08-Artificial-Datasets.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.datasets import make_regression\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.datasets import make_low_rank_matrix\n",
    "from sklearn.datasets import make_blobs # sample data for clustering\n",
    "from sklearn.datasets import make_circles\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To generate sample data for Regression\n",
    "X, y = make_regression(n_samples=100, n_features=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 10)\n",
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_features = pd.DataFrame(X, columns= ['f1','f2','f3','f4','f5','f6','f7','f8','f9','f10'])\n",
    "df_target = pd.DataFrame(y, columns=['target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_df = pd.concat([df_features, df_target], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>f1</th>\n",
       "      <th>f2</th>\n",
       "      <th>f3</th>\n",
       "      <th>f4</th>\n",
       "      <th>f5</th>\n",
       "      <th>f6</th>\n",
       "      <th>f7</th>\n",
       "      <th>f8</th>\n",
       "      <th>f9</th>\n",
       "      <th>f10</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.913168</td>\n",
       "      <td>0.927409</td>\n",
       "      <td>1.415906</td>\n",
       "      <td>-0.822259</td>\n",
       "      <td>1.464733</td>\n",
       "      <td>-1.338005</td>\n",
       "      <td>1.991330</td>\n",
       "      <td>-0.399388</td>\n",
       "      <td>2.100044</td>\n",
       "      <td>1.342076</td>\n",
       "      <td>394.051890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.674431</td>\n",
       "      <td>1.054641</td>\n",
       "      <td>-0.387112</td>\n",
       "      <td>0.104318</td>\n",
       "      <td>0.993041</td>\n",
       "      <td>0.268246</td>\n",
       "      <td>-0.725284</td>\n",
       "      <td>1.518438</td>\n",
       "      <td>1.514252</td>\n",
       "      <td>0.644414</td>\n",
       "      <td>148.349068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.044795</td>\n",
       "      <td>-0.383434</td>\n",
       "      <td>0.140073</td>\n",
       "      <td>-0.128181</td>\n",
       "      <td>-2.025158</td>\n",
       "      <td>-0.317908</td>\n",
       "      <td>1.591418</td>\n",
       "      <td>0.143590</td>\n",
       "      <td>-1.092297</td>\n",
       "      <td>-1.026773</td>\n",
       "      <td>-40.759026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.231025</td>\n",
       "      <td>-0.553408</td>\n",
       "      <td>-0.385695</td>\n",
       "      <td>0.011788</td>\n",
       "      <td>-1.244047</td>\n",
       "      <td>-0.607165</td>\n",
       "      <td>1.034472</td>\n",
       "      <td>0.490176</td>\n",
       "      <td>-1.451153</td>\n",
       "      <td>-0.558683</td>\n",
       "      <td>-103.955576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.127745</td>\n",
       "      <td>1.007503</td>\n",
       "      <td>0.559915</td>\n",
       "      <td>-0.815956</td>\n",
       "      <td>0.404320</td>\n",
       "      <td>0.116163</td>\n",
       "      <td>0.220923</td>\n",
       "      <td>-2.370364</td>\n",
       "      <td>0.077747</td>\n",
       "      <td>-0.408616</td>\n",
       "      <td>65.073547</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         f1        f2        f3        f4        f5        f6        f7  \\\n",
       "0 -0.913168  0.927409  1.415906 -0.822259  1.464733 -1.338005  1.991330   \n",
       "1 -0.674431  1.054641 -0.387112  0.104318  0.993041  0.268246 -0.725284   \n",
       "2 -0.044795 -0.383434  0.140073 -0.128181 -2.025158 -0.317908  1.591418   \n",
       "3  0.231025 -0.553408 -0.385695  0.011788 -1.244047 -0.607165  1.034472   \n",
       "4  1.127745  1.007503  0.559915 -0.815956  0.404320  0.116163  0.220923   \n",
       "\n",
       "         f8        f9       f10      target  \n",
       "0 -0.399388  2.100044  1.342076  394.051890  \n",
       "1  1.518438  1.514252  0.644414  148.349068  \n",
       "2  0.143590 -1.092297 -1.026773  -40.759026  \n",
       "3  0.490176 -1.451153 -0.558683 -103.955576  \n",
       "4 -2.370364  0.077747 -0.408616   65.073547  "
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To generate sample data for classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_classification(n_samples=100, n_classes=2, n_features=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 10)\n",
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_features = pd.DataFrame(X, columns= ['f1','f2','f3','f4','f5','f6','f7','f8','f9','f10'])\n",
    "df_target = pd.DataFrame(y, columns=['Target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "cl_df = pd.concat([df_features, df_target], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>f1</th>\n",
       "      <th>f2</th>\n",
       "      <th>f3</th>\n",
       "      <th>f4</th>\n",
       "      <th>f5</th>\n",
       "      <th>f6</th>\n",
       "      <th>f7</th>\n",
       "      <th>f8</th>\n",
       "      <th>f9</th>\n",
       "      <th>f10</th>\n",
       "      <th>Target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-2.026620</td>\n",
       "      <td>-0.358752</td>\n",
       "      <td>0.015310</td>\n",
       "      <td>-2.003685</td>\n",
       "      <td>0.252852</td>\n",
       "      <td>-2.635484</td>\n",
       "      <td>0.934125</td>\n",
       "      <td>0.615134</td>\n",
       "      <td>-1.437701</td>\n",
       "      <td>0.142010</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-1.776940</td>\n",
       "      <td>1.919003</td>\n",
       "      <td>0.695889</td>\n",
       "      <td>-0.085970</td>\n",
       "      <td>2.284320</td>\n",
       "      <td>-1.836520</td>\n",
       "      <td>-2.346665</td>\n",
       "      <td>1.229582</td>\n",
       "      <td>-1.183572</td>\n",
       "      <td>0.090022</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-1.811194</td>\n",
       "      <td>-1.634538</td>\n",
       "      <td>0.720920</td>\n",
       "      <td>0.088268</td>\n",
       "      <td>0.365835</td>\n",
       "      <td>-2.228433</td>\n",
       "      <td>0.786816</td>\n",
       "      <td>-1.294814</td>\n",
       "      <td>-1.264271</td>\n",
       "      <td>0.117686</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>-0.797181</td>\n",
       "      <td>-1.575730</td>\n",
       "      <td>0.359327</td>\n",
       "      <td>-1.144602</td>\n",
       "      <td>0.580876</td>\n",
       "      <td>0.277411</td>\n",
       "      <td>0.027376</td>\n",
       "      <td>-0.854599</td>\n",
       "      <td>-0.352169</td>\n",
       "      <td>-0.039711</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>-0.468045</td>\n",
       "      <td>0.559827</td>\n",
       "      <td>-0.056853</td>\n",
       "      <td>0.863555</td>\n",
       "      <td>0.711841</td>\n",
       "      <td>2.010979</td>\n",
       "      <td>0.797358</td>\n",
       "      <td>0.257760</td>\n",
       "      <td>0.093292</td>\n",
       "      <td>-0.157724</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>-0.257217</td>\n",
       "      <td>-0.025957</td>\n",
       "      <td>-0.186582</td>\n",
       "      <td>1.839095</td>\n",
       "      <td>0.823546</td>\n",
       "      <td>2.281162</td>\n",
       "      <td>-0.095549</td>\n",
       "      <td>1.451633</td>\n",
       "      <td>0.242208</td>\n",
       "      <td>-0.172208</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>2.507956</td>\n",
       "      <td>-2.017396</td>\n",
       "      <td>1.397697</td>\n",
       "      <td>2.181058</td>\n",
       "      <td>0.573114</td>\n",
       "      <td>-0.559795</td>\n",
       "      <td>0.514619</td>\n",
       "      <td>-1.101878</td>\n",
       "      <td>1.158747</td>\n",
       "      <td>0.102171</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>-0.315652</td>\n",
       "      <td>-0.413489</td>\n",
       "      <td>1.132358</td>\n",
       "      <td>-1.017091</td>\n",
       "      <td>0.535803</td>\n",
       "      <td>0.265350</td>\n",
       "      <td>-2.107606</td>\n",
       "      <td>1.444493</td>\n",
       "      <td>-0.114197</td>\n",
       "      <td>-0.027034</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-1.468423</td>\n",
       "      <td>0.426380</td>\n",
       "      <td>0.707451</td>\n",
       "      <td>0.144921</td>\n",
       "      <td>-1.582110</td>\n",
       "      <td>-1.695074</td>\n",
       "      <td>-0.143985</td>\n",
       "      <td>-0.084334</td>\n",
       "      <td>-1.006883</td>\n",
       "      <td>0.087295</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>1.073761</td>\n",
       "      <td>0.209472</td>\n",
       "      <td>0.082074</td>\n",
       "      <td>0.778967</td>\n",
       "      <td>-0.118991</td>\n",
       "      <td>0.351435</td>\n",
       "      <td>-0.044081</td>\n",
       "      <td>-0.501446</td>\n",
       "      <td>0.592081</td>\n",
       "      <td>0.000754</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          f1        f2        f3        f4        f5        f6        f7  \\\n",
       "23 -2.026620 -0.358752  0.015310 -2.003685  0.252852 -2.635484  0.934125   \n",
       "15 -1.776940  1.919003  0.695889 -0.085970  2.284320 -1.836520 -2.346665   \n",
       "12 -1.811194 -1.634538  0.720920  0.088268  0.365835 -2.228433  0.786816   \n",
       "50 -0.797181 -1.575730  0.359327 -1.144602  0.580876  0.277411  0.027376   \n",
       "97 -0.468045  0.559827 -0.056853  0.863555  0.711841  2.010979  0.797358   \n",
       "85 -0.257217 -0.025957 -0.186582  1.839095  0.823546  2.281162 -0.095549   \n",
       "82  2.507956 -2.017396  1.397697  2.181058  0.573114 -0.559795  0.514619   \n",
       "35 -0.315652 -0.413489  1.132358 -1.017091  0.535803  0.265350 -2.107606   \n",
       "14 -1.468423  0.426380  0.707451  0.144921 -1.582110 -1.695074 -0.143985   \n",
       "62  1.073761  0.209472  0.082074  0.778967 -0.118991  0.351435 -0.044081   \n",
       "\n",
       "          f8        f9       f10  Target  \n",
       "23  0.615134 -1.437701  0.142010       0  \n",
       "15  1.229582 -1.183572  0.090022       0  \n",
       "12 -1.294814 -1.264271  0.117686       0  \n",
       "50 -0.854599 -0.352169 -0.039711       0  \n",
       "97  0.257760  0.093292 -0.157724       1  \n",
       "85  1.451633  0.242208 -0.172208       1  \n",
       "82 -1.101878  1.158747  0.102171       1  \n",
       "35  1.444493 -0.114197 -0.027034       0  \n",
       "14 -0.084334 -1.006883  0.087295       0  \n",
       "62 -0.501446  0.592081  0.000754       1  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cl_df.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To generate sample data for dimentiality reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def variance_plot(n_samples=100, n_features=10, effective_rank=2, tail_strength=0.5):\n",
    "    \n",
    "    X = make_low_rank_matrix(n_samples=n_samples,\n",
    "                             n_features=n_features,\n",
    "                             effective_rank=effective_rank,\n",
    "                             tail_strength=tail_strength)\n",
    "    \n",
    "    pca = PCA(n_components=n_features)\n",
    "    X_reduced = pca.fit_transform(X)\n",
    "    \n",
    "    cum_variance= np.cumsum(pca.explained_variance_ratio_)\n",
    "    print('comulative variance {}'.format(cum_variance))\n",
    "    \n",
    "    plt.figure(figsize=(12,10))\n",
    "    plt.plot(cum_variance)\n",
    "    plt.xlabel('n_components')\n",
    "    plt.ylabel('cumulative variance')\n",
    "    \n",
    "    return { 'matrix': X, 'pca_model': PCA}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "comulative variance [0.53297291 0.87046136 0.9642102  0.98167374 0.98672269 0.98993426\n",
      " 0.99287004 0.99549062 0.99786827 1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot = variance_plot(tail_strength=0.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "comulative variance [0.48078877 0.79658486 0.90532142 0.93697819 0.95229848 0.96345978\n",
      " 0.97402975 0.98358841 0.99217372 1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_1 = variance_plot(tail_strength=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "comulative variance [0.42443073 0.70905565 0.82766063 0.87500381 0.90363728 0.92659967\n",
      " 0.94775997 0.96695881 0.98428221 1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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TAoAo1AAAhY6129nQdmYLvaO+TZI0Ljddb58zQddOG6tl1cUak85/bADA2fgnIwAkqLaeAa2t9emlfT6t8TbK39kvY6T55fn69FtrdO20sZo1MZen0ABwERRqAEgQ1lrVho+1e2lfozYfaVEgfKzdypoSrZo+VitqSlSYneZ2VACIKRRqAIhjPf0BvXLQHy7RPjW0ho61mzEhV38dPtZuHsfaAcCwUKgBIM4ca+7WS+ETOV4JH2uXlRY61u7+VaFj7SbkcawdAIwUCjUAxLiBQFCbDjfr5f0+vbivUXXhY+0mF2XpPYvfONYuPYVj7QDACRRqAIhBjR29enm/Ty8POdYuLTlJi6sKz5wNXVmc7XZMAEgIFGoAiAHBoNWO8LF2L591rN0tc8PH2k0tVjbH2gHAqOOfvAAQpdp6BuTx+vTS/kat2e9TU1e/kow0v6JAn7lxmq6dVqKZEzjWDgDcRqEGgChhrZX3VOeZy1VeDx9rl5815Fi76hIVcKwdAEQVCjUAuKinP6ANB/zhKccbx9rNnJCrv1k5RddNL9G88gIlJ/EUGgCiFYUaAEbZseZuvbgvfKzdwSb1h4+1Wza1WJ9YNVXXThur8XkZbscEAESIQg0ADusfDGrz4eYzZ0Mf8HVJkiqLs/XexZO0avpYXVVZwLF2ABCjKNQA4IDu/kH9fvcpvbD7pNbW+tU55Fi7v1o8SddxrB0AxA1HC7Ux5iZJ/yopWdIPrbXfOOvPJ0l6XFKJpGZJ77XW1juZCQCcEghabTjg11NbGvS73SfV3R/Q+NwM3Tp3oq6bVqKlHGsHAHHJsX+yG2OSJX1f0g2S6iVtMsasttbuGfKxb0v6ibX2CWPMKklfl/Q+pzIBgBP2nmjXU1sb9My2Bp1q71NORopunzdR75xfpoWTCpTEFwoBIK45+ahkkaQ6a+1BSTLG/FzS7ZKGFuqZkv4+/PuXJD3tYB4AGDGN7b16Zttx/WpLvfad7FBKktG108bq4VtLtWr6WGWksocGgEThZKEulXRsyOt6SYvP+sx2SXcoNAt5p6QcY0yRtbZp6IeMMfdJuk+SKioqHAsMABfS1Teo3+85qV9vadD6Or+CVppbnq8v3TZLt8yZoKIx6W5HBAC4wO0x36clfc8Yc48kj6QGSYGzP2StfUzSY5K0cOFCO5oBASS2c+2iywoy9fHrpuod80s1pWSM2xEBAC5zslA3SCof8ros/N4Z1trjCj2hljFmjKR3WWtbHcwEABFhFw0AiJSThXqTpGpjTKVCRfouSe8Z+gFjTLGkZmttUNLnFDrxAwBccaq9V89sa9CvtzSwiwYARMyxQm2tHTTG3C/pBYWOzXvcWrvbGPOopM3W2tWSrpX0dWOMVWjy8XGn8gDAuXT1DeqF3Sf11NY3dtHzyvP16O2zdMuciSrMTnM7IgAgyhlrY2uSvHDhQrt582a3YwCIYYGg1fo6v57a2qAXwrvo8sJMvXNeqd4xv1RV7KIBAJKMMa9baxde7HNufykRAEbN6V3001sb1NhxehddqjsWlGrhpAIZwy4aAHDpKNQA4tr5dtF3LGAXDQAYGRRqAHGHXTQAYDRRqAHEhaG76N/tOqmegdAu+v7wedHsogEATqFQA4hpe46366mt9Xpm23E1dvQpNyNF75jPLhoAMHoo1ABizsm20C76qa2hXXRqcngXPb9U17GLBgCMMgo1gJjQ1Teo3+0K76IP+GWtNL8iX18O76IL2EUDAFxCoQYQtc63i/7Eqmq9c36pKouz3Y4IAACFGkD0Odcu+p0LSvXO+eyiAQDRh0INICpcaBe9asZYpaewiwYARCcKNQDXsIsGAMQDCjWAURUIWq2r8+upLfV6YfcpdtEAgJhHoQbgOGut9pxo11NbGvTM9uPyDdlF3zG/VFeyiwYAxDAKNQDHnGzr1dPbGvTUlgbtPxXaRV83bazuWBA6L5pdNAAgHlCoAYyo8+6i33GFbpk9gV00ACDuUKgBjIjegYD+4+UDesxzUD0DAVUUZrGLBgAkBAo1gGH7455T+tJvdutYc4/ePmeCPrhkMrtoAEDCoFADuGxHm7r1pWd360/7GjV17Bj99COLtWRKsduxAAAYVRRqAJesdyCg/7fmgP795QNKTTL6/M3T9cGllUpNTnI7GgAAo45CDeCS/GnvKT3ybGjecevcifrHm2dofF6G27EAAHANhRpARI41h+Ydf9wbnnfcu1hLpjLvAACAQg3ggnoHAvrPNQf17y/XKTnJ6HNvC8070lKYdwAAIFGoAVzAi/tO6ZHVe3S0uVu3zJmgf3z7DE3Iy3Q7FgAAUYVCDeDPhOYde/THvac0pSRb/3vvYi1l3gEAwDlRqAGc0TsQ0GOeg/r+S6F5x4Nvm64PMe8AAOCCKNQAJEkv7W/UI6t360hTt94+OzTvmJjPvAMAgIuhUAMJ7lhzt778mz36/Z5TqirJ1v98eLGWVTPvAAAgUhRqIEH1DgT0A89Bfe+lOiUZo8/eNF0fXsa8AwCAS0WhBhLQy+F5x+Gmbt08e7y+8PaZzDsAALhMFGoggdS3hOYdL+w+paribP3kQ4u0oqbE7VgAAMQ0CjWQAPoGA/rh2kP6txdrJUmfuXGa7l1eqfSUZJeTAQAQ+yjUQJxb4/XpkdW7dcjfpZtmjdcXb52pUuYdAACMGAo1EKcaWnv0ld/s0W93nVRlcbae+NAirWTeAQDAiKNQA3Hm9Lzjey/Wycoy7wAAwGEUaiCOeMLzjoP+Lt04a5y+eMtMlRVkuR0LAIC4RqEG4sDx1h595bk9en7nSU0uytKPPniVrps21u1YAAAkBAo1EMP6B4P64bqD+rc/heYdn35rje5dXqWMVOYdAACMFgo1EKPW1fr10OpdOujr0ltnhuYd5YXMOwAAGG0UaiDGnGjr0Vd+s1fP7TyhSUVZ+tE9V+m66cw7AABwC4UaiBH9g0E9vv6QvvunWgWCVn9/Q43uW8G8AwAAt1GogRiwvs6vh57ZpQO+Lt0wc5weYt4BAEDUoFADUexEW4++8txePbfjhCoKs/T4PQu1avo4t2MBAIAhKNRAFOofDOpH6w/pX8Pzjk9dX6O/Xsm8AwCAaEShBqLMhjq/Hlq9W3WNnbp+xjg9fCvzDgAAohmFGogSJ9t69ZXn9ug3O06ovDBT//WBhXrLDOYdAABEOwo14LKBQHje8cdaDQSt/u76an105RTmHQAAxAgKNeCiDQf8eviZ3apt7NRbpo/Vw7fOUkUR8w4AAGIJhRpwwan2Xn31ub1avf24ygsz9cP3L9T1M5l3AAAQiyjUwCgaCAT14/WH9S9/9GogaPXJt1Trb65l3gEAQCyjUAOj5JUDTXromV2qbezUddNK9MhtszSpKNvtWAAAYJgo1IDDTrX36mvP79Uz246rrCBTP3j/Ql0/Y6yMMW5HAwAAI4BCDThkIBDUExsO61/+WKv+QFB/+5ZqfYx5BwAAcYdCDTjg1YOheYf3VKeunVaiR26dpcnFzDsAAIhHFGpgBDWG5x1Pbzuu0vxMPfa+K3XDzHHMOwAAiGMUamAEDAaCeuKVI/rOH7zqHwzqE6um6mPXTlVmGvMOAADiHYUaGKbNh5v1had3ad/JDq2sCZ3eUcm8AwCAhEGhBobBe6pD7/nBayrJSdd/vu9KvZV5BwAACYdCDVymwUBQn/nldo3JSNEz9y9V8Zh0tyMBAAAXUKiBy/SDtYe0vb5N33vPfMo0AAAJLMntAEAsqj3Voe/8wau3XTFeb589we04AADARRRq4BINBoL69JM7lJ2erEdvv4LNNAAACY7JB3CJ/mvdIW0/1qrv3j1fJTlMPQAASHQ8oQYuQV1jp/75D17dOGucbp3D1AMAAFCogYgFglafeXK7stKS9eV3MPUAAAAhTD6ACD2+7pC2Hm3Vv941T2NzMtyOAwAAogRPqIEIHPB16tu/368bZo7TbXMnuh0HAABEEQo1cBGBoNUDT+5QRmqyvsrUAwAAnIXJB3ARP1p/SK8fadF3/nKuxuYy9QAAAG/GE2rgAg75u/StF/br+hlj9Y55pW7HAQAAUYhCDZxHIGj1mV9uV3pKkr76ztlMPQAAwDlRqIHzeGLDYW0+0qKHb52lcUw9AADAeVCogXM47O/SN1/Yp1XTx+qOBUw9AADA+VGogbMEw6d6pCYn6WtMPQAAwEVQqIGz/OSVw9p4uFkP3TJT4/OYegAAgAujUANDHGnq0j/9br+unVaiO68sczsOAACIARRqIOz01CMlyejrdzD1AAAAkaFQA2H/89oRvXaoWV+8ZaYm5GW6HQcAAMQIRwu1MeYmY8x+Y0ydMebBc/x5hTHmJWPMVmPMDmPMzU7mAc7naFO3vvHbfVpRU6J3L2TqAQAAIudYoTbGJEv6vqS3SZop6W5jzMyzPvYFSb+w1s6XdJekf3cqD3A+waDVA7/armRj9A2mHgAA4BI5+YR6kaQ6a+1Ba22/pJ9Luv2sz1hJueHf50k67mAe4Jz+d+NRvXqwWV+4ZYYm5jP1AAAAl8bJQl0q6diQ1/Xh94Z6RNJ7jTH1kp6X9Ilz/SBjzH3GmM3GmM0+n8+JrEhQx5q79fXn92p5dbH+YmG523EAAEAMcvtLiXdL+rG1tkzSzZL+2xjzZ5mstY9ZaxdaaxeWlJSMekjEJ2utPvurHUoyRt941xymHgAA4LI4WagbJA195FcWfm+oD0v6hSRZa1+RlCGp2MFMwBk/3XhUGw406R/fPkOlTD0AAMBlcrJQb5JUbYypNMakKfSlw9VnfeaopLdIkjFmhkKFmk0HHHesuVtfe26vlk0t1l1XMfUAAACXz7FCba0dlHS/pBck7VXoNI/dxphHjTG3hT/2D5I+YozZLulnku6x1lqnMgFSaOrx4K93SJK+8S5O9QAAAMOT4uQPt9Y+r9CXDYe+99CQ3++RtNTJDMDZfrbxmNbXNemr77xCZQVZbscBAAAxzu0vJQKjqr6lW199bo+WTCnSexZVuB0HAADEAQo1Eoa1Vp/79U5ZSf/EqR4AAGCEUKiRMP5v0zGtrfXrczfPUHkhUw8AADAyKNRICA2tPfrKc3t1TVWR/oqpBwAAGEEUasS901OPoLX65p1zlJTE1AMAAIwcCjXi3i8318vj9enBt01n6gEAAEYchRpx7URbj778mz1aXFmo9y6e5HYcAAAQhyjUiFunpx6DQaYeAADAORRqxK0nX6/Xy/t9+uxN0zSpKNvtOAAAIE5RqBGXTrb16tHf7NGiyYV6/zWT3Y4DAADiGIUaccdaq88/tVMDgSBTDwAA4DgKNeLOr7c06MV9jXrgxumaXMzUAwAAOItCjbhyqr1XX3p2t66aXKB7lkx2Ow4AAEgAFGrEDWutPv/rneobDOqbd85l6gEAAEYFhRpx4+ltDfrTvkZ95sZpqmTqAQAARgmFGnGhsb1Xj6zeoysnFeiDSyvdjgMAABIIhRoxL3Sqxy71DgT0zTvnKJmpBwAAGEUUasS81duP6497T+nTb52mKSVj3I4DAAASDIUaMa2xo1cPr96t+RX5+tAyph4AAGD0UagRs6y1+sJTu9TdH9C37pzL1AMAALgiokJtjJlkjLk+/PtMY0yOs7GAi3t2xwn9fs8p/cMNNZo6lqkHAABwx0ULtTHmI5KelPSf4bfKJD3tZCjgYnwdfXr4mV2aV56ve5dXuR0HAAAksEieUH9c0lJJ7ZJkra2VNNbJUMCFWGv1xad3qas/oG+/m1M9AACAuyIp1H3W2v7TL4wxKZKsc5GAC3tu5wn9bvdJfer6Gk0dy/oIAAC4K5JCvcYY83lJmcaYGyT9UtKzzsYCzs3f2aeHntmtuWV5+shyTvUAAADui6RQPyjJJ2mnpL+W9LykLzgZCjifh5/Zrc7eQX373XOVkswhNQAAwH0pEXwmU9Lj1tofSJIxJjn8XreTwYCzPbfjhJ7beUIP3DRN1eOYegAAgOgQySO+PylUoE/LlPRHZ+IA59bU2acvPrNLc8rydB+negAAgCgSSaHOsNZ2nn4R/n2Wc5GAP/fQ6tDU41t3MvUAAADRJZJm0mWMWXD6hTHmSkk9zkUC3uz5nSf03I4T+uT11Zo2nqkHAACILpFRuUIDAAAgAElEQVRsqP9O0i+NMcclGUnjJf2lo6mAsOaufn3x6V2aXZqnv17B1AMAAESfixZqa+0mY8x0SdPCb+231g44GwsIeXj1brX3Duh/372YqQcAAIhKkTyhlqSrJE0Of36BMUbW2p84lgqQ9LtdJ/Ts9uP6hxtqNH18rttxAAAAzumihdoY89+SpkjaJikQfttKolDDMS1d/frC07s0a2KuPnrtFLfjAAAAnFckT6gXSpppreW6cYyaR57drdbuAf33hxcrlakHAACIYpE0lV0KfRERGBUv7D6pZ7Yd1ydWVWvGBKYeAAAgukXyhLpY0h5jzEZJfafftNbe5lgqJKzW7n7941O7NHNCrj52HVMPAAAQ/SIp1I84HQI47UvP7lFrd7+e+NBVTD0AAEBMiOTYvDWjEQT4w55Temprgz75lmrNmpjndhwAAICIXPQRoDHmamPMJmNMpzGm3xgTMMa0j0Y4JI7W7n59/qmdmj4+Rx+/bqrbcQAAACIWyf+m/j1Jd0uqlZQp6V5J33cyFBLPo7/Zo+aufn373XOVlsLUAwAAxI6Imou1tk5SsrU2YK39kaSbnI2FRPKnvaf06y0N+vi1U3RFKVMPAAAQWyL5UmK3MSZN0jZjzDclnVCERRy4mLbugTNTj/tXVbsdBwAA4JJFUozfJylZ0v2SuiSVS3qXk6GQOL783B75O/v1rTuZegAAgNgUySkfR8K/7ZH0JWfjIJG8tK9RT75er/uvm6rZZUw9AABAbDpvoTbG/MJa+xfGmJ2S/uzacWvtHEeTIa619Qzoc7/eqZpxY/SJt3CqBwAAiF0XekL9yfC/3jIaQZBYvvrcHvk6+/TY+69Uekqy23EAAAAu23kLtbX2hDEmWdKPrbXXjWImxLmX9zfqF5vr9bFrp2hOWb7bcQAAAIblgt8Cs9YGJAWNMQxcMSLae0NTj+qxY/TJ6znVAwAAxL5Ijs3rlLTTGPMHhU75kCRZa//WsVSIW197bq9OtffqPz62lKkHAACIC5EU6l+HfwHD4vH69PNNx/TRlVM0r5ypBwAAiA+RHJv3xGgEQXzr6B3Qg7/aoSkl2fo7ph4AACCOXLRQG2OqJX1d0kxJGafft9ZWOZgLceZrz+/TyfZePfk3S5SRytQDAADEj0iupvuRpP+QNCjpOkk/kfQ/ToZCfFlX69fPNh7VR5ZXaUFFgdtxAAAARlQkhTrTWvsnScZae8Ra+4iktzsbC/Gio3dAn/3VDlWVZOtTN9S4HQcAAGDERfKlxD5jTJKkWmPM/ZIaJI1xNhbixdd/u0/H23r05EeZegAAgPgUyRPqT0rKkvS3kq6U9F5JH3AyFOLDulq/fvraUd27rFJXTmLqAQAA4lMkT6gD1tpOhc6j/qDDeRAnOvsGQ1OP4mz9w1unuR0HAADAMZE8of5nY8xeY8yXjTFXOJ4IceEbv92r4209+uadc5h6AACAuHbRQm2tvU6h0z18kv7TGLPTGPMFx5MhZm2o8+t/Xj2qDy+t1MLJhW7HAQAAcFQkT6hlrT1prf2upI9K2ibpIUdTIWZ19Q3qgV/tUCVTDwAAkCAuWqiNMTOMMY8YY3ZK+jdJGySVOZ4MMemffrdPDa2hqUdmGlMPAAAQ/yL5UuLjkn4u6UZr7XGH8yCGvXKgST955Yg+tLRSVzH1AAAACeKihdpae81oBEFs6+4f1AO/2q5JRVn6zI1MPQAAQOKI5Ak1cFHf/N1+1bf06P/uu4apBwAASCgRfSkRuJBXDzbpxxsO6wPXTNaiSqYeAAAgsURcqI0xWU4GQWzq7g9d4FJRmKUHbmLqAQAAEk8kp3wsMcbskbQv/HquMebfHU+GmPCtF/brSFO3vnnnHGWlsSACAACJJ5In1N+RdKOkJkmy1m6XtMLJUIgNGw81h6cek3R1VZHbcQAAAFwR6cUux856K+BAFsSQnv6AHnhyu8oKMvXATdPdjgMAAOCaSP43+mPGmCWSrDEmVdInJe11Nhai3bd/v1+Hm7r1048sVnY6Uw8AAJC4InlC/VFJH5dUKqlB0rzwaySozYeb9fj6Q3rf1ZO0ZEqx23EAAABcFcmjRWOt/SvHkyBmPOY5qOIx6XrwbUw9AAAAInlCvd4Y83tjzIeNMfmOJ0JUGwgEteFAk66fMY6pBwAAgCIo1NbaGklfkDRL0hZjzG+MMe91PBmi0pYjLersG9TKGqYeAAAAUuSnfGy01v69pEWSmiU94WgqRK21tX4lJxktmUqhBgAAkCK72CXXGPMBY8xvJW2QdEKhYo0E5Kn1aX55vnIzUt2OAgAAEBUieUK9XaGTPR611tZYaz9rrX09kh9ujLnJGLPfGFNnjHnwHH/+HWPMtvAvrzGm9RLzYxQ1d/VrZ0ObVtSUuB0FAAAgakTyrbIqa6291B9sjEmW9H1JN0iql7TJGLPaWrvn9GestZ8a8vlPSJp/qX8djJ61tT5ZKwo1AADAEOct1MaYf7HW/p2k1caYPyvU1trbLvKzF0mqs9YeDP+8n0u6XdKe83z+bkkPR5QarvB4/crPStXs0jy3owAAAESNCz2h/u/wv377Mn92qaShV5bXS1p8rg8aYyZJqpT04nn+/D5J90lSRUXFZcbBcFhrtbbWp6VTi5WcZNyOAwAAEDXOu6EespOeZ61dM/SXQpvqkXSXpCettYHzZHnMWrvQWruwpIS5gRv2nexQY0efVlbz/38AAIChIvlS4gfO8d49EfzfNUgqH/K6LPzeudwl6WcR/Ey4ZG2tT5K0nPOnAQAA3uRCG+q7Jb1HUqUxZvWQP8pR6Czqi9kkqdoYU6lQkb4r/PPO/utMl1Qg6ZVLyI1R5vH6VTNujCbkZbodBQAAIKpcaEN9+szpYkn/POT9Dkk7LvaDrbWDxpj7Jb0gKVnS49ba3caYRyVtttaeLul3Sfr55ZwkgtHR0x/QxsPNev/Vk9yOAgAAEHXOW6ittUckHZF0zeX+cGvt85KeP+u9h856/cjl/nyMjlcPNal/MMhxeQAAAOcQyU2JVxtjNhljOo0x/caYgDGmfTTCITp4vD6lpyRpUWWh21EAAACiTiRfSvyeQmdE10rKlHSvQhe2IEF4vD4tqixURmqy21EAAACiTiSFWtbaOknJ1tqAtfZHkm5yNhaiRUNrjw74urSSuQcAAMA5RXL1eLcxJk3SNmPMNxX6omJERRyxb603dFwe+2kAAIBzi6QYv0+hUzrul9Sl0NnS73IyFKKHp9an8bkZqh47xu0oAAAAUemiT6jDp31IUo+kLzkbB9FkMBDUulq/brpivIzhunEAAIBzudDFLjslnfdsaGvtHEcSIWpsr29Te+8gcw8AAIALuNAT6ltGLQWiksfrkzHS0ilcNw4AAHA+F7vYBQnMU+vTnLJ8FWSnuR0FAAAgakVysUuHMaY9/KuXi10SQ1v3gLYfa9XKap5OAwAAXEgkX0rMOf17E/pm2u2SrnYyFNy3/oBfQctxeQAAABdzSedJ25CnJd3oUB5ECY/Xp5yMFM0rz3c7CgAAQFS76BNqY8wdQ14mSVooqdexRHCdtVYer09LpxQrJZk7fAAAAC4kkpsSbx3y+0FJhxWafSBOHfB16nhbr+5fxdwDAADgYiLZUH9wNIIgeqzx+iVJy/lCIgAAwEVFMvmolPQJSZOHft5ae5tzseAmj9enquJslRdmuR0FAAAg6kUy+Xha0n9JelZS0Nk4cFvvQECvHWrSXVdVuB0FAAAgJkRSqHuttd91PAmiwubDLeodCGpFDXMPAACASERSqP/VGPOwpN9L6jv9prV2i2Op4BpPrU9pyUm6uqrI7SgAAAAxIZJCPVvS+ySt0huTDxt+jTjj8fq0cHKBstIi+bcGAAAAImlN75ZUZa3tdzoM3HWqvVf7TnboszdNdzsKAABAzIjk1o5dkrguLwF4vD5JYj8NAABwCSJ5Qp0vaZ8xZpPevKHm2Lw446n1q3hMumaMz3U7CgAAQMyIpFA/7HgKuC4YtFpX69N108YqKcm4HQcAACBmRHJT4prRCAJ37TreppbuAa2o4bpxAACASxHJTYkdCp3qIUlpklIldVlr2QXEkdP76WVcNw4AAHBJInlCnXP698YYI+l2SVc7GQqjz+P164rSXBWPSXc7CgAAQEyJ5JSPM2zI05JudCgPXNDRO6AtR1u0vJq5BwAAwKWKZPJxx5CXSZIWSup1LBFG3YYDTRoMWq2gUAMAAFyySE75uHXI7wclHVZo9oE44fH6lJ2WrCsnFbgdBQAAIOZEsqH+4GgEgXvW1vp1zZQipaVc0gIIAAAAimBDbYx5whiTP+R1gTHmcWdjYbQc9nfpaHM3x+UBAABcpkgeSc6x1raefmGtbZE037lIGE2e2vB14+ynAQAALkskhTrJGHNmXGuMKVRk22vEAI/Xp4rCLE0uznY7CgAAQEyKpBj/s6RXjDG/DL9+t6SvOhcJo6V/MKhXDjTpHfNL3Y4CAAAQsyL5UuJPjDGbJa0Kv3WHtXaPs7EwGl4/0qKu/gD7aQAAgGGIaLoRLtCU6DizttanlCSjJVOK3I4CAAAQszgnLYF5an1aUFGgnIxUt6MAAADELAp1gvJ39mlXQ7tW1BS7HQUAACCmUagT1LpavySxnwYAABgmCnWC8nh9KshK1RUT89yOAgAAENMo1AkoGLTy1Pq1rLpESUnG7TgAAAAxjUKdgPaebJe/s08rqtlPAwAADBeFOgGtZT8NAAAwYijUCcjj9Wn6+ByNy81wOwoAAEDMo1AnmO7+QW0+3MLTaQAAgBFCoU4wrx5sUn8gqBXVFGoAAICRQKFOMB6vXxmpSVo4ucDtKAAAAHGBQp1gPF6fFlcWKSM12e0oAAAAcYFCnUCONXfroL+L/TQAAMAIolAnkNPH5a2s4fxpAACAkUKhTiAer08T8zI0pWSM21EAAADiBoU6QQwGglp/wK8VNSUyhuvGAQAARgqFOkFsO9aqjt5B9tMAAAAjjEKdIDxen5KMtHQK+2kAAICRRKFOEGtq/Zpbnq+8rFS3owAAAMQVCnUCaOnq1476Vm5HBAAAcACFOgGsP+CXtWI/DQAA4AAKdQLweH3KzUjR3LI8t6MAAADEHQp1nLPWyuP1a1l1sVKS+dsNAAAw0mhYca62sVMn23vZTwMAADiEQh3nPF6fJGk5+2kAAABHUKjj3BqvT1NKslWan+l2FAAAgLhEoY5jvQMBbTzUzOkeAAAADqJQx7GNh5rVNxikUAMAADiIQh3HPF6f0lKSdHVlkdtRAAAA4haFOo55an1aNLlQmWnJbkcBAACIWxTqOHWirUfeU51aUVPsdhQAAIC4RqGOU2u9fknScs6fBgAAcBSFOk6tqfVpbE66po/PcTsKAABAXKNQx6FA0Gp9nV/Lq0tkjHE7DgAAQFyjUMehnQ1tau0eYD8NAAAwCijUccjj9ckY9tMAAACjgUIdhzxen2aX5qkwO83tKAAAAHGPQh1n2nsHtPVYq1bwdBoAAGBUUKjjzIY6vwJBq+XV7KcBAABGA4U6zqzx+jUmPUULJhW4HQUAACAhOFqojTE3GWP2G2PqjDEPnuczf2GM2WOM2W2M+amTeeKdtVYer0/XTClSajL/XQkAAGA0pDj1g40xyZK+L+kGSfWSNhljVltr9wz5TLWkz0laaq1tMcaMdSpPIjjk71JDa48+eu0Ut6MAAAAkDCcfYy6SVGetPWit7Zf0c0m3n/WZj0j6vrW2RZKstY0O5ol7Hq9PkrSSLyQCAACMGicLdamkY0Ne14ffG6pGUo0xZr0x5lVjzE3n+kHGmPuMMZuNMZt9Pp9DcWOfp9avyUVZqijKcjsKAABAwnB7aJsiqVrStZLulvQDY0z+2R+y1j5mrV1orV1YUsLT13PpGwzolQNNXOYCAAAwypws1A2Syoe8Lgu/N1S9pNXW2gFr7SFJXoUKNi7R64db1DMQ0IoaCjUAAMBocrJQb5JUbYypNMakSbpL0uqzPvO0Qk+nZYwpVmgCctDBTHFrTa1PKUlG10wpcjsKAABAQnGsUFtrByXdL+kFSXsl/cJau9sY86gx5rbwx16Q1GSM2SPpJUmfsdY2OZUpnq31+nXlpAKNSXfs4BYAAACcg6Pty1r7vKTnz3rvoSG/t5L+PvwLl8nX0ac9J9r1mRunuR0FAAAg4bj9pUSMgLW14ePy2E8DAACMOgp1HPB4fSrKTtPMCbluRwEAAEg4FOoYFwxara31a1l1sZKSjNtxAAAAEg6FOsbtOdGupq5+reD8aQAAAFdQqGPcmvB148tril1OAgAAkJgo1DFuba1PMybkamxOhttRAAAAEhKFOoZ19Q3q9SMtWsHTaQAAANdQqGPYKweaNBCwWsl+GgAAwDUU6hjmqfUpMzVZV04ucDsKAABAwqJQxzCP16erqwqVnpLsdhQAAICERaGOUUebunW4qVsruB0RAADAVRTqGOUJXzdOoQYAAHAXhTpGebw+leZnqqo42+0oAAAACY1CHYMGAkFtONCkFTUlMobrxgEAANxEoY5BW4+2qrNvUCs5fxoAAMB1FOoY5PH6lJxkdM0UCjUAAIDbKNQxyFPr07zyfOVlprodBQAAIOFRqGNMc1e/dja0aQW3IwIAAEQFCnWMWVfnl7XSCvbTAAAAUYFCHWM8Xp/ys1I1pyzf7SgAAAAQhTqmWGu1ttanpVOLlZzEcXkAAADRgEIdQ/af6tCp9j6tZD8NAAAQNSjUMcTjDV03vpz9NAAAQNSgUMcQj9ev6rFjNCEv0+0oAAAACKNQx4ie/oA2Hm7WihrmHgAAANGEQh0jXjvUpP7BIIUaAAAgylCoY4TH61d6SpIWVxa6HQUAAABDUKhjhKfWp0WVhcpITXY7CgAAAIagUMeA4609qmvs1ErmHgAAAFGHQh0DzhyXx/nTAAAAUYdCHQM8tT6Nz81QzbgxbkcBAADAWSjUUW4wENS6Wr+WVxfLGK4bBwAAiDYU6ii3o6FN7b2DHJcHAAAQpSjUUc7j9ckYadlUrhsHAACIRhTqKOfx+jSnLF8F2WluRwEAAMA5UKijWFv3gLYda9XKap5OAwAARCsKdRRbf8CvoJWWs58GAACIWhTqKObx+pSTnqJ55fluRwEAAMB5UKijlLVWa2v9WjK1SKnJ/G0CAACIVjS1KHXA16WG1h6OywMAAIhyFOoodfq68RVcNw4AABDVKNRRylPrU1VxtsoLs9yOAgAAgAugUEeh3oGAXj3YxNwDAAAgBlCoo9Dmwy3qHQhqOedPAwAARD0KdRTy1PqUmmx0dVWR21EAAABwERTqKOTx+rRwUqGy01PcjgIAAICLoFBHmcb2Xu072cF+GgAAIEZQqKOMp9YvSVpRw34aAAAgFlCoo4zH61PxmHTNGJ/rdhQAAABEgEIdRYJBq3V1fi2vLlZSknE7DgAAACJAoY4iu463qbmrn7kHAABADKFQR5HT140v57pxAACAmEGhjiKeWr9mTcxV8Zh0t6MAAAAgQhTqKNHRO6AtR1o4Lg8AACDGUKijxCsHmjQYtFrB3AMAACCmUKijhKfWp6y0ZF05qcDtKAAAALgEFOoo4fH6dU1VkdJS+FsCAAAQS2hvUeCwv0tHm7vZTwMAAMQgCnUU8NSGjsujUAMAAMQeCnUU8Hj9Ki/M1OSiLLejAAAA4BJRqF3WPxjUKwf8WlFdImO4bhwAACDWUKhdtuVoi7r6A8w9AAAAYhSF2mUer0/JSUZLphS5HQUAAACXgULtMk+tTwsq8pWTkep2FAAAAFwGCrWL/J192tXQzu2IAAAAMYxC7aJ1tX5JHJcHAAAQyyjULvLU+lSQlaorSvPcjgIAAIDLRKF2ibVWa2v9WlZdouQkjssDAACIVRRql+w90SFfR59WVBe7HQUAAADDQKF2CdeNAwAAxAcKtUs8Xp+mjcvRuNwMt6MAAABgGCjULujuH9Tmwy1aUcPcAwAAINZRqF3w2sFm9QeCzD0AAADiAIXaBWu8PmWkJumqyYVuRwEAAMAwUahd4Kn1aXFlkTJSk92OAgAAgGGiUI+y+pZuHfR1MfcAAACIExTqUebxhq4bX8kXEgEAAOKCo4XaGHOTMWa/MabOGPPgOf78HmOMzxizLfzrXifzRAOP16cJeRmaUjLG7SgAAAAYASlO/WBjTLKk70u6QVK9pE3GmNXW2j1nffT/rLX3O5UjmgwGglp/wK+br5ggY7huHAAAIB44+YR6kaQ6a+1Ba22/pJ9Lut3Bv17U217fqo7eQfbTAAAAccTJQl0q6diQ1/Xh9872LmPMDmPMk8aY8nP9IGPMfcaYzcaYzT6fz4mso2KN168kIy2byn4aAAAgXrj9pcRnJU221s6R9AdJT5zrQ9bax6y1C621C0tKYvfprsfr09zyfOVlpbodBQAAACPEyULdIGnoE+ey8HtnWGubrLV94Zc/lHSlg3lc1drdrx31rVpRHbv/hQAAAAB/zslCvUlStTGm0hiTJukuSauHfsAYM2HIy9sk7XUwj6vW1fkVtNIKjssDAACIK46d8mGtHTTG3C/pBUnJkh631u42xjwqabO1drWkvzXG3CZpUFKzpHucyuM2j9ennIwUzS3LdzsKAAAARpBjhVqSrLXPS3r+rPceGvL7z0n6nJMZooG1Vh6vX8umFisl2e3ZOgAAAEYS7W4U1DV26mR7L8flAQAAxCEK9ShY4w0d9UehBgAAiD8U6lHgqfVrSkm2SvMz3Y4CAACAEUahdljvQECvHWzi6TQAAECcolA7bOOhZvUNBjl/GgAAIE5RqB3m8fqUlpykxVWFbkcBAACAAyjUDvPU+nRVZYGy0hw9oRAAAAAuoVA76GRbr7ynOpl7AAAAxDEKtYM8tRyXBwAAEO8o1A7yeH0am5Ou6eNz3I4CAAAAh1CoHRIIWq2r82t5dYmMMW7HAQAAgEMo1A7Z2dCm1u4BragpdjsKAAAAHEShdojH65Mx0rKpFGoAAIB4RqF2yNpan66YmKeiMeluRwEAAICDKNQOaO8d0Jajrcw9AAAAEgCF2gEb6poUCFrOnwYAAEgAFOr/397dBtlZ3nUc//6yCyQkECChIiEmEBJjrPIgUigPRelomXas2ulUrB1xxjqMraW1nYqO0xnrm2o7HTsOtVOx8AKGWhFGrNiitmXTFlPC81PZDYSHUErPQnkKkJDk74u9gyGw2d2cc3KfdL+fV3uuuc59fmfnnt3f3Oe6z9UHI2MdFhw0zMnLDm87iiRJkvrMQt1jVcXIaIfTVyzigCF/vZIkST/pbHw9tnF8M5t+/CJnr3T9tCRJ0mxgoe6xkVG3G5ckSZpNLNQ9tnZsnGWLDmbZovltR5EkSdI+YKHuoa3bdnDTg0/67R6SJEmziIW6h9Y//BQvbN3ucg9JkqRZxELdQyOj4wzPCaevWNR2FEmSJO0jFuoeGhntcPKyw1lw0HDbUSRJkrSPWKh7pPPcFu59/Fne4nIPSZKkWcVC3SNrx5qvy/OGREmSpFnFQt0ja8fGWTT/QH7+6EPbjiJJkqR9yELdAzt2FGvHOpy5cjFz5qTtOJIkSdqHLNQ9cO/jzzL+/FaXe0iSJM1CFuoeGGnWT5+1cnHLSSRJkrSvWah7YGS0w+qjDuENh85tO4okSZL2MQt1lzZv2cYtD//Yr8uTJEmapSzUXbrpgSd5eXu53bgkSdIsZaHu0tqxDvMOGOKU5Ye3HUWSJEktsFB3aWRsnNOOO4KDhofajiJJkqQWWKi78OhTL7BxfLPLPSRJkmYxC3UXbhxtthu3UEuSJM1aFuoujIx2WHLYPI5bPL/tKJIkSWqJhXovvbx9B9994EnOXrWYxO3GJUmSZisL9V66/dGneX7LNrcblyRJmuUs1HtpZLTD0Jzw5uPdblySJGk2s1DvpZHRDicuPYyF8w5oO4okSZJaZKHeC09t3sqdjz3jcg9JkiRZqPfGtzeMUwVnr3K5hyRJ0mxnod4LI6MdFs47gF885rC2o0iSJKllFuoZqirWjnU48/jFDM3x6/IkSZJmOwv1DI0+8TxPPLvF5R6SJEkCLNQzNuJ245IkSdqFhXqGRsY6rHzDAn564by2o0iSJGkAWKhn4MWt21m38SmvTkuSJOkVFuoZWLfxSbZu22GhliRJ0iss1DMwMjrOgcNzOHX5EW1HkSRJ0oCwUM/AyFiHNx17BPMOHGo7iiRJkgaEhXqafvD0i2z40fNuNy5JkqRXsVBP09oxvy5PkiRJr2WhnqaR0XGOOnQuq35qQdtRJEmSNEAs1NOwfUfx7Q3jnLVyMYnbjUuSJOn/Wain4Y5NT/PMiy9zlss9JEmStBsL9TQcvXAeF5+3mrOOX9x2FEmSJA2Y4bYD7A+OWjiXC9+you0YkiRJGkBeoZYkSZK6YKGWJEmSumChliRJkrpgoZYkSZK6YKGWJEmSumChliRJkrpgoZYkSZK6YKGWJEmSumChliRJkrpgoZYkSZK6YKGWJEmSumChliRJkrpgoZYkSZK6YKGWJEmSumChliRJkrpgoZYkSZK60NdCneRtSe5PsiHJxXuY964kleSUfuaRJEmSeq1vhTrJEHAJcB6wBjg/yZrXmXcIcBGwrl9ZJEmSpH7p5xXqU4ENVfVgVW0Fvgy883Xm/TXwN8BLfcwiSZIk9UU/C/US4NFdHm9qxl6R5GRgaVX9x54OlOSPkqxPsr7T6fQ+qSRJkrSXWrspMckc4LPAR6eaW1VfrKpTquqUI488sv/hJEmSpGnqZ6F+DFi6y+NjmrGdDgHeCHwryUPAacB13pgoSZKk/Umqqj8HToaBUeBcJor0zcDvVtU9k8z/FvCxqlo/xXE7wMO9TTtti4Hxll5bg81zQ5Px3NBkPDe0J54fg2FZVU25PGK4X69eVduSfBD4OjAEfKmq7knySWB9VV23l8dtbc1Hkk8q4rUAAAYISURBVPVV5RV0vYbnhibjuaHJeG5oTzw/9i99K9QAVXU9cP1uY5+YZO45/cwiSZIk9YM7JUqSJEldsFDPzBfbDqCB5bmhyXhuaDKeG9oTz4/9SN9uSpQkSZJmA69QS5IkSV2wUEuSJEldsFBPQ5K3Jbk/yYYkF7edR4MhydIk30xyb5J7klzUdiYNliRDSW5L8tW2s2iwJDksydVJvp/kviSnt51JgyHJR5r/KXcnuSrJ3LYzaWoW6ikkGQIuAc4D1gDnJ1nTbioNiG3AR6tqDRM7fX7Ac0O7uQi4r+0QGkifA75WVauBE/A8EZBkCfAh4JSqeiMT+3j8TrupNB0W6qmdCmyoqgeraivwZeCdLWfSAKiqx6vq1ubn55j4h7ik3VQaFEmOAd4OXNp2Fg2WJAuBs4F/AqiqrVX1dLupNECGgXnNjtMHAz9oOY+mwUI9tSXAo7s83oSlSbtJshw4CVjXbhINkL8DPg7saDuIBs6xQAe4rFkSdGmS+W2HUvuq6jHgM8AjwOPAM1V1Q7upNB0WaqlLSRYA/wp8uKqebTuP2pfkHcCPquqWtrNoIA0DJwP/UFUnAZsB788RSQ5n4lPwY4GjgflJfq/dVJoOC/XUHgOW7vL4mGZMIskBTJTpK6vqmrbzaGCcAfxGkoeYWCb2q0muaDeSBsgmYFNV7fxE62omCrb0VmBjVXWq6mXgGuDNLWfSNFiop3YzsDLJsUkOZOLmgOtazqQBkCRMrIG8r6o+23YeDY6q+vOqOqaqljPxN+MbVeVVJgFQVT8EHk3ys83QucC9LUbS4HgEOC3Jwc3/mHPxhtX9wnDbAQZdVW1L8kHg60zcbfulqrqn5VgaDGcA7wPuSnJ7M/YXVXV9i5kk7R/+BLiyuVDzIPAHLefRAKiqdUmuBm5l4pukbsMtyPcLbj0uSZIkdcElH5IkSVIXLNSSJElSFyzUkiRJUhcs1JIkSVIXLNSSJElSFyzUkqSeSnJOEjejkDRrWKglSb12Du7uJmkWsVBLUh8kWZ7kviT/mOSeJDckmTfJ3OOT/HeSO5LcmmRFJnw6yd1J7krynmbuOUluTPJvSR5M8qkk703yvWbeimbe5Um+kGR9ktEk72jG5ya5rJl7W5JfacYvSHJNkq8lGUvyt7vk+7UkNzXZ/iXJgmb8oSR/1YzflWR1kuXAhcBHktye5Kwk727exx1JRvr5e5ekNrhToiT1z0rg/Kp6f5KvAO8CrnideVcCn6qqa5PMZeJix28DJwInAIuBm3cpoycAPwc8xcQue5dW1alJLmJiB74PN/OWA6cCK4BvJjke+ABQVfULSVYDNyRZ1cw/ETgJ2ALcn+TvgReBvwTeWlWbk/wZ8KfAJ5vnjFfVyUn+GPhYVf1hki8Az1fVZwCS3AX8elU9luSwvf5tStKA8gq1JPXPxqrauS39LUwU3FdJcgiwpKquBaiql6rqBeBM4Kqq2l5VTwA3Ar/cPO3mqnq8qrYADwA3NON37fYaX6mqHVU1xkTxXt0c94rmtb4PPAzsLNT/U1XPVNVLwL3AMuA0YA3wnSS3A7/fjO90zZ7eX+M7wOVJ3g8MTTJHkvZbXqGWpP7ZssvP24HXXfLR5XF37PJ4B6/+u167PW/3x3s67vbmWAH+q6rOn+I5O+e/RlVdmORNwNuBW5L8UlU9OUUWSdpveIVaklpUVc8Bm5L8JkCSg5IcDKwF3pNkKMmRwNnA92Z4+HcnmdOsqz4OuL857nub11oF/EwzPpn/Bc5olouQZP4uS0Qm8xxwyM4HSVZU1bqq+gTQAZbO8H1I0kCzUEtS+94HfCjJncB3gaOAa4E7gTuAbwAfr6ofzvC4jzBRwv8TuLBZyvF5YE6zrvmfgQuapSOvq6o6wAXAVU2+m5hYOrIn/w781s6bEoFPNzct3t28vztm+D4kaaClaqpPACVJ+5sklwNfraqr284iST/pvEItSZIkdcEr1JK0jyS5BDhjt+HPVdVlbeSRJPWGhVqSJEnqgks+JEmSpC5YqCVJkqQuWKglSZKkLlioJUmSpC5YqCVJkqQu/B/hpntAw8LypgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_3 = variance_plot(tail_strength=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "# to generate sample data for fitting clustering model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_blobs(n_samples=100, n_features=2, centers=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2)\n",
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "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": [
    "for i in range(len(X)):\n",
    "    colors = ['r', 'g', 'b', 'y', 'g', 'w']\n",
    "    plt.scatter(X[i][0], X[i][1], c=colors[y[i]])\n",
    "plt.show()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "X , color = make_circles(n_samples=200, noise=0.05, factor=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 2)\n",
      "(200,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(color.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0,\n",
       "       1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1,\n",
       "       1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1,\n",
       "       0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1,\n",
       "       1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1,\n",
       "       0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0,\n",
       "       1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0,\n",
       "       1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,\n",
       "       0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1,\n",
       "       1, 0])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,10))\n",
    "plt.scatter(X[:,0], X[:,1], c=color, s=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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