 -0.810000  0.625000 -1.387779e-17  0.170000   \n",
       "4  0.485000 -0.465000  0.395000  0.905000  0.200000 -5.000000e-03  0.085000   \n",
       "\n",
       "          8         9        10    ...         6821      6822      6823  \\\n",
       "0 -0.315000 -0.450000 -0.654981    ...    -0.990019  0.000000  0.030000   \n",
       "1  0.724961 -0.040039 -0.285020    ...    -0.270058 -0.300039 -0.250039   \n",
       "2  0.645000  0.430000  0.475019    ...     0.319981  0.120000 -0.740000   \n",
       "3  0.245000  0.020000  0.095019    ...    -1.240020 -0.110000 -0.160000   \n",
       "4  0.110000  0.235000  1.490019    ...     0.554980 -0.775000 -0.515000   \n",
       "\n",
       "       6824      6825      6826      6827      6828      6829      6830  \n",
       "0 -0.175000  0.629981 -0.030000  0.000000  0.280000 -0.340000 -1.930000  \n",
       "1 -0.535039  0.109941 -0.860039 -1.250049 -0.770039 -0.390039 -2.000039  \n",
       "2 -0.595000 -0.270020 -0.150000  0.000000 -0.120000 -0.410000  0.000000  \n",
       "3  0.095000 -0.350020 -0.300000 -1.150010  1.090000 -0.260000 -1.100000  \n",
       "4 -0.320000  0.634980  0.605000  0.000000  0.745000  0.425000  0.145000  \n",
       "\n",
       "[5 rows x 6830 columns]"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64, 6830)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "y= pd.read_csv('Dataset/NCI60_y.csv').drop('Unnamed: 0', axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64, 1)"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examining the cancer types for the cell lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NSCLC          9\n",
       "RENAL          9\n",
       "MELANOMA       8\n",
       "BREAST         7\n",
       "COLON          7\n",
       "LEUKEMIA       6\n",
       "OVARIAN        6\n",
       "CNS            5\n",
       "PROSTATE       2\n",
       "MCF7A-repro    1\n",
       "K562B-repro    1\n",
       "MCF7D-repro    1\n",
       "K562A-repro    1\n",
       "UNKNOWN        1\n",
       "Name: x, dtype: int64"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.x.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA on the NCI60 Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "std_X= scaler.fit_transform(X)\n",
    "pr_out=PCA().fit(std_X)\n",
    "pr_out_df= pd.DataFrame(PCA().fit_transform(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.13589419e-01, 6.75620253e-02, 5.75184223e-02, 4.24755448e-02,\n",
       "       3.73497235e-02, 3.61863019e-02, 3.06622240e-02, 2.68590309e-02,\n",
       "       2.52949807e-02, 2.37586884e-02, 2.35655815e-02, 2.16412198e-02,\n",
       "       2.04909747e-02, 1.97881793e-02, 1.91541737e-02, 1.77176082e-02,\n",
       "       1.66272971e-02, 1.61075898e-02, 1.59433320e-02, 1.55991861e-02,\n",
       "       1.50721674e-02, 1.48009892e-02, 1.43576234e-02, 1.36277104e-02,\n",
       "       1.32350200e-02, 1.27519917e-02, 1.25903703e-02, 1.20979413e-02,\n",
       "       1.18098781e-02, 1.12098170e-02, 1.08277440e-02, 1.04477523e-02,\n",
       "       1.02647051e-02, 9.88274535e-03, 9.74257138e-03, 9.31114503e-03,\n",
       "       9.14795316e-03, 8.95640894e-03, 8.72950586e-03, 8.42575751e-03,\n",
       "       8.13979814e-03, 7.89749805e-03, 7.39000998e-03, 7.20101586e-03,\n",
       "       7.08918353e-03, 6.90272334e-03, 6.78495251e-03, 6.47012955e-03,\n",
       "       6.40883777e-03, 6.01193511e-03, 5.66418607e-03, 5.63402788e-03,\n",
       "       5.38935217e-03, 5.12786334e-03, 5.11796180e-03, 4.81620125e-03,\n",
       "       4.38498746e-03, 4.10056057e-03, 3.69138981e-03, 3.21224918e-03,\n",
       "       2.55289125e-03, 2.43978225e-03, 2.39116326e-03, 2.24015629e-32])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr_out.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Principal components')"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,65), pr_out.explained_variance_ratio_, marker= 'o', alpha=0.5)\n",
    "plt.ylabel('explained variance ratio')\n",
    "plt.xlabel('Principal components')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Principal components')"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,65), np.cumsum(pr_out.explained_variance_ratio_), marker= 'o', alpha =0.3)\n",
    "plt.ylabel('cumulative explained variance ratio')\n",
    "plt.xlabel('Principal components')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Principal Component 1')"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9GiJBGmLwkQLwDXEDO93J2R5SCrrPrbYG0GaFA+DdIEhwgn4wBXluRl144P9Lmpphbq+MtESQEjm5QLCbNqgrS7Iy/rY2Nw+u2gzz74NgI3TlQPZRWPQTOGc7LCuemNhnAEsUpq9dT0HuICu588pg70uuXEdvHc2wbyPsXQ+tJyYkhA6Os4/fsoPvUsuvaOcwj3AP7bRQzlxyKaCAWcxhHq/xMlt5YcA5DvMUPrL77AsBkEEZjWyng2OczkIE6CKMT5SzZ+1gZcEuYl4XxLJ4W0Y2f18Ky2fweKdku7EGOVvgoKB73SI676885KIJfPvIyoK3XwD7D/Xd8KKjEzq74PKLemLyC96nfUhI0D3qHrsVouJmPcVLkaAH4e1vQsYCOB6EhigczQBfFbx7G/iaJy7+ac66nkxfka7B10+I5wazY/FOaVXX+th8n1uvAcQkBkuuwFt5o7s7HIN6XmUH/4YSxUcWdWyill+zhzqK+nXfCEIBs1jP7zm93wrvTo7jG2QNgxuF8BGhlVJq+ACX8hPWEcBHlhcikHOEFTnCLbybFfbnAYAUCr61PvQmhU4gd3wrt4d0/dXQ0AgvbYbu6Qf+AHz0AzC/71RWqRC8r8cHy48pXpHAsn7rKMJbXVfWmRXQFnZjFiGfmyYbrYXIDgieM/HfxzRkfwmmr8rTYd8GN5MKIBZxBQE7W2DWArfPBMCBLa6UR0Elnf5mGthOZ+wYmdueozN7EyWLbyXUrzjfSCK08zr/QYB8Ar2mjrZwgnxexGMF9FsT4SdIG60DzpXLIlpYR7Df6u8YEQQI4bodLmU1CyjnGV7lKA3MYzbns5zZ/TvlRxAjxivs5mm20EQ7y6jmbZw26oKHaUsVCRyI34WXAEnotgmF4C8/DNccgtr9EAzAkkVuMHsQJwfLhzxhpGdgPCvgHn0MMxJv+khpohCR/wLeBRxV1eXxY0XAfUANsAe4QdXNczCTYOnVLlG0HIWWOjj+pksU0U44/c9cGfPMfNj+EGQV0O5v4BjP4yNI0CskmpeNt+1Rti6McZr3JYKjeKNsZDtR2sik7wKrLArx4yfMHvz9thJtoo7Vg9SLKuNiDrOOMM0EcC0kJUYr+5jDFX0SUQ1l1DDGwom4JPEjHucptpBLJiEC/I4XeZxNfIEbmEf5yCdJZ9Ej0HYHRHfjeqtjEDgbsm4CScLK8opy9xgv/xLQaM/07m4ac8d8qStHP9WkeoziR8CV/Y59Efi9qi4Cfh//3EyWgkq47FZoOQ7710MsDNmzYNGl0HQA/ud2twivYS+akUcDW/GRgY8sQCAYItQRIBI+ypH4+oFERWgb9LiHRzk1NHOYLjoAN6upCXf/cA6XDfiaTMpYwmeIEaaVvfHHPsq4iLm8d3Q/kxFso5an2EINsymhgDyyqaaUAD5+wKN9NjGacrQDWv4ZoofAq3b9+14VhF+E1u+nOrrh+RZAYBVE94DGx9a0w30eugh8Y785mGlS2qJQ1T+ISE2/w9cCF8c/vht4CvjCpAVlXHmOQBasuN6NTQQyeu7I6va4bqesWUS7ThDJaCbQq9UgkQjq9xHwz+YYf6SKaxK/7DB39bMo5TzO4TleoYujKEoxZdzIJylhzqBfU8gy1vBNmtlJlE6yqCQjCV0mz/IqOWTi9bvvKiKXfRzjAMepHNXWTGmk62WInQB/Tc8x8VzSiGyG6AHwTdQc2QkmHmT/FXT8FrrWQawLJBMy3weh1FfunUrScYxitqoein98GJg92ItEZC2wFqC6eqLKXhoA6ve6wejQIH3DgUxX+O/UK5E//jsa0p7p7KoEGptpXL4E9QneKDfnyWUBuSykhd1kUYkgKEoHR8ikjFXczHkoxziInwAlzBlxAyCPAPmcOqo4RquZtkG3Z+2OrXOQ6btTRnQXSMbA4/G1JkQPpW+iAJAQZL4XMq4FbQPJBknHt730luqup2GpqsLg7XZVvVNV16jqmpKSKXq3lq58gb5TFHuLRtzainnn4y18B9n14NUfI9DQRLC+kfby2TQvW0QnxynhglFdVvBYwqfIZylt7KWNfbSylywqWcrf4GmUQHgnc8KtlGphWuwSB7CceTQN0m0WJoIPH2WjHBhPlB5VdGsM3a2u4F4yeHm4vVAHC0DdHfpUIAHw8i1JjFE6/tSOiEi5qh4SkXKI73RjJk/xQpcMulpdCY9usZjbZ6JqDXg+5OybCS6cx8ED/4jEPKJzFtJekk+7d4BMypg9hk2JguSzjM/RxiE6OUGQfNe66HwGOu7p6WvGBxnvcV0IY6kBPoHOZxmPsJ6jNFBCPoLQRYR9HON6LiB7DDv4DUfbldgPY+h6jY8tKzJH8P7Sh1RO8M8icCZ0/Nr93KVXsatYE3i54F88sdczaSkdWxQPAt1V5z4EPJDCWGYmfxDOvhlaj0PjIbcqu/UE1O12ZTyK47NFRMgtvpSKlXcRW30N9bO7CHtNVHAVy/m7k7ONxiKLcgpZTjZVSHgbtP0ApAB81e7hlUD7T6HrxQn6pscun2y+yPsop4i9HGUvxzhBE+/lQq5h4ufpx+6KJ4kqRapA5oqrnHp7FG2d4JaFrxwy/gyiByG6H2J1ENkL2gLZn3B36mbaEx2qi2EyLi7yM9zAdTFwBPgS8BvgflxNylrc9Ni64c6zZs0a3bBhQ3KDnYnqauGNJ+DYTsgqgsWXQcWqIRfTKZqc7qDmf4TYIfD6rcuINbm73NyvpbxVAe77fz3SwAvtXbSHC6jxhzg7C4omsN2uh5XoF6MwVwdUYdU94H1Y8C5OQj2uSC10PQexo+CfD8HzB/7/MFOOiGxU1TUjvS7Vs56GKnU6NWowT3dFc+Gcjyb88qSNGUR3gTfIgKnkQmwvrg89NPD5SfZqu/DtukKiChkC6xV+3Qx/XTSBZUAOu+6mQUt1Zym6S3rmDE4k/1z3mETapj3bps4XJDP1NwMzVTqOUZj+omE4sgPaG9yahilU6ntCSD7QAQO2DQ3HZ+Sk/te4NQbfrYMCD7J7Nbha4se/WQ5ZE9HRmyXxiQaDvGl2DqzyOhWpKrF1MfTnCpF4oggI3o2CXOwNvZ+FSZrU/4WZ4dXvhaf/Ddq6C+4J5M6Giz/j/p0JQu+A9nvAN6+ni0kVYgcg9C63b3iKbe2ADoWyfskgx4PjUXi1A86aiEXMC0BmCVqvSGGv3d26XFE87+x0HHYcHd2g6I9jUMXJ6rTaqcR+qHiFgqyyRDHZpv5v1XQW7oAnv+VaFEU18cdcV0bjqX/pKdA33YXeDoHVbkVt9LArKRHdA/5TIONdqY4OgMYoyFDDfQrNE/S/SnyC9wkfhAWtBT2u6H7goCAfEKRiar+Jqir6QAyK6VPCXEKutaQPxFIY3cxlLYp0dvAV6GhwCaK33FI30HxkB5QvS0lok0qCkP3XENkO4fW4WkNngH952sy6KQ8w5KZrIlA2gWHKPMH3NR+xF2OwS6AIvPM8pGpqJwkAIrjEN9hwSIEbsFcdOJBvkssSRTprPjzMWIT26o5KkVgjdP4ews+54muBsyHjHcmZDSM+CKxwjzS0NATlfjgUgTJffItxhcNRqPDDkgkea5d8wfeO1He5TTg/kI0rZ95/QXiHm79gSWLyWddTOssuHr57KSOFJaxjDdDy/1wdHfxuULlrHTT/X9c1NMP4BT5b7JJFbQT2ht2/FQH4TPHM3SFvtEQEuUzgkNB76r6qwiGBd9gPMhWsRZHO5qx0tZU6miCj174KbfWQWQhlS1MXW8ejED3ed8qkr8oViev4NWR/fGznjcXgxC5ob3QzvIpq0mKNRCKK/fClUtgTdpupFfpgbmDKhJ82vKs8Ym/E0O2KZsaTRTvIaYJ3ud3bpsKIiUJEAqoa7nesWFWPD/U1ZoKEsuGiT8PT/wptdeD53UZCoTy4+BZXkymJFKWFPTTxBoJHAcvI6q7UGn5m8DLNXhmEXwK9efTjB40H4ZnvQNPheN9NzK0CP/8TkF00/m9oEojAvODIrzNDkwzB+5wH24TYRpcovDMFlgpiTbOUGDJRiMglwE+ADBHZBKxV1T3xpx8HTk9+eIbSU+Cab8D+l6H1GOSVu5ZGMLnF2GKEeZPvc5yX6D1KO4d3UMP7EO0aYlpqfGMbRjk7JdIJT34TIh1uZhe4Tv76ffCHb8MVfz/m7VXN1CN+gZWCb2WqIzEwfIvin4ErVHWbiLwXeEJEPqiqLzDk/A6TFKFsWDC6SqzjdYBHOcYL5DDv5IprJcoBHiaHGkoCayC8EXz99oLQE+Bb4so7j8bBV9zgfO8ZXiJuS9a6PXB8J5RaATpjUmG4W7Sgqm4DUNVfANcBd4vIdQxR+ttMMUePwoMPwve/D48/Dg0NAMSIcpBHyeq334PgI0QxB3ikZ/1C9Ki781d1G9xoq6v/P1oN+1zX2lBajo3+nMaYCTFciyIsImWqehgg3rK4FPgdYJvNTnUvvgh33OE+zsiA55+HX/0KPvtZoosriNJOxiC7svnJoZ0jbrOanNug416I7HBP+uZB5qfAv3D08WQWDj3DSwRCOYM/Z4xJuuESxRdxu8sd7j6gqvtF5CLgk8kOzCRRXZ1rRZSUQGavsY6mJvj3f8f3jX/CH8wmQjv+fnspRGjqGdD2z4WcL0CsBVCQnLFP8ak8HTbd40qaB3vVumhvhGAuzE7OLnUxIri9+Gz8w5ihDJkoVHXdEMcbga8mLSKTfC+/DNFo3yQBkJcHtbV423ZQUbSM3XoPOW2zkfI5UFBATKJ0Usc8Ptj367wJuNvPzIfz/hKe+57rZvKH3AB3IAMu/pzbI2MCNfIatfySZnbiEaSMS6jgnQTJG/mLJ0kXTTTzBjGi5DCPTEpTHZKZoWwdxUxUXw/+If7XR6Pw/e9T3tZM+0VwZNFmOLEJyspgwUKqvfcwizOSE1fV6fAn/wT71kPzEcivhOo1fdeQTIATbGQH3yZAHtnMRYlwkMdp4FVWcBv+AVVqJ99B1rGHn6HEENxU5TIuZR5/hsc0XJFt0polipmouhrC4YHHVaG2FmbNwluxgoW1C5hT10xzwXHkycPkXXEDGWe/M7mxZRfBkiuSdvoYUXbzU0KUEMC1hIQAOcylhd0c4wXKeXvSrp+IBrbxFj8mi0p8uJaUEuMQj5PBLCq4OuFzddFIhDZCFOFLgz07zNQ0YsesiPxpIsfMFLJyJRQXu1lPqq4VsW8fPPYY7NkDubluhTSQ1ZzL7H3zKK1fSsZDqd92dLw6OEwXDSeTRG9BCjnOH1MQVV8HeIgAeSeTBIDgkUUFB3iEGJERz9FJHTv4Dhv4DJv536znFvbyADFmSMVhM6ESaVHcCvw8gWNmqgiF4G/+Br77XXjrLdi+3U2NLS52z23e7BLHuedCIL66OisLTiRQhLCpCZ57DjZtcrOpLrwQVq/uOY8ZUQt7Bx0r8ZFBB0eJ0EqQoet8RelgG7fTyXGyqETwiNLFXn5JlHbmcWMywzfT0HArs68CrgYqROTbvZ7KgwRuacZJRK4E/g3wAT9Q1a8n+5ozSlkZfOUr8J//6ZLE294GOTluPYXP55LCzp1wany2UWMjzB1hK8yjR+Ef/9G9tqAAIhHYssUlik9+Mi2SRSblBCkiTDMBcvs810U9VVyXosh6ZFBCF/UE6TuAH6MLjwA+hl+Vf4KXaecQOdScPOYjSDZzOcTjVHAlQQqSEbqZpobrejoIbMDtQbmx1+NBIHmdyICI+IDvAlcBS4H3i0gKK+BNY1u3wvLlkJ/vEsTixdDSAtnZrrWhCp2drqXwzhHGJ376U2hvdwklPx9mzYJ589wsqxdemJzvZwSCx3w+SCcn6OAYihKlkxb2kEU1xZyd6hCZw5V0cgLt1U2kKG0cYDaX9OmSGkwDWwcdkO8eBG9l78QGbKa94abHbgG2iMg9/YsCToKzgJ2q+haAiNwLXAtsn+Q4prdYDNra3HqKbvPnuzf7nTtdwqitdS2Bj3wElg2zSVJTE7zyClRV9T0u4hLG//yP64ZKA0WsZAV/xz4eoIHt+MikgndSwVUD1o2kQjFn0swVHGJdfH2HhxKhgOVUJ9Di8ZNFjKH/ZL0REo0x/SUyRnGWiHwZt+eUH1fnSVV1fhLjqgD29fp8P0wKtknvAAAgAElEQVTgrZ4qRF93m+5ED7mFY8FLwZ/MbykN+Xzujv/ECSiKV2cVcS2MoiJXhG/tWtfKyBlkrYSqG/zeuRNaW13LY7DCfcGgSzpJ0EmMN2ijkxiVhChLcGZPHotZxufReDUaSaPyZYLHPD7AbN5GHVuIEaaApeSxOKGFgcWcxSGeiE+t7Xl9mBb8ZJNrhRXMKCWSKO4CPoPrdkqbKRMishZYC1BdXT26L+58GNrvB8kCyYauDdD5HGR9FEKTW3wv5a67Dr75Tbf4rnsBXns7dHS4Ae/TThv86zo74c47YeNG97mqGwRvb3df03uFdl1dUloTr9DMHRygnSiK6545lwI+zBxCCa60TqcE0ZsgZFNNNqP83QZyWUQZl3KIJwhSgI8MumhAibKET+OR+rEiM7UkkigaVfWRpEfS1wGgdx9GZfzYSap6J3AnwJo1axIvUhg9Ah2/AF9lr/0SckA7oP1uCKyamJXGU8XKla7V8LOfwbF44b3MTPjYx4ZOEuCKCW7YADU1PUkhFnMzngoL3VoNVTdQLgKXXz6hYR+kk39jH0X4KYm/8SnK8zSQhY8PUj6h15tKBGE+f04hKzjEOjqpo4TzKOcysqka+QTG9JNIonhSRG4HfoXbyRYAVd2UtKhgPbBIRObhEsSNwJ9NyJnDW1zt2/6b6kgGaAQir0HwzAm51JRxwQVw1lmwNz7IWV3tuouG0tUF69ZBRUXflsP8+dDc7KbbgksUc+bApz4F5RP7xv0kdQiQ3WuVsiBUkcHT1HMdJeTO4PWkgkcRqylidapDMdNAIn9J3WMDa3odU0je8lVVjYjIJ4HHcNNj/6u75Pn4tYMM1S2h9MqFM0swCAsTrPra0uJWdvdPJiJuOm1Vleu2CgRcgkjCXqBv0U7eIKUs/PGupBOEZ3SiMGYijfiXpKqXTEYgg1z3YeDhCT+xbyEQdXe7vd/AVN0wvW+EtQLGDWwHAq5l0T9ZNDe7FslIay7GqZQgB+ggr9+vsJvuquRaPSRjJkwiJTxmi8hdIvJI/POlInJz8kNLEv8Slyyi+0DjY/Magdge8K8BrzKl4U0JwaAbc9i/3yXYbuGwmyZ75ZVJD+FiCmknRqTflqsH6eI0cphlU0BNP21tsP45+NVP4cnHoC6BQgPGSaRt/iPgh8Bt8c/fAO7DzYaaesQH2Z+G9nsg3F27SCB4GWTekJRukmnpmmvcSuyXXnKfq7rptjfcACtWJP3yi8niekr5DccQIIDQSYw5ZPAh5oz49WZmObgfvnc7NDdCIASRMPz2PvjAWjjjnFRHl/5EdfgJQyKyXlXPFJGXVXV1/NhmVV01KREmYM2aNbphw4bRf2GsCbQJpBC87IkPbLpTdQPgu3a5rqilS93iukm0nw420EQrURaTxUpyCdomRKaXaBS+dqtrURQV9xzv6IC6Y3Db12HWwM0cZwQR2aiqa0Z6XSItilYRmUV8n2wROQdoHGd86cHLgzTaqGbKEXFjEUkejxhOJRlUkpGy65v0t2cXHD8Glf1+TTMy3L3Ophfh8neN/fydjdCwCxAoXOg2ZJxuEkkUn8XVd1ogIs8BJcB7kxqVMcZMkNZm8IboUQ6GoO742M6rCjt/CzsfIH4b7e6dFr8X5l05vXqxE5n1tCm+T/YpuHlBr6eg9pMxxoxJUQlEYwMnOgJ0dQxsaSTqwPPw+s8hrxp88WVZ0TC89jPILIHyETt0po5EO3PPAlYCp+Mqud6UvJCMMWbiVFTBolPh8IG+k/Qa6yEzG1aO4Q1dFXb9FrJKepIEuI8zitxz08mILQoR+QmwANhMT60nBX6cxLiMMWlAFTbXwkObofYElOTCFafBBYvBN0XmDIjATR+Hu/8Ddr7uPhcgvwj+16chZwxjCrEItB6G/JqBz4XyoWnv4C2YqSqRMYo1wFIdaXqUMWbaeWwr/PR5KMyGsnxo64QfPAU7D8NfXDR13gjz8uGTX4T9tXD8KGTnwPzF4B/j4n3PD8EciHSAv99cikgbZBROnZ9NIhK5J3gVKEt2IMaY9NLUDj9/CaqLoCjbtSByM2FeCfzhddh9LNURjo4IVNXA6rNg8dLBk8ThBnjqNXhyOxysH/5cNVdAy8G+3VmqrqUx70po7YTXDsCbhyGSNnW3xyaRfFoMbBeRl+hbFPCapEVljEm5Nw65gsCBfu8SnoDfB1v2wvzS1MQ20WIxuO9F14Lq7ZJT4c/PH7ybbd4V0LATjm4GL14IINYFs8+CLYXw0H9D1NW/JzcDbr4ITht91fi0kEii+HKygzDGpJ+YwlDbdQjuzXW6eO5NeHgL1BT3JIVYDNZtg4pCuGz5wK/xBeGMW6DudTi6xbUySlfBhk745fOuJdadZFs64F8fgy+9G+YWDzxXuhux60lVnwZ2ALnxx2vxY8aYaWxBqUsI0X4JQRXCUVg2jcqiPbQZSnP7thw8z43LPLylb/dSb+LBrFPh1BthyfsgbyH8djPMKejbEsvJcJ93t1haO12Lbc+xqZFwE5n1dANwO/AU7vfmOyLyeVX9RZJjM8ak0KxcuGIF/G6ze8PMDkFnGA42wMpqWDxNRi5V4XAjzB2k+kx2yM32CkchmED/S2MbtHbBrEH2PivMhB0H4DcbXWLqTsCzcmDtJbAojX+eiXQ93QacqapHAUSkBFgHWKIwZpr707PclNjfvuzeMDMCcO0Z8M6Vg2+P3i0ShW0HYP1b7vMzamBFlRvbSDciLhG2dLjB+t7aOqEgEwIJxp0RBNQlgf7jGh1hONYCv1wP1bN6ztnQBv/8EPzDe6CsYNzfTlIkkii87iQRd4LEF+oZY6Ywz4O3L4OLT3VvdKHAyOsnOsPw7cfh1f2QFR/kfeZ1OHUOfPqK+JtpmnnnKrjzScgK9RqjiLc0brog8amu2SE4az5s2A2VRT3HVeFoM7R3wZLyvomnIAtaOuHJ1+D9507c9zSREkkUj4rIY8DP4p+/j2RsKGSMSVue595EE/HEqy5J1BT3vMGqwmsH4ZFX4N1pWNri/EWw9zg80W8fzYtPhUuWju5cN57jWl97jkNOCCIxlyBWVLmpsqHAwK8pyHQtsES1dcLGPe5nmpcJZy/o+/OeaInUevq8iFwPXBA/dKeq/jo54RhjprrHX3VdOb3ftETcAO+6bXDdGem3GM3z4APnu9bTjoOuNbGkHOaMYeFcQTb8/XWwcbebQhwKwLkL3c/kb342+IrtzgjMzk/s/EcaXVdVXStkBqArCo++Atesdkk4GT/bRNclPo8r3xED1o/3oiLyp7hpt6cCZ6nqhl7P3QrcHL/eX6vqY+O9njFmcqhCczsUZg18Luh3s30i0YFrM9JFeYF7jFdmEC44xT16W1bpWhW9rxFTN07xoQsYkSrc9bT7OfYefI9E4YFN7vynlI8//v4S2Qr1o8BLwLtx5cVfEJG/GOd1XwWuB/7Q71pLgRuBZcCVwH+ISBoOfxljBiPiVm43tA18rqkdqmal54D2ZLnpgp6ZVHUtrnWw5zhctARW14z89UebXKKZ3W8bHb/PtS6efi0pYSfUovg8sFpVTwDENzF6HvivsV5UVV+Ln6v/U9cC96pqJ7BbRHbiKtf+cazXMsZMrmtOh28+4gayu/vjO8NwvAU+cF76dTtNptI8+Mp74MVdrlsqOwTnL4alc4afRdatpcO9brCfYWYQTrROfMyQWKI4ATT3+rw5fiwZKoAXen2+P35s+otF4cgOOPY6BDJhzirIT0Ib0pgkWzUXbn4b/OxFCEcAAb8HH7oQzpiX6uhSLycDLl3mHqNVGm9JRKIDW2ZNHa6qbzIkkih2Ai+KSPc+TtcCr4jIZwFU9VuDfZGIrGPwYoK3qeoDY4y39/nXAmsBqqunaAGVbp0t8Id/g6NvuIL2GoWX74Pl18GKa2f2LZiZki5eCucshLfihQPnlbg7XjM+uZmu/tTjr0LNrJ5WSFO7m9Z74ZLkXDeRRLEr/ujW/SY/bBV3Vb1sDPEcAKp6fV4ZPzbY+e8E7gRYs2bN1C6BvuleOL4Timp6kkI0Aq/8CkoWQfkYbj2MSbGMICydGf0Bk+qGs91Mp2fie2ugkJ8Ff3NVT4tjoiUyPfb/JufSg3oQuEdEvgXMARbhBtKnr84WqP0j5Ff2bTn4/JCRC2+ss0RhjDkp6Ie/eBtcuxr217tB7PmlyZ0kkEitpzW4Mh5ze79eVU8b60VF5N3Ad4AS4CER2ayqV6jqNhG5H9gORIBPqOoUr+Q+go748I83yP/lYDY0H57ceIwxU8KsXPeYDIl0Pf0UN/NpK24dxbjFF+wNumhPVb8KfHUirjMlZBa4EpTRcN/NdwE6GqFidWriMsaYuEQSxTFVfTDpkcxUwUxYdCm89kjfMYpwh3uccnlKwzPGmEQSxZdE5AfA7+m7w92vkhbVTHPa9dDeALW9Zgb7AnDu/4LiBamLyxhjSCxRfARYAgTo6XpSwBLFRPEH4fyPw7I/gfpat3XW7CUQGqSovTHGTLJEEsWZqnrKyC8z41ZQ4R7GGJNGEtlX4vl4DSZjjDEzUCItinOAzSKyGzdGIYCOZ3qsMcaYqSORRHFl0qMwxhiTtkbselLVWqAA+JP4oyB+zBhjzAyQyH4Ut+AW3ZXGH/8tIp9KdmDGGGPSQyJdTzcDZ6tqK4CI/BNuf4jvJDMwY4wx6SGRWU+C25a0WzR+zBhjzAyQSIvih7j9KLprM10H3JW8kIwxxqSTRMqMf0tEngK6t/7+iKq+nNSojDHGpI0hE4WInAkUq+ojqroJ2BQ/frWIeKq6cbKCNMYYkzrDjVH8E25fiP62AbcnJxxjjDHpZrhEkTvYeon4seLkhWSMMSadDJcoCod5LmuiAzHGGJOehksU60TkqyI9GzmL8xXgf5IfmjHGmHQwXKL4HDAf2CkivxSRXwJvAouBz47noiJyu4jsEJFXROTXIlLQ67lbRWSniLwuIleM5zrGGGPGb8hZT/GV2O8XkfnAsvjhbar61gRc9wngVlWNxFd63wp8IV7O/Mb49ebgWjWLVTU6zLmMMcYkUSLrKN4CJiI59D7n470+fQF4b/zja4F7VbUT2C0iO4GzcCVDjDHGpEAiJTyS7S+AR+IfVwD7ej23P37MGGNMiiRSwmNMRGQdUDbIU7ep6gPx19wGRHDVaUd7/rXAWoDq6upxRGqMMWY4w63MLhruC1W1boTnLxvueRH5MPAu4FJV1fjhA0BVr5dVxo8Ndv47gTsB1qxZo4O9xhhjzPgN16LYCCiDV4pV3IyoMRGRK4G/BS5S1bZeTz0I3CMi38INZi8CXhrrdYwxxozfcLOe5iXxuv8OhIAn4ss0XlDVj6vqNhG5H1c6JAJ8wmY8GWNMaiU0RiEihbi7+4zuY6r6h7FeVFUXDvPcV4GvjvXcxhhjJtaIiUJEPgrcghsv2Aycg5uu+vbkhmaMMSYdJDI99hbgTKBWVS8BVgMNSY3KGGNM2kgkUXSoageAiIRUdQdwSnLDMsYYky4SGaPYH6/F9Bvc4HM9MKD8uDHGmOkpkRIe745/+GUReRLIBx5NalTGGGPSRqKznk7H7ZmtwHOq2pXUqIwxxqSNEccoROTvgbuBWbid7X4oIv872YEZY4xJD4m0KD4ArOw1oP113DTZ/5fMwIwxxqSHRGY9HaTXQjvciupB6y8ZY4yZfhJpUTQC20TkCdwYxeXASyLybQBV/eskxmeMMSbFEkkUv44/uj2VnFCMMcako0Smx949GYEYY4xJT8PtR3G/qt4gIltxXU59qOppSY3MGGNMWhiuRXFL/N93TUYgxhhj0tNw+1Ecin/oAYd6TY/NBGZPQmzGGGPSQCLTY38OxHp9Ho0fM8YYMwMkkij8vUt2xD8OJi8kY4wx6SSRRHFMRK7p/kRErgWOJy8kY4wx6SSRRPFx4O9EZK+I7AO+AHxsPBcVkX8QkVdEZLOIPC4ic+LHRUS+LSI748+fPp7rGGOMGb8RE4Wq7lLVc4ClwKmqep6q7hzndW9X1dNUdRXwO+Dv48evwu3NvQhYC3xvnNcxxhgzTonsmR0C3gPUAH4RAUBVvzLWi6pqU69Ps+lZp3Et8GNVVeAFESkQkfJeM7CMMcZMskRKeDyAq/e0EeicqAuLyFeBm+LnviR+uALY1+tl++PHLFEYY0yKJJIoKlX1ytGeWETWAWWDPHWbqj6gqrcBt4nIrcAngS+N8vxrcd1TVFdXjzY8Y4wxCUokUTwvIitUdetoTqyqlyX40p8CD+MSxQGgqtdzlQxR0lxV7wTuBFizZs2AEiPGGGMmRiKzni4ANorI6/GZSFtF5JXxXFREFvX69FpgR/zjB4Gb4rOfzgEabXzCGGNSK5EWxVVJuO7XReQU3IrvWtwUXHAti6uBnUAb8JEkXNsYY8woDFc9Ni8+O6l5oi+qqu8Z4rgCn5jo65mppZkI7cQoxE8goUavMSaZhmtR3IOrHLsRN31Vej2nwPwkxmVmoDrC3MMhNtGMAJn4+BNKuJwivD6/fsaYyTRc9dh3iVs0cZGq7p3EmMwM1EaUr7OHesJUEsJD6CDKf3OIDqJcS2mqQzRmxhq2XR/vCnpokmIxM9h6mjhKFxXxJAGQgY9qQvyO47QSTfhcB+jgNxzlbg7yHA20j+JrjTEDJTKYvUlEzlTV9UmPxsxYW2gmZ5D7lgAeUZR9dLCE7BHP8yjHuZcj+IAAwpPUMYsgf8tcZhNKQuTGTH+JjBSejSunsWuipsca018mHpGBO+6eFEhgjGI37fyMw1QQpIoMyghRQyZtRLmTA+gw5zfGDC2RFsUVSY/CzHjnUsAzNKAo0ispNBMhHz81ZI54jmdpIIg3YKZUKQHeop2DdFJBRsIxtRBhA03soYNiApxFPqW2FYuZgYabHpuBW9+wENgK3KWqkckKzMwsS8nmfAp4lgaK8JOBRz0RosBnqMKXQIviGF1kDtJIFgQPaBnFWMUe2vkGtbQSJQOPTmL8mmN8lDmcS8EovjNjpr7hWhR3A2HgGdyiu6XALZMRlJl5PISPUsFKcvg9dTQQ4RzyuZxZVCXYClhAJq/SQhGBPsdj8U6nkgRbAxFifId9eMDcXtfuIMoPOMhCshI+lzHTwXCJYqmqrgAQkbuAlyYnJDNT+RDOoYBzxnjHfj4FPMRxmoiQF//VVpS9dHIe+QMSyFB20k4d4T5JAtwsrBhh1tPE1RSPKUZjpqLhBrPD3R9Yl5OZCooJ8jnmEgVq6WAvHdTSyZnk8UHKEz5PM5EhO7pCCHU9fxrGzAjDtShWikj3BkMCZMY/F9wSi7ykR2fMKJ1CNt9gEW/SRjsx5hCifJTTYksJEoMBA+sAHSjVoxgQN2Y6GG5ltm8yAzFmNBqJcJwu8vAPGC8I4LGUnDGfu5oMTiWbN2mlgtDJZHGCMPn4OQO7RzIzSyLTY41JGx1E+SmHeY4GBIgCy8nmL6hIeAxiJILwl1Tyn+znNVpdExo3GP4pqsjG7qHMzGKJwkwZivJ9DrCRZqoI4UNQlNdp4xvU8mXmE5ygarN5+Pk8c9lHJ8foIhcfC8hKaJquMdONJQozZRygk400M7dXd5AgVBBiDx28SgunT2C3kCBUk2FjEmbGs2L/Zso4QCcCAwaYAYIIb9I2+UEZMwNYojBTRsYwv64RlBwbOzAmKSxRmCnjFLLIxBtQcjxMDAWbjWRMkqQ0UYjI50RERaQ4/rmIyLdFZGe8Uu3pqYzPpJcMfHycSuqJsJ9OGolwkE7208X7mE2ZlRE3JilSNpgtIlXAO4Deu+ddBSyKP84Gvhf/1xgATiOXf2ABf6Cet2injBBvo4AFZKU6NGOmrVTOevoX4G+BB3oduxb4cXxnvRdEpEBEylX1UEoiNGmpnBDvoyzVYRgzY6Sk60lErgUOqOqWfk9VAPt6fb4/fswYY0yKJK1FISLrYNDbvtuAv8N1O43n/GuBtQDV1dXjOZUxxphhJC1RqOplgx0XkRXAPGCLiABU4vblPgs4AFT1enll/Nhg578TuBNgzZo1tselMcYkyaR3PanqVlUtVdUaVa3BdS+drqqHgQeBm+Kzn84BGm18whhjUivdSng8DFwN7ATagI+kNhxjjDEpTxTxVkX3xwp8InXRGGOM6c9WZhtjjBmWJQpjjDHDSnnXk5nZFOUt2llPEy1EOZVsTieXTCvwZ0zasERhUkZR7uUwj3KCIB4BhGepp5QQX2Aus/ptcWqMSQ3rejIp8yqtPMIJqsmgghClBKkhkwbC3I3NijYmXViLwqTMU9SRg2/A9qLlBNlKC3WE8SM8RwMbaCKEx/kUcCZ5E7bl6WRTlCaiKEo+/kE3YTIm3ViiMClTR5jMQd7wBcFD2EsHP+EQJ+iikABRlDvYzzNk8xnmEppiyWI37dzDYXbGd+KrJMSNzGYZuSmOzJjhTa2/NDOtLCSLxn6bEIHbiMgDnqSOZiLUkEk+fooIMI8MttPKM9RPfsDjsJ8OvsZuDtJBNSGqCdFEhNvZyw5aUx2eMcOyRGFS5hKKUKCZyMljUZS9dPI2CthKC2X9BrQFoYQAv6du4gOKvAWt/wlNn4Pmr0LXS6CxCTn1wxwHoIQgEv+vkAC5+PgFR1CsXJlJX5YoTMrMIcRnqCIM1NLBXjrYTyeXM4srmQWAN0gffhCPNibmDfykrg3Q/BUIvwwEIHYUWr8D7T8CHf+b+CaaKSUw4HgRfnbSTsdEfz/GTCAbozAptZxcvskidtFOFzEqyaCIADGUYoI0EyG336/pCSKcNZH7Y2sntP8X+EpB4jvlSQZIPnQ+DcELwb9oXJcIIEQY+AcXA3wwYEDfmHRiLQqTcgE8lpDNaeRSFL/r9hCup5RjhGmLj2MoSgNhYujJFseEiOyCWHtPkugmHkgQutaP+xIXU8gROgccP0wXZ5I/ZWdxmZnBWhQmbZ1NHmEquJ8jHCeM4rZB/SvKqSRjAq8UARnqjt4PtI/7Cpczi/U0sYcOSgggwAnC5ODnekrHfX5jkskShUlbgnAhhZxDPofpwo9QFh8MnlC++A6JGgHp/yfRDv7Txn2JPPzcxjyepp5naCCKciXFXErRyVaUMenKEoVJewE8qia0BdGPVwDBK6Dzd+CrcOMTGoXoQfBVQWDlhFwmFz/vooR3UTIh5zNmsliiMAYg873g5ULnQxA75o4Fz4bMG904hTEzmCUKYwDEBxlXQ+hy0EYgE7zsVEdlTFqwRGFMbxIAKU51FMakFZuTZ4wxZlgpSRQi8mUROSAim+OPq3s9d6uI7BSR10XkilTEZ4wxpkcqu57+RVW/0fuAiCwFbgSWAXOAdSKyWFUHVo4zxhgzKdKt6+la4F5V7VTV3cBO4KwUx2TM8DQG/7+9ew+ysq7jOP7+sKu4qEkgiQq2DjI6qElKXhIbp6hMHdFyAicvlEU2ajrZmJeatLLJSs2GclI0tWEyRBHGTAVvYyYgILeVVBTUVbyLF0SQ3U9//H6bR9g963J299mzfl8zZ/Z5fs9zzvn+eNj9Ptfvr/k1aH676EhC6BJFHlGcIelkYD5wju03gF2BOSXrNOa2zUiaCEwE2G233bo41BDasGEuvHczNL0OMtTuC3UnQM3ORUcWQqfpsiMKSbMlLWvlNRa4ChgGjARWA5d19PNtX217lO1RgwbFA0yhABvmwNpJqbps7W7QZyhsfALe+TU0d0EZ9BAK0mVHFLbHfJT1JF0D3J5nnweGliwekttC6FncBOumQp/BHzxvoT5QMxg2Pgvr74e6rxcaYgidpai7nkqPy48DluXpmcB4SX0l7Q4MB+Z1d3whtKv5VfCa1h/K6zMA3l/Q/TGF0EWKukbxW0kjAQOrgO8D2G6QNBV4DNgInB53PIUeSbWA02mnzSrPNoH6FhFVCF2ikERh+6Qyyy4BLunGcELoOA2AmmHQ/OKHn+S20x1Q24wtLrYQOllPuz02hOogQd2J4PehqRG8Lt0e27QKaveErQ8uOsIQOk3UegphS9XWw/YXw/pZsHERqA7qToK+o1Op8hB6iUgUIVSiZjD0Owlo82xqCFUvTj2FEEIoKxJFCCGEsiJRhBBCKCsSRQghhLIiUYQQQihLtouOoWKSXgGeKTqODtgReLXoILpY9LF3iD5Wv3L9+7Ttdquq9opEUW0kzbc9qug4ulL0sXeIPla/zuhfnHoKIYRQViSKEEIIZUWiKMbVRQfQDaKPvUP0sfpV3L+4RhFCCKGsOKIIIYRQViSKAkg6R5KlNJCBkj9KWiFpiaT9i45xS0n6naT/5n5Ml9S/ZNn5uY+PS/pqkXFWStIRuR8rJJ1XdDyVkjRU0n2SHpPUIOms3D5A0ixJT+afnyw61kpJqpH0qKTb8/zukubmbfkPSVsXHWMlJPWXNC3/Hi6XdEil2zESRTeTNBT4CvBsSfPXSMO+DgcmAlcVEFpnmQXsY/szwBPA+QCSRgDjgb2BI4A/S6opLMoK5Lj/RNpuI4ATcv+q2UbgHNsjgIOB03OfzgPusT0cuCfPV7uzgOUl85cCV9jeA3gDOLWQqDrPlcCdtvcC9iP1taLtGImi+10BnEsaBrbFWOBGJ3OA/puMK141bN9te2OenQMMydNjgZtsr7e9ElgBHFhEjJ3gQGCF7adtbwBuIvWvatlebXthnn6b9MdlV1K/bsir3QAcW0yEnUPSEOAoYHKeF/BFYFpepar7KGkH4AvAtQC2N9heQ4XbMRJFN5I0Fnje9uJNFu0KPFcy35jbqt13gH/l6d7Ux97Ul81Iqgc+C8wFdrK9Oi96EdipoLA6yx9IO2rNeX4gsKZk56bat+XuwCvAX/PptcmStqXC7RgDF3UySbOBwa0suhC4gHTaqaqV66PtGXmdC0mnM6Z0Z2yhMpK2A24Bzrb9VtrhTmxbUtXeJinpaOBl2wskHV50PF2kFtgfONP2XElXsslppi3ZjpEoOpntMUjCZ6wAAAXASURBVK21S9qXlO0X51++IcBCSQcCzwNDS1Yfktt6pLb62ELSBOBo4Ev+4P7rqupjO3pTX/5P0lakJDHF9q25+SVJO9tenU+HvlxchBU7FDhG0pHANsAnSOfz+0uqzUcV1b4tG4FG23Pz/DRSoqhoO8app25ie6ntT9mut11P2qD7234RmAmcnO9+Ohh4s+QwsapIOoJ0aH+M7XdLFs0ExkvqK2l30oX7eUXE2AkeAYbnu2W2Jl2kn1lwTBXJ5+qvBZbbvrxk0UzglDx9CjCju2PrLLbPtz0k//6NB+61/S3gPuD4vFq19/FF4DlJe+amLwGPUeF2jCOKnuEO4EjSBd53gW8XG05FJgF9gVn5yGmO7dNsN0iaSvpPuxE43XZTgXFuMdsbJZ0B3AXUANfZbig4rEodShr4e6mkRbntAuA3wFRJp5IqNH+zoPi60k+AmyT9CniUfCG4ip0JTMk7MU+T/p70oYLtGE9mhxBCKCtOPYUQQigrEkUIIYSyIlGEEEIoKxJFCCGEsiJRhBBCKCsSRSicpCZJiyQtk3SzpH5trHdHaTXaDnz+LpKmtb9mm+9f1VLpd5P27ST9RdJTkhZIul/SQVv6PT2BpJH5gbTWlg3MFWbfkTSpu2MLxYlEEXqCdbZH2t4H2ACcVrowP4jYx/aRucBZh9h+wfbx7a/ZYZOB14Hhtg8g3a++WUKpMiNJz/S05j3gZ8CPuy+c0BNEogg9zYPAHpLq83gPNwLLgKEte/Z52XJJ1+SxE+6WVAcgaQ9JsyUtlrRQ0rC8/rK8fIKkGXnv/0lJP2/5Ykm35SODBkkTywUpaRhwEPBT280Atlfa/mde/qN8hLRM0tm5rT6PEXC9pCckTZE0RtJDOZYD83oXSfqbpIdz+/dyu5TG+1gmaamkcbn98NyfljEIpuQnrZF0gKQHcr/uyuUbyOtfKmlejuWw/IDWL4Bx+QhvXGmfba+1/W9SwggfJ7bjFa9CX8A7+WctqbTAD4B6UoXPg0vWW0XaY68nPd09MrdPBU7M03OB4/L0NkC/vP6y3DYBWE2qGlpHSkKj8rIB+WdL+8DS790k5mOA6W305wBgKbAtsB3QQKrG2hL3vqSdtAXAdYBIZaBvy++/CFic49iRVKl2F+AbpPE+akjVP58FdgYOB94k1SnqAzwMjAa2Av4DDMqfO470FDnA/cBlefpIYHbJv8+kdrZXu+vEq3e9ooRH6AnqSspGPEgqobAL8IzT+BytWWm75T0LgHpJ2wO72p4OYPs9AJVUQM1m2X4tL7uV9Ed1PvBDScfldYaS6lG9tgX9GU1KImtLvuMwUr2dlbaX5vYG0mAylrSUlEhazLC9Dlgn6T7SGBijgb87lT55SdIDwOeAt4B5thvz5y7Kn7UG2IcPyqnUkJJki5bCfws2+e4QPiQSRegJ1tkeWdqQ/7CtLfOe9SXTTaS9749q07o1Vio7PQY4xPa7ku4nHZG0pQHYT1KNO1azqjTu5pL5Zj78+7hZjB343Kb8WQIabB/Sznta1g+hVXGNIvQaTiOzNUo6FkCpUm1rd1B9WWkM4TrSSF8PATsAb+QksRdpONBy3/UU6Sjk4pLrAfWSjiIdFR0rqZ/SoDHH5baOGCtpG0kDSaeWHsmfMU5pzOdBpJHMylXgfRwYJOmQHN9WkvZu53vfBrbvYKyhl4tEEXqbk0inkJaQzs+3NsDSPNK4C0uAW2zPB+4EaiUtJ1VMbeuUV6nvkq4VrMgXy68nDYyzME/PI10zmWz70Q72Ywmp/PUc4Je2XwCm5/bFwL3AuU5lpVvlNEzr8cClkhYDi4DPt/O99wEjWruYDelWYeByYIKkRlX/WOHhI4jqseFjRWlQpVG2zyg6lrZIuoh0gf/3RccSAsQRRQghhHbEEUUIIYSy4ogihBBCWZEoQgghlBWJIoQQQlmRKEIIIZQViSKEEEJZkShCCCGU9T8LrxuK8rqG+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "color_idx = pd.factorize(y.x)[0]\n",
    "plt.scatter(pr_out_df.iloc[:,0], -pr_out_df.iloc[:,1], c=color_idx, cmap=plt.cm.hsv, alpha=0.5, s=50)\n",
    "plt.ylabel('Principal Component 2')\n",
    "plt.xlabel('Principal Component 1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Principal Component 1')"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(pr_out_df.iloc[:,0], -pr_out_df.iloc[:,2], c=color_idx, cmap=plt.cm.hsv, alpha=0.5, s=50)\n",
    "plt.ylabel('Principal Component 3')\n",
    "plt.xlabel('Principal Component 1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering the Observations of the NCI60 Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "deng_plot= pd.DataFrame(std_X, index=y.x)\n",
    "hc_c= linkage(std_X, method='complete')\n",
    "fig, axes = plt.subplots(1, 1, figsize=(20, 8))\n",
    "dendrogram(hc_c, labels=deng_plot.index)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hc_s= linkage(std_X, method='single')\n",
    "fig, axes = plt.subplots(1, 1, figsize=(20, 8))\n",
    "dendrogram(hc_s, labels=deng_plot.index)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hc_a= linkage(std_X, method='average')\n",
    "fig, axes = plt.subplots(1, 1, figsize=(20, 8))\n",
    "dendrogram(hc_a, labels=deng_plot.index)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kmean with n=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=4, n_init=20, n_jobs=None, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k4= KMeans(n_clusters=4, n_init=20)\n",
    "k4.fit(std_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n",
       "      dtype=int32)"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k4.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": "3.6.5"
  }
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