Chapter 12.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "bd068c3f",
   "metadata": {},
   "source": [
    "# Chapter 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a7651be4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.datasets import get_rdataset\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.metrics import pairwise_distances\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from ISLP import load_data\n",
    "from sklearn.cluster import (KMeans, AgglomerativeClustering)\n",
    "from scipy.cluster.hierarchy import (linkage,dendrogram, cut_tree)\n",
    "from ISLP.cluster import compute_linkage"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "117aa0d1",
   "metadata": {},
   "source": [
    "## Exercise 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b6072f57",
   "metadata": {},
   "outputs": [],
   "source": [
    "USArrests=get_rdataset('USArrests').data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e9dea16d",
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rownames</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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",
       "rownames                                   \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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "USArrests.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "96c7071c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 4)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "USArrests.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a13955c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler=StandardScaler(with_std=True,with_mean=True)\n",
    "USArrestscaled=scaler.fit_transform(USArrests)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f108bbc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Compute the squared Euclidian distance matrix\n",
    "Eucl_matrix=pairwise_distances(USArrestscaled.transpose())\n",
    "Eucl_matrix_sq=np.square(Eucl_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5916b776",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eucl_matrix_sq.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "acc4de7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Return the correlation matrix\n",
    "corr_matrix=np.corrcoef(USArrestscaled, rowvar=False)\n",
    "Comp_corr_matrix=1-corr_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "10401782",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kabousselham\\AppData\\Local\\Temp\\ipykernel_15476\\2748945556.py:1: RuntimeWarning: divide by zero encountered in divide\n",
      "  prop_matrix  = (Comp_corr_matrix)/Eucl_matrix_sq\n",
      "C:\\Users\\kabousselham\\AppData\\Local\\Temp\\ipykernel_15476\\2748945556.py:1: RuntimeWarning: invalid value encountered in divide\n",
      "  prop_matrix  = (Comp_corr_matrix)/Eucl_matrix_sq\n"
     ]
    }
   ],
   "source": [
    "prop_matrix  = (Comp_corr_matrix)/Eucl_matrix_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4836804a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ inf, 0.01, 0.01, 0.01],\n",
       "       [0.01,  nan, 0.01, 0.01],\n",
       "       [0.01, 0.01,  inf, 0.01],\n",
       "       [0.01, 0.01, 0.01,  nan]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prop_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67c1da7c",
   "metadata": {},
   "source": [
    "The cited assertion in the exercise instruction is proved for the case of USArrests data set. The proportionality coefficient is 0.01."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1864bb3",
   "metadata": {},
   "source": [
    "## Exercise 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "21ab0736",
   "metadata": {},
   "outputs": [],
   "source": [
    "USArrests=get_rdataset('USArrests').data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "075e0af5",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler=StandardScaler(with_std=True,with_mean=True)\n",
    "USArrestscaled=scaler.fit_transform(USArrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59bbbc11",
   "metadata": {},
   "source": [
    "### (a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "28ea5e3e",
   "metadata": {},
   "outputs": [
    {
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       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>PCA()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PCA</label><div class=\"sk-toggleable__content\"><pre>PCA()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "PCA()"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pcaUS = PCA()\n",
    "pcaUS.fit(USArrestscaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6d7a69a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_exp=pcaUS.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ba3b2bf",
   "metadata": {},
   "source": [
    "### (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7ba71c91",
   "metadata": {},
   "outputs": [],
   "source": [
    "loadings=pcaUS.components_\n",
    "X=USArrestscaled.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "da8abec5",
   "metadata": {},
   "outputs": [],
   "source": [
    "exp_var=np.zeros(4)\n",
    "for i in range(4):\n",
    "    exp_var[i]=np.sum(np.matmul(loadings[i,:],X)**2)/np.sum(X**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b86e28b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.62006039, 0.24744129, 0.0891408 , 0.04335752])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "55f4fe79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1.])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_exp/exp_var"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0ff14a4",
   "metadata": {},
   "source": [
    "The two matrices obtained in (a) and (b) are the same."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78eae4c9",
   "metadata": {},
   "source": [
    "## Exercise 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d751ce0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "USArrests=get_rdataset('USArrests').data\n",
    "scaler=StandardScaler(with_std=True,with_mean=True)\n",
    "USArrestscaled=scaler.fit_transform(USArrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "704af212",
   "metadata": {},
   "source": [
    "### (a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "77315e90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>AgglomerativeClustering(distance_threshold=0, linkage=&#x27;complete&#x27;,\n",
       "                        n_clusters=None)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">AgglomerativeClustering</label><div class=\"sk-toggleable__content\"><pre>AgglomerativeClustering(distance_threshold=0, linkage=&#x27;complete&#x27;,\n",
       "                        n_clusters=None)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "AgglomerativeClustering(distance_threshold=0, linkage='complete',\n",
       "                        n_clusters=None)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HClust = AgglomerativeClustering\n",
    "hc_comp = HClust(distance_threshold=0,n_clusters=None,linkage='complete')\n",
    "hc_comp.fit(USArrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75132ead",
   "metadata": {},
   "source": [
    "### (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "fcd898dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linkage_comp = compute_linkage(hc_comp)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n",
    "dendrogram(linkage_comp,ax=ax,color_threshold=120, above_threshold_color='black');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "bd56c287",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Alabama', 'Alaska', 'Arizona', 'Arkansas', 'California', 'Colorado',\n",
       "       'Connecticut', 'Delaware', 'Florida', 'Georgia', 'Hawaii', 'Idaho',\n",
       "       'Illinois', 'Indiana', 'Iowa', 'Kansas', 'Kentucky', 'Louisiana',\n",
       "       'Maine', 'Maryland', 'Massachusetts', 'Michigan', 'Minnesota',\n",
       "       'Mississippi', 'Missouri', 'Montana', 'Nebraska', 'Nevada',\n",
       "       'New Hampshire', 'New Jersey', 'New Mexico', 'New York',\n",
       "       'North Carolina', 'North Dakota', 'Ohio', 'Oklahoma', 'Oregon',\n",
       "       'Pennsylvania', 'Rhode Island', 'South Carolina', 'South Dakota',\n",
       "       'Tennessee', 'Texas', 'Utah', 'Vermont', 'Virginia', 'Washington',\n",
       "       'West Virginia', 'Wisconsin', 'Wyoming'],\n",
       "      dtype='object', name='rownames')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "USArrests.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e8b04248",
   "metadata": {},
   "outputs": [],
   "source": [
    "df1=pd.DataFrame(cut_tree(linkage_comp, n_clusters=3),index=USArrests.index)\n",
    "df1.index.name='State'\n",
    "df1.rename(columns={0:'Cluster'},inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b3091316",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>Cluster</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>0</td>\n",
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       "      <th>Arizona</th>\n",
       "      <td>0</td>\n",
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       "      <th>Arkansas</th>\n",
       "      <td>1</td>\n",
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       "      <th>California</th>\n",
       "      <td>0</td>\n",
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       "      <th>Colorado</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Cluster\n",
       "State                  \n",
       "Alabama               0\n",
       "Alaska                0\n",
       "Arizona               0\n",
       "Arkansas              1\n",
       "California            0\n",
       "Colorado              1\n",
       "Connecticut           2\n",
       "Delaware              0\n",
       "Florida               0\n",
       "Georgia               1\n",
       "Hawaii                2\n",
       "Idaho                 2\n",
       "Illinois              0\n",
       "Indiana               2\n",
       "Iowa                  2\n",
       "Kansas                2\n",
       "Kentucky              2\n",
       "Louisiana             0\n",
       "Maine                 2\n",
       "Maryland              0\n",
       "Massachusetts         1\n",
       "Michigan              0\n",
       "Minnesota             2\n",
       "Mississippi           0\n",
       "Missouri              1\n",
       "Montana               2\n",
       "Nebraska              2\n",
       "Nevada                0\n",
       "New Hampshire         2\n",
       "New Jersey            1\n",
       "New Mexico            0\n",
       "New York              0\n",
       "North Carolina        0\n",
       "North Dakota          2\n",
       "Ohio                  2\n",
       "Oklahoma              1\n",
       "Oregon                1\n",
       "Pennsylvania          2\n",
       "Rhode Island          1\n",
       "South Carolina        0\n",
       "South Dakota          2\n",
       "Tennessee             1\n",
       "Texas                 1\n",
       "Utah                  2\n",
       "Vermont               2\n",
       "Virginia              1\n",
       "Washington            1\n",
       "West Virginia         2\n",
       "Wisconsin             2\n",
       "Wyoming               1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "891d0e3f",
   "metadata": {},
   "source": [
    "### (c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e749681c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>AgglomerativeClustering(distance_threshold=0, linkage=&#x27;complete&#x27;,\n",
       "                        n_clusters=None)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">AgglomerativeClustering</label><div class=\"sk-toggleable__content\"><pre>AgglomerativeClustering(distance_threshold=0, linkage=&#x27;complete&#x27;,\n",
       "                        n_clusters=None)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "AgglomerativeClustering(distance_threshold=0, linkage='complete',\n",
       "                        n_clusters=None)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HClust = AgglomerativeClustering\n",
    "hc_comp = HClust(distance_threshold=0,n_clusters=None,linkage='complete')\n",
    "hc_comp.fit(USArrestscaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9169d3ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linkage_comp = compute_linkage(hc_comp)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n",
    "dendrogram(linkage_comp,ax=ax,color_threshold=4, above_threshold_color='black');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a1a6734d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df2=pd.DataFrame(cut_tree(linkage_comp, n_clusters=3),index=USArrests.index)\n",
    "df2.index.name='State'\n",
    "df2.rename(columns={0:'Cluster'},inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "37c08f84",
   "metadata": {
    "scrolled": true
   },
   "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>Cluster</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Cluster\n",
       "State                  \n",
       "Alabama               0\n",
       "Alaska                0\n",
       "Arizona               1\n",
       "Arkansas              2\n",
       "California            1\n",
       "Colorado              1\n",
       "Connecticut           2\n",
       "Delaware              2\n",
       "Florida               1\n",
       "Georgia               0\n",
       "Hawaii                2\n",
       "Idaho                 2\n",
       "Illinois              1\n",
       "Indiana               2\n",
       "Iowa                  2\n",
       "Kansas                2\n",
       "Kentucky              2\n",
       "Louisiana             0\n",
       "Maine                 2\n",
       "Maryland              1\n",
       "Massachusetts         2\n",
       "Michigan              1\n",
       "Minnesota             2\n",
       "Mississippi           0\n",
       "Missouri              2\n",
       "Montana               2\n",
       "Nebraska              2\n",
       "Nevada                1\n",
       "New Hampshire         2\n",
       "New Jersey            2\n",
       "New Mexico            1\n",
       "New York              1\n",
       "North Carolina        0\n",
       "North Dakota          2\n",
       "Ohio                  2\n",
       "Oklahoma              2\n",
       "Oregon                2\n",
       "Pennsylvania          2\n",
       "Rhode Island          2\n",
       "South Carolina        0\n",
       "South Dakota          2\n",
       "Tennessee             0\n",
       "Texas                 1\n",
       "Utah                  2\n",
       "Vermont               2\n",
       "Virginia              2\n",
       "Washington            2\n",
       "West Virginia         2\n",
       "Wisconsin             2\n",
       "Wyoming               2"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe068c39",
   "metadata": {},
   "source": [
    "### (d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "eb29f05e",
   "metadata": {},
   "outputs": [],
   "source": [
    "df= df1.join(df2, lsuffix='_Unscaled', rsuffix='_Scaled')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ef8d01db",
   "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>Cluster_Unscaled</th>\n",
       "      <th>Cluster_Scaled</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Cluster_Unscaled  Cluster_Scaled\n",
       "State                                           \n",
       "Alabama                        0               0\n",
       "Alaska                         0               0\n",
       "Arizona                        0               1\n",
       "Arkansas                       1               2\n",
       "California                     0               1\n",
       "Colorado                       1               1\n",
       "Connecticut                    2               2\n",
       "Delaware                       0               2\n",
       "Florida                        0               1\n",
       "Georgia                        1               0\n",
       "Hawaii                         2               2\n",
       "Idaho                          2               2\n",
       "Illinois                       0               1\n",
       "Indiana                        2               2\n",
       "Iowa                           2               2\n",
       "Kansas                         2               2\n",
       "Kentucky                       2               2\n",
       "Louisiana                      0               0\n",
       "Maine                          2               2\n",
       "Maryland                       0               1\n",
       "Massachusetts                  1               2\n",
       "Michigan                       0               1\n",
       "Minnesota                      2               2\n",
       "Mississippi                    0               0\n",
       "Missouri                       1               2\n",
       "Montana                        2               2\n",
       "Nebraska                       2               2\n",
       "Nevada                         0               1\n",
       "New Hampshire                  2               2\n",
       "New Jersey                     1               2\n",
       "New Mexico                     0               1\n",
       "New York                       0               1\n",
       "North Carolina                 0               0\n",
       "North Dakota                   2               2\n",
       "Ohio                           2               2\n",
       "Oklahoma                       1               2\n",
       "Oregon                         1               2\n",
       "Pennsylvania                   2               2\n",
       "Rhode Island                   1               2\n",
       "South Carolina                 0               0\n",
       "South Dakota                   2               2\n",
       "Tennessee                      1               0\n",
       "Texas                          1               1\n",
       "Utah                           2               2\n",
       "Vermont                        2               2\n",
       "Virginia                       1               2\n",
       "Washington                     1               2\n",
       "West Virginia                  2               2\n",
       "Wisconsin                      2               2\n",
       "Wyoming                        1               2"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3d35f9ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Cluster_Unscaled'][df['Cluster_Unscaled']==0].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2dc23538",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Cluster_Scaled'][df['Cluster_Scaled']==0].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cdf99342",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Cluster_Unscaled'][df['Cluster_Unscaled']==1].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "29948c45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Cluster_Scaled'][df['Cluster_Scaled']==1].count()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c513ed80",
   "metadata": {},
   "source": [
    "Scaling variables tends to increase the observations in the third cluster.<br>\n",
    "The variables should be scaled before doing hierchical clustering in this case because feature units are different. For example, `Murder` is a rate per 100,000 while `UrbanPop` is a percentage of urban poulation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27696c71",
   "metadata": {},
   "source": [
    "## Exercise 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "d2491f2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "X = np.random.rand(60,50)\n",
    "X[:20,:20] += 1\n",
    "X[20:40,20:40] -= 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "4cf76316",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Label the classes\n",
    "y=np.concatenate((np.repeat(0,20),np.repeat(1,20),np.repeat(2,20)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f106b55",
   "metadata": {},
   "source": [
    "### (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "dc10dfce",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca=PCA()\n",
    "pca_X=pca.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "fb94c6ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(pca_X[:,0], pca_X[:,1], c=y, cmap=mpl.cm.Paired)\n",
    "plt.xlabel('Z1')\n",
    "plt.ylabel('Z2');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d6332a5",
   "metadata": {},
   "source": [
    "### (c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "086ab0f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kabousselham\\AppData\\Local\\anaconda3\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1436: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "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>y</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kmeans_3C</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "y           0   1   2\n",
       "kmeans_3C            \n",
       "0           0  20   0\n",
       "1          20   0   0\n",
       "2           0   0  20"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans_3C = KMeans(n_clusters=3,random_state=2,n_init=20).fit(X)\n",
    "pd.crosstab(index=kmeans_3C.labels_,columns=y,rownames=['kmeans_3C'],colnames=['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "021a54c6",
   "metadata": {},
   "source": [
    "Since K-means clustering arbitrarily numbers the clusters, we conclude that is had correctly identified the 3 real clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e47ae4f4",
   "metadata": {},
   "source": [
    "### (d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "75a368c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kabousselham\\AppData\\Local\\anaconda3\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1436: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>y</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kmeans_2C</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "y           0   1   2\n",
       "kmeans_2C            \n",
       "0          20   0   0\n",
       "1           0  20  20"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans_2C = KMeans(n_clusters=2,random_state=3,n_init=20).fit(X)\n",
    "pd.crosstab(index=kmeans_2C.labels_,columns=y,rownames=['kmeans_2C'],colnames=['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be45caaf",
   "metadata": {},
   "source": [
    "K-means identifies classes 1 and 2 as pertaining to the same cluster."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d69c89e",
   "metadata": {},
   "source": [
    "### (e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "fe93216c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kabousselham\\AppData\\Local\\anaconda3\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1436: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
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       "      <th>kmeans_4C</th>\n",
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       "y           0   1   2\n",
       "kmeans_4C            \n",
       "0           0  20   0\n",
       "1          10   0   0\n",
       "2           0   0  20\n",
       "3          10   0   0"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans_4C = KMeans(n_clusters=4,random_state=4,n_init=20).fit(X)\n",
    "pd.crosstab(index=kmeans_4C.labels_,columns=y,rownames=['kmeans_4C'],colnames=['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b27b1c5",
   "metadata": {},
   "source": [
    "K-means splits class 0 in two halves over two clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8603ec5c",
   "metadata": {},
   "source": [
    "### (f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "5f48c19f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kabousselham\\AppData\\Local\\anaconda3\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1436: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
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       "    <tr>\n",
       "      <th>kmeans_3C_pca</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
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      "text/plain": [
       "y               0   1   2\n",
       "kmeans_3C_pca            \n",
       "0              20   0   0\n",
       "1               0   0  20\n",
       "2               0  20   0"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans_3C_pca = KMeans(n_clusters=3,random_state=5,n_init=20).fit(pca_X[:,:2])\n",
    "pd.crosstab(index=kmeans_3C_pca.labels_,columns=y,rownames=['kmeans_3C_pca'],colnames=['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acee19e5",
   "metadata": {},
   "source": [
    "Again, like with the raw data, K-means correctly identifies clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77bf18fb",
   "metadata": {},
   "source": [
    "### (g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "02423994",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kabousselham\\AppData\\Local\\anaconda3\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1436: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>kmeans_3C_stds</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
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       "      <th>1</th>\n",
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       "      <td>0</td>\n",
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       "      <th>2</th>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "</table>\n",
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      "text/plain": [
       "y                0   1   2\n",
       "kmeans_3C_stds            \n",
       "0                0   0  20\n",
       "1               20   0   0\n",
       "2                0  20   0"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaled_X=StandardScaler().fit_transform(X)\n",
    "kmeans_3C_stds = KMeans(n_clusters=3,random_state=6,n_init=20).fit(scaled_X)\n",
    "pd.crosstab(index=kmeans_3C_stds.labels_,columns=y,rownames=['kmeans_3C_stds'],colnames=['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d33b778",
   "metadata": {},
   "source": [
    "Once again, K-means correctly identifies the clusters formed in (b)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a04c52b",
   "metadata": {},
   "source": [
    "## Exercise 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "ede2d049",
   "metadata": {},
   "outputs": [],
   "source": [
    "def complete(data,thresh=1e-7,print_result=False,M=1):\n",
    "    \"\"\"Function which performs matrix completion where missing values are random\n",
    "    data: The data matrix to complete.\n",
    "    thresh: Threshold below which the objective is considered no more decreasing.\n",
    "    print_result: If True the function must print out the progress in each iteration.\n",
    "    M: The number of principal components following the SVD decomposition of data.\"\"\"\n",
    "    data_hat=data.copy()\n",
    "    \n",
    "    #Store the rows and columns indexes of missing values\n",
    "    r_idx=np.argwhere(np.isnan(data_hat))\n",
    "    if r_idx.size==0:\n",
    "        print('Sorry, the inserted matrix is already complete')\n",
    "        return\n",
    "    c_index=np.where(np.any(data_hat==np.isnan,axis=0))\n",
    "    #Step 1 of algorithm 12.1\n",
    "    data_bar=np.nanmean(data_hat,axis=0)\n",
    "    data_hat[np.split(r_idx,2,axis=1)[0],np.split(r_idx,2,axis=1)[1]]=data_bar[\n",
    "        np.split(r_idx,2,axis=1)[1]]\n",
    "    #Prepare data for step 2\n",
    "    rel_err = 1\n",
    "    count = 0\n",
    "    ismiss = np.isnan(data)\n",
    "    mssold = np.mean(data_hat[~ismiss]**2)\n",
    "    mss0 = np.mean(data[~ismiss]**2)\n",
    "    #Proceed to step 2\n",
    "    while rel_err > thresh:\n",
    "        count += 1\n",
    "        # Step 2(a)\n",
    "        U, D, V = np.linalg.svd(data_hat)\n",
    "        L = U[:,:M] * D[None,:M]\n",
    "        data_app=L.dot(V[:M])    \n",
    "        # Step 2(b)\n",
    "        data_hat[ismiss] = data_app[ismiss]\n",
    "        # Step 2(c)\n",
    "        mss = np.mean(((data - data_app)[~ismiss])**2)\n",
    "        rel_err = (mssold - mss) / mss0\n",
    "        mssold = mss\n",
    "        if print_result:\n",
    "            print(\"Iteration: {0}, MSS:{1:.3f}, Rel.Err {2:.2e}\".format(count, mss, rel_err))\n",
    "    return data_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "87caade1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Test on Boston data set\n",
    "Boston=load_data('Boston')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d64d64c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1], dtype=int64)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Boston['chas'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "691e8f79",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>crim</th>\n",
       "      <th>zn</th>\n",
       "      <th>indus</th>\n",
       "      <th>chas</th>\n",
       "      <th>nox</th>\n",
       "      <th>rm</th>\n",
       "      <th>age</th>\n",
       "      <th>dis</th>\n",
       "      <th>rad</th>\n",
       "      <th>tax</th>\n",
       "      <th>ptratio</th>\n",
       "      <th>lstat</th>\n",
       "      <th>medv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      crim    zn  indus  chas    nox     rm   age     dis  rad  tax  ptratio  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "   lstat  medv  \n",
       "0   4.98  24.0  \n",
       "1   9.14  21.6  \n",
       "2   4.03  34.7  \n",
       "3   2.94  33.4  \n",
       "4   5.33  36.2  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Boston.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6bad175c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  5,  4,  8,  6,  7, 24], dtype=int64)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Boston['rad'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6170708e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 506 entries, 0 to 505\n",
      "Data columns (total 13 columns):\n",
      " #   Column   Non-Null Count  Dtype  \n",
      "---  ------   --------------  -----  \n",
      " 0   crim     506 non-null    float64\n",
      " 1   zn       506 non-null    float64\n",
      " 2   indus    506 non-null    float64\n",
      " 3   chas     506 non-null    int64  \n",
      " 4   nox      506 non-null    float64\n",
      " 5   rm       506 non-null    float64\n",
      " 6   age      506 non-null    float64\n",
      " 7   dis      506 non-null    float64\n",
      " 8   rad      506 non-null    int64  \n",
      " 9   tax      506 non-null    int64  \n",
      " 10  ptratio  506 non-null    float64\n",
      " 11  lstat    506 non-null    float64\n",
      " 12  medv     506 non-null    float64\n",
      "dtypes: float64(10), int64(3)\n",
      "memory usage: 51.5 KB\n"
     ]
    }
   ],
   "source": [
    "Boston.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7526c463",
   "metadata": {},
   "outputs": [],
   "source": [
    "#First we standardize and scale all the data set features except 'chas' cause it is a dummy variable\n",
    "scaler=StandardScaler(with_std=True,with_mean=True)\n",
    "Boston_scaled=scaler.fit_transform(Boston.loc[:, Boston.columns != \"chas\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "7eef7a62",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(Boston_scaled, columns = Boston.columns.drop(['chas']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "f379b7af",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Recover 'chas' feature of Boston data set\n",
    "df1=df.join(Boston['chas'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "1151c3ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Leave out increasing numbers of observations from 5% to 30%\n",
    "df11=df1.to_numpy()\n",
    "f_omit = 0.05\n",
    "size=df1.size\n",
    "label_data=['5%','10%','15%3','20%','25%','30%']\n",
    "indexes=[(l,M) for l in label_data for M in range(1,9)]\n",
    "dataframes=[]\n",
    "for j in range(10):\n",
    "    #The iteration of the number seed means the repetition of the experience\n",
    "    np.random.seed(j)\n",
    "    r_idx = np.random.choice(np.arange(df11.shape[0]),int(f_omit*Boston.shape[0]),replace=False)\n",
    "    c_idx = np.random.choice(np.arange(df11.shape[1]),int(f_omit*Boston.shape[0]),replace=True)\n",
    "    df11_f5_na = df11.copy()\n",
    "    df11_f5_na[r_idx, c_idx] = np.nan\n",
    "    row=[r_idx]\n",
    "    column=[c_idx]\n",
    "    data=[df11_f5_na]\n",
    "    app_error=[]\n",
    "    for i in range(1,6):\n",
    "        r_idx=np.delete(np.arange(df1.shape[0]),row[i-1])\n",
    "        c_idx=np.delete(np.arange(df1.shape[1]),column[i-1])\n",
    "        row.append(np.random.choice(r_idx,int(f_omit*Boston.shape[0]),replace=False))\n",
    "        column.append(np.random.choice(c_idx,int(f_omit*Boston.shape[0]),replace=True))\n",
    "        X=data[i-1].copy()\n",
    "        X[row,column]=np.nan\n",
    "        data.append(X)\n",
    "    combined=[(d,M) for d in data for M in range(1,9)]\n",
    "     \n",
    "    for d,M in combined:\n",
    "        #Restore binary values for the last column of complete function\n",
    "        complete_modif=complete(d,M).copy()\n",
    "        complete_modif[:,12]=np.where(complete_modif[:,12]<0.5,0,1)\n",
    "        app_error.append((1/size*np.sum((complete_modif-df11)**2))**(1/2))\n",
    "    dataframes.append(pd.DataFrame(app_error,index=indexes))\n",
    "    dataframes[-1].index.name='(Missing fraction , M)'\n",
    "    dataframes[-1].rename(columns={0:'Rep_'+str(j+1)},inplace=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "c130215e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now let's define the dataframe which sums up the approximation errors\n",
    "dataframe_errors=dataframes[0].join(dataframes[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "b5ef53ee",
   "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>Rep_1</th>\n",
       "      <th>Rep_2</th>\n",
       "      <th>Rep_3</th>\n",
       "      <th>Rep_4</th>\n",
       "      <th>Rep_5</th>\n",
       "      <th>Rep_6</th>\n",
       "      <th>Rep_7</th>\n",
       "      <th>Rep_8</th>\n",
       "      <th>Rep_9</th>\n",
       "      <th>Rep_10</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(Missing fraction , M)</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>(5%, 1)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5%, 2)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5%, 3)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5%, 4)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5%, 5)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5%, 6)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5%, 7)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5%, 8)</th>\n",
       "      <td>0.054628</td>\n",
       "      <td>0.069940</td>\n",
       "      <td>0.057594</td>\n",
       "      <td>0.081803</td>\n",
       "      <td>0.065842</td>\n",
       "      <td>0.088969</td>\n",
       "      <td>0.066072</td>\n",
       "      <td>0.060569</td>\n",
       "      <td>0.083808</td>\n",
       "      <td>0.065350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 1)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 2)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 3)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 4)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 5)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 6)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 7)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10%, 8)</th>\n",
       "      <td>0.077680</td>\n",
       "      <td>0.079349</td>\n",
       "      <td>0.087846</td>\n",
       "      <td>0.101879</td>\n",
       "      <td>0.084274</td>\n",
       "      <td>0.105155</td>\n",
       "      <td>0.090011</td>\n",
       "      <td>0.082083</td>\n",
       "      <td>0.106743</td>\n",
       "      <td>0.070425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 1)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 2)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 3)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 4)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 5)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 6)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 7)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15%3, 8)</th>\n",
       "      <td>0.102269</td>\n",
       "      <td>0.110290</td>\n",
       "      <td>0.097949</td>\n",
       "      <td>0.113089</td>\n",
       "      <td>0.102321</td>\n",
       "      <td>0.130029</td>\n",
       "      <td>0.111324</td>\n",
       "      <td>0.092196</td>\n",
       "      <td>0.126715</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 1)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 2)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 3)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 4)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 5)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 6)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 7)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(20%, 8)</th>\n",
       "      <td>0.119814</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.114521</td>\n",
       "      <td>0.128956</td>\n",
       "      <td>0.117251</td>\n",
       "      <td>0.148637</td>\n",
       "      <td>0.128380</td>\n",
       "      <td>0.110313</td>\n",
       "      <td>0.140227</td>\n",
       "      <td>0.093595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 1)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 2)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 3)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 4)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 5)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 6)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 7)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(25%, 8)</th>\n",
       "      <td>0.138637</td>\n",
       "      <td>0.132927</td>\n",
       "      <td>0.123150</td>\n",
       "      <td>0.137275</td>\n",
       "      <td>0.132226</td>\n",
       "      <td>0.154564</td>\n",
       "      <td>0.143698</td>\n",
       "      <td>0.119013</td>\n",
       "      <td>0.153577</td>\n",
       "      <td>0.114008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 1)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 2)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 3)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 4)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 5)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 6)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 7)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30%, 8)</th>\n",
       "      <td>0.151727</td>\n",
       "      <td>0.142109</td>\n",
       "      <td>0.145652</td>\n",
       "      <td>0.146527</td>\n",
       "      <td>0.145377</td>\n",
       "      <td>0.161635</td>\n",
       "      <td>0.153358</td>\n",
       "      <td>0.131034</td>\n",
       "      <td>0.172065</td>\n",
       "      <td>0.141096</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Rep_1     Rep_2     Rep_3     Rep_4     Rep_5  \\\n",
       "(Missing fraction , M)                                                     \n",
       "(5%, 1)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(5%, 2)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(5%, 3)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(5%, 4)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(5%, 5)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(5%, 6)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(5%, 7)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(5%, 8)                 0.054628  0.069940  0.057594  0.081803  0.065842   \n",
       "(10%, 1)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(10%, 2)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(10%, 3)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(10%, 4)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(10%, 5)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(10%, 6)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(10%, 7)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(10%, 8)                0.077680  0.079349  0.087846  0.101879  0.084274   \n",
       "(15%3, 1)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(15%3, 2)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(15%3, 3)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(15%3, 4)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(15%3, 5)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(15%3, 6)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(15%3, 7)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(15%3, 8)               0.102269  0.110290  0.097949  0.113089  0.102321   \n",
       "(20%, 1)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(20%, 2)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(20%, 3)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(20%, 4)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(20%, 5)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(20%, 6)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(20%, 7)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(20%, 8)                0.119814  0.120031  0.114521  0.128956  0.117251   \n",
       "(25%, 1)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(25%, 2)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(25%, 3)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(25%, 4)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(25%, 5)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(25%, 6)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(25%, 7)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(25%, 8)                0.138637  0.132927  0.123150  0.137275  0.132226   \n",
       "(30%, 1)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "(30%, 2)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "(30%, 3)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "(30%, 4)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "(30%, 5)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "(30%, 6)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "(30%, 7)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "(30%, 8)                0.151727  0.142109  0.145652  0.146527  0.145377   \n",
       "\n",
       "                           Rep_6     Rep_7     Rep_8     Rep_9    Rep_10  \n",
       "(Missing fraction , M)                                                    \n",
       "(5%, 1)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(5%, 2)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(5%, 3)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(5%, 4)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(5%, 5)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(5%, 6)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(5%, 7)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(5%, 8)                 0.088969  0.066072  0.060569  0.083808  0.065350  \n",
       "(10%, 1)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(10%, 2)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(10%, 3)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(10%, 4)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(10%, 5)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(10%, 6)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(10%, 7)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(10%, 8)                0.105155  0.090011  0.082083  0.106743  0.070425  \n",
       "(15%3, 1)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(15%3, 2)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(15%3, 3)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(15%3, 4)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(15%3, 5)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(15%3, 6)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(15%3, 7)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(15%3, 8)               0.130029  0.111324  0.092196  0.126715  0.088596  \n",
       "(20%, 1)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(20%, 2)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(20%, 3)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(20%, 4)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(20%, 5)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(20%, 6)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(20%, 7)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(20%, 8)                0.148637  0.128380  0.110313  0.140227  0.093595  \n",
       "(25%, 1)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(25%, 2)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(25%, 3)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(25%, 4)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(25%, 5)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(25%, 6)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(25%, 7)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(25%, 8)                0.154564  0.143698  0.119013  0.153577  0.114008  \n",
       "(30%, 1)                0.161635  0.153358  0.131034  0.172065  0.141096  \n",
       "(30%, 2)                0.161635  0.153358  0.131034  0.172065  0.141096  \n",
       "(30%, 3)                0.161635  0.153358  0.131034  0.172065  0.141096  \n",
       "(30%, 4)                0.161635  0.153358  0.131034  0.172065  0.141096  \n",
       "(30%, 5)                0.161635  0.153358  0.131034  0.172065  0.141096  \n",
       "(30%, 6)                0.161635  0.153358  0.131034  0.172065  0.141096  \n",
       "(30%, 7)                0.161635  0.153358  0.131034  0.172065  0.141096  \n",
       "(30%, 8)                0.161635  0.153358  0.131034  0.172065  0.141096  "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataframe_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "d94b5374",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Missing fraction , M)\n",
       "(5%, 1)      0.069458\n",
       "(5%, 2)      0.069458\n",
       "(5%, 3)      0.069458\n",
       "(5%, 4)      0.069458\n",
       "(5%, 5)      0.069458\n",
       "(5%, 6)      0.069458\n",
       "(5%, 7)      0.069458\n",
       "(5%, 8)      0.069458\n",
       "(10%, 1)     0.088544\n",
       "(10%, 2)     0.088544\n",
       "(10%, 3)     0.088544\n",
       "(10%, 4)     0.088544\n",
       "(10%, 5)     0.088544\n",
       "(10%, 6)     0.088544\n",
       "(10%, 7)     0.088544\n",
       "(10%, 8)     0.088544\n",
       "(15%3, 1)    0.107478\n",
       "(15%3, 2)    0.107478\n",
       "(15%3, 3)    0.107478\n",
       "(15%3, 4)    0.107478\n",
       "(15%3, 5)    0.107478\n",
       "(15%3, 6)    0.107478\n",
       "(15%3, 7)    0.107478\n",
       "(15%3, 8)    0.107478\n",
       "(20%, 1)     0.122172\n",
       "(20%, 2)     0.122172\n",
       "(20%, 3)     0.122172\n",
       "(20%, 4)     0.122172\n",
       "(20%, 5)     0.122172\n",
       "(20%, 6)     0.122172\n",
       "(20%, 7)     0.122172\n",
       "(20%, 8)     0.122172\n",
       "(25%, 1)     0.134907\n",
       "(25%, 2)     0.134907\n",
       "(25%, 3)     0.134907\n",
       "(25%, 4)     0.134907\n",
       "(25%, 5)     0.134907\n",
       "(25%, 6)     0.134907\n",
       "(25%, 7)     0.134907\n",
       "(25%, 8)     0.134907\n",
       "(30%, 1)     0.149058\n",
       "(30%, 2)     0.149058\n",
       "(30%, 3)     0.149058\n",
       "(30%, 4)     0.149058\n",
       "(30%, 5)     0.149058\n",
       "(30%, 6)     0.149058\n",
       "(30%, 7)     0.149058\n",
       "(30%, 8)     0.149058\n",
       "dtype: float64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#We'll get the required approximation errors by computing the mean of each line\n",
    "dataframe_errors.mean(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31e3f5e9",
   "metadata": {},
   "source": [
    "As expected the averaged approximation errors increase with the fraction of missing values. The number of principal components does not affect those errors<br>.\n",
    "For the case of Boston dataset, the averaged errors range from approximately 7% to 15%."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81ba06de",
   "metadata": {},
   "source": [
    "## Exercise 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "7b0075df",
   "metadata": {},
   "outputs": [],
   "source": [
    "def complete_pca(data,thresh=1e-7,print_result=False,M=1):\n",
    "    \"\"\"Function which performs matrix completion using PCA where missing values are random\n",
    "    data: The data matrix to complete.\n",
    "    thresh: Threshold below which the objective is considered no more decreasing.\n",
    "    print_result: If True the function must print out the progress in each iteration.\n",
    "    M: The number of principal components following the SVD decomposition of data.\"\"\"\n",
    "    pca=PCA()\n",
    "    data_hat=data.copy()\n",
    "    #Store the rows and columns indexes of missing values\n",
    "    r_idx=np.argwhere(np.isnan(data_hat))\n",
    "    if r_idx.size==0:\n",
    "        print('Sorry, the inserted matrix is already complete')\n",
    "        return\n",
    "    c_index=np.where(np.any(data_hat==np.isnan,axis=0))\n",
    "    #Step 1 of algorithm 12.1\n",
    "    data_bar=np.nanmean(data_hat,axis=0)\n",
    "    data_hat[np.split(r_idx,2,axis=1)[0],np.split(r_idx,2,axis=1)[1]]=data_bar[\n",
    "        np.split(r_idx,2,axis=1)[1]]\n",
    "    #Prepare data for step 2\n",
    "    rel_err = 1\n",
    "    count = 0\n",
    "    ismiss = np.isnan(data)\n",
    "    mssold = np.mean(data_hat[~ismiss]**2)\n",
    "    mss0 = np.mean(data[~ismiss]**2)\n",
    "    #Proceed to step 2\n",
    "    while rel_err > thresh:\n",
    "        count += 1\n",
    "        # Step 2(a)\n",
    "        pca.fit(data_hat)\n",
    "        data_app=pca.transform(data_hat)[:,:M].dot(pca.components_[:M])\n",
    "        # Step 2(b)\n",
    "        data_hat[ismiss] = data_app[ismiss]\n",
    "        # Step 2(c)\n",
    "        mss = np.mean(((data - data_app)[~ismiss])**2)\n",
    "        rel_err = (mssold - mss) / mss0\n",
    "        mssold = mss\n",
    "        if print_result:\n",
    "            print(\"Iteration: {0}, MSS:{1:.3f}, Rel.Err {2:.2e}\".format(count, mss, rel_err))\n",
    "    return data_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f811c598",
   "metadata": {},
   "source": [
    "## Exercise 13"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9e1b654",
   "metadata": {},
   "source": [
    "### (a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "90a3d7ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_csv('Ch12Ex13.csv', header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f7bbd5f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>-0.961933</td>\n",
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       "      <td>-0.975005</td>\n",
       "      <td>1.417504</td>\n",
       "      <td>0.818815</td>\n",
       "      <td>0.316294</td>\n",
       "      <td>-0.024967</td>\n",
       "      <td>-0.063966</td>\n",
       "      <td>0.031497</td>\n",
       "      <td>-0.350311</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.509591</td>\n",
       "      <td>-0.216725</td>\n",
       "      <td>-0.055506</td>\n",
       "      <td>-0.484449</td>\n",
       "      <td>-0.521581</td>\n",
       "      <td>1.949135</td>\n",
       "      <td>1.324335</td>\n",
       "      <td>0.468147</td>\n",
       "      <td>1.061100</td>\n",
       "      <td>1.655970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.292526</td>\n",
       "      <td>-1.139267</td>\n",
       "      <td>0.195837</td>\n",
       "      <td>-1.281121</td>\n",
       "      <td>-0.251439</td>\n",
       "      <td>2.511997</td>\n",
       "      <td>-0.922206</td>\n",
       "      <td>0.059543</td>\n",
       "      <td>-1.409645</td>\n",
       "      <td>-0.656712</td>\n",
       "      <td>...</td>\n",
       "      <td>1.700708</td>\n",
       "      <td>0.007290</td>\n",
       "      <td>0.099062</td>\n",
       "      <td>0.563853</td>\n",
       "      <td>-0.257275</td>\n",
       "      <td>-0.581781</td>\n",
       "      <td>-0.169887</td>\n",
       "      <td>-0.542304</td>\n",
       "      <td>0.312939</td>\n",
       "      <td>-1.284377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.258788</td>\n",
       "      <td>-0.972845</td>\n",
       "      <td>0.588486</td>\n",
       "      <td>-0.800258</td>\n",
       "      <td>-1.820398</td>\n",
       "      <td>-2.058924</td>\n",
       "      <td>-0.064764</td>\n",
       "      <td>1.592124</td>\n",
       "      <td>-0.173117</td>\n",
       "      <td>-0.121087</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.615472</td>\n",
       "      <td>0.009999</td>\n",
       "      <td>0.945810</td>\n",
       "      <td>-0.318521</td>\n",
       "      <td>-0.117889</td>\n",
       "      <td>0.621366</td>\n",
       "      <td>-0.070764</td>\n",
       "      <td>0.401682</td>\n",
       "      <td>-0.016227</td>\n",
       "      <td>-0.526553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.152132</td>\n",
       "      <td>-2.213168</td>\n",
       "      <td>-0.861525</td>\n",
       "      <td>0.630925</td>\n",
       "      <td>0.951772</td>\n",
       "      <td>-1.165724</td>\n",
       "      <td>-0.391559</td>\n",
       "      <td>1.063619</td>\n",
       "      <td>-0.350009</td>\n",
       "      <td>-1.489058</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.284277</td>\n",
       "      <td>0.198946</td>\n",
       "      <td>-0.091833</td>\n",
       "      <td>0.349628</td>\n",
       "      <td>-0.298910</td>\n",
       "      <td>1.513696</td>\n",
       "      <td>0.671185</td>\n",
       "      <td>0.010855</td>\n",
       "      <td>-1.043689</td>\n",
       "      <td>1.625275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.195783</td>\n",
       "      <td>0.593306</td>\n",
       "      <td>0.282992</td>\n",
       "      <td>0.247147</td>\n",
       "      <td>1.978668</td>\n",
       "      <td>-0.871018</td>\n",
       "      <td>-0.989715</td>\n",
       "      <td>-1.032253</td>\n",
       "      <td>-1.109654</td>\n",
       "      <td>-0.385142</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.692998</td>\n",
       "      <td>-0.845707</td>\n",
       "      <td>-0.177497</td>\n",
       "      <td>-0.166491</td>\n",
       "      <td>1.483155</td>\n",
       "      <td>-1.687946</td>\n",
       "      <td>-0.141430</td>\n",
       "      <td>0.200778</td>\n",
       "      <td>-0.675942</td>\n",
       "      <td>2.220611</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 40 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         0         1         2         3         4         5         6   \\\n",
       "0 -0.961933  0.441803 -0.975005  1.417504  0.818815  0.316294 -0.024967   \n",
       "1 -0.292526 -1.139267  0.195837 -1.281121 -0.251439  2.511997 -0.922206   \n",
       "2  0.258788 -0.972845  0.588486 -0.800258 -1.820398 -2.058924 -0.064764   \n",
       "3 -1.152132 -2.213168 -0.861525  0.630925  0.951772 -1.165724 -0.391559   \n",
       "4  0.195783  0.593306  0.282992  0.247147  1.978668 -0.871018 -0.989715   \n",
       "\n",
       "         7         8         9   ...        30        31        32        33  \\\n",
       "0 -0.063966  0.031497 -0.350311  ... -0.509591 -0.216725 -0.055506 -0.484449   \n",
       "1  0.059543 -1.409645 -0.656712  ...  1.700708  0.007290  0.099062  0.563853   \n",
       "2  1.592124 -0.173117 -0.121087  ... -0.615472  0.009999  0.945810 -0.318521   \n",
       "3  1.063619 -0.350009 -1.489058  ... -0.284277  0.198946 -0.091833  0.349628   \n",
       "4 -1.032253 -1.109654 -0.385142  ... -0.692998 -0.845707 -0.177497 -0.166491   \n",
       "\n",
       "         34        35        36        37        38        39  \n",
       "0 -0.521581  1.949135  1.324335  0.468147  1.061100  1.655970  \n",
       "1 -0.257275 -0.581781 -0.169887 -0.542304  0.312939 -1.284377  \n",
       "2 -0.117889  0.621366 -0.070764  0.401682 -0.016227 -0.526553  \n",
       "3 -0.298910  1.513696  0.671185  0.010855 -1.043689  1.625275  \n",
       "4  1.483155 -1.687946 -0.141430  0.200778 -0.675942  2.220611  \n",
       "\n",
       "[5 rows x 40 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40f021c4",
   "metadata": {},
   "source": [
    "### (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7d46f648",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Before doing hierchical clustering we should transpose the dataframe cause for meaningful results\n",
    "# genes should be attributes of each patient.\n",
    "df=df.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3ca2c74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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//w13d3dMmTIFo0aNKpqCiUi25Lij14YcG7PqO7iaUiAtCoU9sinlqKYhw6NR361nz56hXr16GDJkCHr27PnG6W/evIkOHTpgxIgR2LhxI3799VeMGTMG5cuX12p+IqKCyHFHT4ULrqYYSItCUR7ZNGR4NOq3OTg4GMHBwVpPv2rVKlSuXBlLly4FAPj6+iImJgZffvklAw4REWlgcC0cQx3ZLIrwWKze9dOnTyMoKEhtWLt27bB27VpkZ2fD0tJSY57MzExkZmaqnqemphq8TiIiIjkozgGxWN2qITExES4uLmrDXFxckJOTg0ePHuU7z4IFC2Bvb696eHh4FEWpREREZETFKuAA0GiIJITId3ie0NBQpKSkqB537twxeI1ERERkXMXquJOrqysSExPVhiUlJcHCwgJOTk75zmNtbQ1ra+uiKI+ISjBtLqtl3ytERadYBZyAgADs2bNHbdihQ4fg7++fb/sbIqKioMtltex7hciwjHqK6unTp7hw4QIuXLgA4MVl4BcuXEB8fDyAF6eXBg4cqJp+1KhRuH37NkJCQhAXF4d169Zh7dq1mDx5sjHKJyICYJjLavMunyUi3Rj1CE5MTAxatmypeh4SEgIAGDRoECIiIpCQkKAKOwDg5eWFqKgoTJw4EStXroS7uzuWL1/OS8SJyGQU9rLaktr3CpG+GTXgtGjRQtVIOD8REREaw5o3b45z584ZsCoikqP82si8qU2MLu1givNltUSGUFTfvVfxW0hEsqdNG5n82sSwHQxR4Rjzu1fsLhMnIpJK1zYybAdDVDjG/O7xCA4RlSjatJFhOxjt8fJ40lZRf/cYcIioRGEbGf3h5fHSvCkMyj0IFvV3j99yIiLSiSEvj5dbCJUaBosqCBqrAXBRkNcniIiIjIKXx7+evsOgPoKg3BvfM+AQEVGh8dSf9goTBvUZBAvbANjU32/Tro6IiEhmTDEMyrHxvWm9wkRERFTkTDF0FZa8toaIqBiRcwNPImNjwCEiMgK5N/CkwtMlAAMMwXkYcIiIjEDuDTypcHQNwABDcB5+Q4iIjEyODTyLG1M7XViYy8oZgl8o2VtPRGQC5NjAszgx9dOF2l5WzhCsjt8oIiIq0Uz9dCEDsG74ihEREf0PTxfKBwMOERHR//BoiXyYGbsAIiIiIn1jwCEiIiLZ4XE4IiIqUqZ2STbJEwMOEZGMmVqYMPVLskk+GHCIiGTKFMOEqV+STfLBTwoRkUyZepjgJdlkSAw4REQlgCmGCV6STYbETxYRUQnAMEElDS8TJyIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2dE54Fy/fh0HDx5ERkYGAEAIobeiiIiIiApDcsB5/Pgx2rRpg+rVq6NDhw5ISEgAAAwfPhyTJk3Se4FEREREUkkOOBMnToSFhQXi4+NhZ2enGt6nTx8cOHBAr8URERER6cJC6gyHDh3CwYMHUalSJbXhPj4+uH37tt4KIyIiItKV5CM4z549Uztyk+fRo0ewtrbWS1FEREREhSE54DRr1gwbNmxQPVcoFFAqlVi8eDFatmyp1+KIiIiIdCH5FNXixYvRokULxMTEICsrC1OmTMHff/+N5ORk/Prrr4aokYiIiEgSyUdwatWqhT/++AONGjVC27Zt8ezZM/To0QPnz59HtWrVDFEjERERkSSSj+AAgKurK2bPnq3vWoiIiIj0QvIRnPXr12Pbtm0aw7dt24bvvvtOL0URERERFYbkgLNw4UI4OztrDK9QoQLmz5+vl6KIiIiICkNywLl9+za8vLw0hnt6eiI+Pl4vRREREREVhuSAU6FCBfzxxx8awy9evAgnJye9FEVERERUGJIDTt++fTFu3DgcPXoUubm5yM3NxZEjRzB+/Hj07dvXEDUSERERSSL5Kqq5c+fi9u3baN26NSwsXsyuVCoxcOBAtsEhIiIikyA54FhZWSEyMhJffPEFLl68CFtbW9SpUweenp6GqI+IiIhIMsmnqPJUr14d7733Hjp16lSocBMWFgYvLy/Y2NjAz88PJ06ceO30mzZtQr169WBnZwc3NzcMGTIEjx8/1nn9REREJD+Sj+Dk5uYiIiIChw8fRlJSEpRKpdr4I0eOaL2syMhITJgwAWFhYWjSpAlWr16N4OBgXLp0CZUrV9aY/uTJkxg4cCC++uordO7cGffu3cOoUaMwfPhw7Ny5U+qmEBERkUxJDjjjx49HREQEOnbsiNq1a0OhUOi88iVLlmDYsGEYPnw4AGDp0qU4ePAgwsPDsWDBAo3pz5w5gypVqmDcuHEAAC8vL4wcORKLFi3SuQYiIiKSH8kBZ8uWLdi6dSs6dOhQqBVnZWUhNjYWn332mdrwoKAgnDp1Kt95AgMDMW3aNERFRSE4OBhJSUnYvn07OnbsWOB6MjMzkZmZqXqemppaqLqJiIjI9Elug2NlZQVvb+9Cr/jRo0fIzc2Fi4uL2nAXFxckJibmO09gYCA2bdqEPn36wMrKCq6urnBwcMCKFSsKXM+CBQtgb2+venh4eBS6diIiIjJtkgPOpEmTsGzZMggh9FLAq6e4hBAFnva6dOkSxo0bhxkzZiA2NhYHDhzAzZs3MWrUqAKXHxoaipSUFNXjzp07eqmbiIiITJfkU1QnT57E0aNHsX//frz11luwtLRUG79jxw6tluPs7Axzc3ONozVJSUkaR3XyLFiwAE2aNMEnn3wCAKhbty5KlSqFpk2bYu7cuXBzc9OYx9raGtbW1lrVJEdCCGRk5xq7jCKRnpWT799yZmtpXqh2cEREciU54Dg4OKB79+6FXrGVlRX8/PwQHR2ttrzo6Gh07do133nS09NVnQvmMTc3BwC9HVGSEyEEeq06jdjbT4xdSpHzn3vY2CUUCX/Pctg2KoAhh4joFZIDzvr16/W28pCQEHzwwQfw9/dHQEAA1qxZg/j4eNUpp9DQUNy7dw8bNmwAAHTu3BkjRoxAeHg42rVrh4SEBEyYMAGNGjWCu7u73uqSi4zs3BIZbkqSmNtPkJGdCzsryV9lIiJZM+qvYp8+ffD48WPMmTMHCQkJqF27NqKiolQdByYkJKjdoXzw4MFIS0vD119/jUmTJsHBwQGtWrXCf/7zH2NtQrER83kb2FmZG7sM0pP0rFz4z/3Z2GUQEZksnQLO9u3bsXXrVsTHxyMrK0tt3Llz5yQta8yYMRgzZky+4yIiIjSGffzxx/j4448lrYMAOytz/pdPREQlhuQ93vLlyzFt2jQMGjQIP/30E4YMGYJ//vkHZ8+exdixYw1RI1GxY+jG3UXZoJoNmYmoOJIccMLCwrBmzRr069cP3333HaZMmYKqVatixowZSE5ONkSNRMVKUTfuNnSDajZkJqLiSHLAiY+PR2BgIADA1tYWaWlpAIAPPvgAjRs3xtdff63fCoszIYDsdOOtP+ulIwhZ6QCM2AbH0g4oITtIuTXuZkNmIiqOJP9iubq64vHjx/D09ISnpyfOnDmDevXq4ebNm7xU+2VCAOvaAXd+M2IN1gD+d9XbYm9AkfnayQ3KozEw9ECJCTl5inPjbjZkJqLiTHLAadWqFfbs2YO3334bw4YNw8SJE7F9+3bExMSgR48ehqixeMpON264AWCnyMQtm/eNWoPKnTMvXhOrUsaupEixcTcRkXFI/uVds2YNlEolAGDUqFFwdHTEyZMn0blz59feMqFEm3wdsLIzdhXGkZUOfFn4e5cRERFJITng3L17V+2Glb1790bv3r0hhMCdO3dQuXJlvRYoC1Z2Je7IBRERkTFJvtmml5cXHj58qDE8OTkZXl5eeimKiIiIqDAkB5yC7vb99OlT2NjY6KUoIiIiosLQ+hRVSEgIAEChUGD69Omws/v/NiW5ubn47bffUL9+fb0XSERERCSV1gHn/PnzAF4cwfnzzz9hZWWlGmdlZYV69eph8uTJ+q+QiIiISCKtA87Ro0cBAEOGDMGyZctQtmxZgxVFJkIfHRVmpef/d2GUoE4DDUEIAZGR8cbplC91FKlMz4AyR7v+fBS2tuz1mIiMTvJVVOvXr1d7npqaiiNHjqBmzZqoWbOm3gojIzNER4X6uly8hHYaqA9CCNx+vz8y/ndE9nWem1sBnecDAK41eRc2uVlvmOMF27ffhuemjQw5RGRUkgNO79690axZM3z00UfIyMiAv78/bt26BSEEtmzZgp49exqiTipqJtBRYYFKaKeB+iAyMrQKNwBgk5uF/bukn3bOOHcOIiMDCrsS2vcTEZkEyQHnl19+wbRp0wAAO3fuhBAC//77L7777jvMnTuXAUeOTKWjQnYaqFc+v56Ema2t3panzMjAtSbv6m15RESFITngpKSkwNHREQBw4MAB9OzZE3Z2dujYsSM++eQTvRdIJoAdFcqSma0tzHiUhYhkSnI/OB4eHjh9+jSePXuGAwcOICgoCADw5MkT9oNDREREJkHyEZwJEyagf//+KF26NDw9PdGiRQsAL05d1alTR9/1mQZdriYq7NVDvFKIiIhIZ5IDzpgxY9CoUSPcuXMHbdu2hZnZi4NAVatWxdy5c/VeoNHp42oiXdqN8EohIiIinUkOOADg7+8Pf39/tWEdO3bUS0Emx1hXE/FKIZMjhEBGzpv7j0nPzn3p7wxA8eb+Y2wtTLfvGK37zXlpGqUW0wPsM4eIDEergBMSEoIvvvgCpUqVUt2yoSBLlizRS2EmqSiuJippVwpJOf2n62k/PZzuE0Jg4P6BuPDwwpunVVoC+AIA0GJrcyjMst84T4MKDfBd++9Mbmcvpd+cl2l7NRX7zCEiQ9Eq4Jw/fx7Z2dmqvwsi+x8pXk2kX4U5/SclBOrhdF9GToZW4QYAFGbZKOP7maTln086j4ycDNhZmtZVTVL6zdEF+8whIkPRKuDk3abh1b+JCqWoTv/p+XTfsd7HYGuhn/5jMnIy0GJrC70sy9D02W8O+8whIkPTqQ0OyUx+p4nedDpI31d5GeL0n4FO99la2JrckZaiwH5ziKg40Srg9OjRQ+sF7tixQ+diyAi0OU2UX0jQ91VePP1HRER6pFVHf/b29qpH2bJlcfjwYcTExKjGx8bG4vDhw7C3tzdYoWQgup4myjvtQ0REZIK0OoLz8h3EP/30U/Tu3RurVq2CufmLy19zc3MxZswYlC1b1jBVyoU2VwxJuVLIGKeJStpVXkREVCxJboOzbt06nDx5UhVuAMDc3BwhISEIDAzE4sWL9VqgbOhyxdCbggRPE5k0bfrNeXn8m6Y15b5yiIhMjeSAk5OTg7i4ONSoUUNteFxcHJRKpd4Kkx1DXDF05wzw7JHmURfe5sHopPSbk+dNV1OZal85RESmSHLAGTJkCIYOHYrr16+jcePGAIAzZ85g4cKFGDJkiN4LlCVtrxgSAtjQFbgXU/A0RdEAmCST0m+Otky1rxwiIlMkOeB8+eWXcHV1xVdffYWEhAQAgJubG6ZMmYJJkybpvUBZ0vZUUNaz14ebgvA2DyalsP3mFKe+cgDtbu0g5bYOvJ0DEelCcsAxMzPDlClTMGXKFKSmpgKAfBoXm0J/MAVhA+BiS0q/OW9qt5PfOFNqm6PLrR3e1OEfb+dARLooVEd/sgk2gOn0B1MQNgB+PV3CKWBS7ZW0abeT35EcU2qbY4hbO/B2DkSkC/ZknKew/cEwfBiPruEUMKn2Srq22zHVtjmFvbUDb+dARIXBgJMfng4qXgpzhZqJBlRt2u2Yetsc3tqBiIyJASc/PB1UfGl7hZqJB9SSer8rIiJ9YcAhwyuoB2dDNOBmOCUiImgZcJYvX671AseNG6dzMSRD2vbgzP58iIhIj7QKOF999ZXa84cPHyI9PR0ODg4AgH///Rd2dnaoUKECAw6pk2H7GCIiMn1aBZybN2+q/v7hhx8QFhaGtWvXqm7XcOXKFYwYMQIjR440TJUkDzJpH0NERKZPchuc6dOnY/v27Wr3oqpRowa++uor9OrVC/3799drgSQjbB9DBciv9+M39XbMHo6J6HUkB5yEhARkZ2drDM/NzcWDBw/0UhQRlRza9H6cX3847OGYiF7HTOoMrVu3xogRIxATEwMhBAAgJiYGI0eORJs2bfReIBHJm669H+f1cExElB/JR3DWrVuHQYMGoVGjRrC0tAQA5OTkoF27dvj222/1XiARlRza9H7MHo6JSBuSA0758uURFRWFq1ev4vLlyxBCwNfXF9WrVzdEfURUgrD3YyLSF507+qtSpQqEEKhWrRosLNhfIBEREZkOyW1w0tPTMWzYMNjZ2eGtt95CfHw8gBcd/C1cuFDvBRIRERFJJTnghIaG4uLFizh27BhsbGxUw9u0aYPIyEi9FkdERESkC8nnlnbt2oXIyEg0btxY7fLMWrVq4Z9//tFrcURERES6kHwE5+HDh6hQoYLG8GfPnrE/CiIiIjIJkgNOw4YNsW/fPtXzvFDzzTffICAgQH+VEREREelI8imqBQsWoH379rh06RJycnKwbNky/P333zh9+jSOHz9uiBqJiIiIJJF8BCcwMBC//vor0tPTUa1aNRw6dAguLi44ffo0/Pz8DFEjERERkSSSAw4A1KlTB9999x3++usvXLp0CRs3bkSdOnV0KiAsLAxeXl6wsbGBn58fTpw48drpMzMzMW3aNHh6esLa2hrVqlXDunXrdFo3ERERyZPkU1Tnzp2DpaWlKtD89NNPWL9+PWrVqoVZs2bByspK62VFRkZiwoQJCAsLQ5MmTbB69WoEBwfj0qVLqFy5cr7z9O7dGw8ePMDatWvh7e2NpKQk5OTkSN0MIiIikjHJR3BGjhyJq1evAgBu3LiBPn36wM7ODtu2bcOUKVMkLWvJkiUYNmwYhg8fDl9fXyxduhQeHh4IDw/Pd/oDBw7g+PHjiIqKQps2bVClShU0atQIgYGBUjeDiIiIZExywLl69Srq168PANi2bRuaN2+OH374AREREfjxxx+1Xk5WVhZiY2MRFBSkNjwoKAinTp3Kd57du3fD398fixYtQsWKFVG9enVMnjwZGa+5o3BmZiZSU1PVHkRERCRvkk9RCSGgVCoBAD///DM6deoEAPDw8MCjR4+0Xs6jR4+Qm5sLFxcXteEuLi5ITEzMd54bN27g5MmTsLGxwc6dO/Ho0SOMGTMGycnJBbbDWbBgAWbPnq11XURERFT8ST6C4+/vj7lz5+L777/H8ePH0bFjRwDAzZs3NcKKNl7tHFAIUWCHgUqlEgqFAps2bUKjRo3QoUMHLFmyBBEREQUexQkNDUVKSorqcefOHck1EhERUfEiOeAsXboU586dw0cffYRp06bB29sbALB9+3ZJbWGcnZ1hbm6ucbQmKSmpwKDk5uaGihUrwt7eXjXM19cXQgjcvXs333msra1RtmxZtQcRERHJm+RTVHXr1sWff/6pMXzx4sUwNzfXejlWVlbw8/NDdHQ0unfvrhoeHR2Nrl275jtPkyZNsG3bNjx9+hSlS5cG8KJNkJmZGSpVqiRxS4iIiEiudOoHJz82NjawtLSUNE9ISAi+/fZbrFu3DnFxcZg4cSLi4+MxatQoAC9OLw0cOFA1/fvvvw8nJycMGTIEly5dwi+//IJPPvkEQ4cOha2trb42hYiIiIo5yUdwcnNz8dVXX2Hr1q2Ij49HVlaW2vjk5GStl9WnTx88fvwYc+bMQUJCAmrXro2oqCh4enoCABISEhAfH6+avnTp0oiOjsbHH38Mf39/ODk5oXfv3pg7d67UzSAiIiIZkxxwZs+ejW+//RYhISGYPn06pk2bhlu3bmHXrl2YMWOG5ALGjBmDMWPG5DsuIiJCY1jNmjURHR0teT1ERERUckg+RbVp0yZ88803mDx5MiwsLNCvXz98++23mDFjBs6cOWOIGomIiIgkkRxwEhMTVbdpKF26NFJSUgAAnTp1wr59+/RbHREREZEOJAecSpUqISEhAQDg7e2NQ4cOAQDOnj0La2tr/VZHREREpAPJAad79+44fPgwAGD8+PGYPn06fHx8MHDgQAwdOlTvBRIRERFJJbmR8cKFC1V/9+rVC5UqVcKpU6fg7e2NLl266LU4IiIiIl1IDjivaty4MRo3bqyPWoiIiIj0QqeAc+XKFaxYsQJxcXFQKBSoWbMmPv74Y9SoUUPf9RERERFJJrkNzvbt21G7dm3ExsaiXr16qFu3Ls6dO4fatWtj27ZthqiRiIiISBLJR3CmTJmC0NBQzJkzR234zJkz8emnn+K9997TW3FEREREutCpH5yX7w+VZ8CAARp3BiciIiIyBskBp0WLFjhx4oTG8JMnT6Jp06Z6KYqIiIioMLQ6RbV7927V3126dMGnn36K2NhY1dVTZ86cwbZt2zB79mzDVElEREQkgVYBp1u3bhrDwsLCEBYWpjZs7NixGDVqlF4KIyIiItKVVgFHqVQaug4iIiIivZHcBudld+/eZfghIiIik1OogFOrVi3cunVLT6UQERER6UehAo4QQl91EBEREelNoQIOERERkSkqVMCZOnUqHB0d9VULERERkV4U6m7ioaGh+qqDiIiISG8kB5zc3FxERETg8OHDSEpK0riK6siRI3orjoiIiEgXkgPO+PHjERERgY4dO6J27dpQKBSGqIuIiIhIZ5IDzpYtW7B161Z06NDBEPUQERERFZrkRsZWVlbw9vY2RC1EREREeiE54EyaNAnLli1jHzhERERksiSfojp58iSOHj2K/fv346233oKlpaXa+B07duitOCIiIiJdSA44Dg4O6N69uyFqISIiItILyQFn/fr1hqiDiIiISG907ujv4cOHuHLlChQKBapXr47y5cvrsy4iIiIinUluZPzs2TMMHToUbm5uaNasGZo2bQp3d3cMGzYM6enphqiRiIiISBLJASckJATHjx/Hnj178O+//+Lff//FTz/9hOPHj2PSpEmGqJGIiIhIEsmnqH788Uds374dLVq0UA3r0KEDbG1t0bt3b4SHh+uzPiIiIiLJJB/BSU9Ph4uLi8bwChUq8BQVERERmQTJAScgIAAzZ87E8+fPVcMyMjIwe/ZsBAQE6LU4IiIiIl1IPkW1bNkytG/fHpUqVUK9evWgUChw4cIF2NjY4ODBg4aokYiIiEgSyQGndu3auHbtGjZu3IjLly9DCIG+ffuif//+sLW1NUSNRERERJLo1A+Ora0tRowYoe9aiIiIiPRCq4Cze/duBAcHw9LSErt3737ttF26dNFLYURERES60irgdOvWDYmJiahQoQK6detW4HQKhQK5ubn6qo2IiIhIJ1oFHKVSme/fRERERKZI8mXiGzZsQGZmpsbwrKwsbNiwQS9FERERERWG5IAzZMgQpKSkaAxPS0vDkCFD9FIUERERUWFIDjhCCCgUCo3hd+/ehb29vV6KIiIiIioMrS8Tb9CgARQKBRQKBVq3bg0Li/+fNTc3Fzdv3kT79u0NUiQRERGRFFoHnLyrpy5cuIB27dqhdOnSqnFWVlaoUqUKevbsqfcCiYiIiKTSOuDMnDkTAFClShX06dMHNjY2BiuKiIiIqDAk92Q8aNAgQ9RBREREpDeSA05ubi6++uorbN26FfHx8cjKylIbn5ycrLfiiIiIiHQh+Sqq2bNnY8mSJejduzdSUlIQEhKCHj16wMzMDLNmzTJAiURERETSSA44mzZtwjfffIPJkyfDwsIC/fr1w7fffosZM2bgzJkzhqiRiIiISBLJAScxMRF16tQBAJQuXVrV6V+nTp2wb98+/VZHREREpAPJAadSpUpISEgAAHh7e+PQoUMAgLNnz8La2lq/1RERERHpQHLA6d69Ow4fPgwAGD9+PKZPnw4fHx8MHDgQQ4cO1XuBRERERFJJDjgLFy7E1KlTAQC9evXCiRMnMHr0aGzbtg0LFy6UXEBYWBi8vLxgY2MDPz8/nDhxQqv5fv31V1hYWKB+/fqS10lERETyJvky8Vc1btwYjRs31mneyMhITJgwAWFhYWjSpAlWr16N4OBgXLp0CZUrVy5wvpSUFAwcOBCtW7fGgwcPdC2diIiIZEqrgLN7926tF9ilSxetp12yZAmGDRuG4cOHAwCWLl2KgwcPIjw8HAsWLChwvpEjR+L999+Hubk5du3apfX6iIiIqGTQKuDk3YfqTRQKBXJzc7WaNisrC7Gxsfjss8/UhgcFBeHUqVMFzrd+/Xr8888/2LhxI+bOnfvG9WRmZiIzM1P1PDU1Vav6iIiIqPjSqg2OUqnU6qFtuAGAR48eITc3Fy4uLmrDXVxckJiYmO88165dw2effYZNmzap3c38dRYsWAB7e3vVw8PDQ+saiYiIqHiS3Mj4Zc+fPy90AQqFQu25EEJjGPDiFhHvv/8+Zs+ejerVq2u9/NDQUKSkpKged+7cKXTNREREZNokB5zc3Fx88cUXqFixIkqXLo0bN24AAKZPn461a9dqvRxnZ2eYm5trHK1JSkrSOKoDAGlpaYiJicFHH30ECwsLWFhYYM6cObh48SIsLCxw5MiRfNdjbW2NsmXLqj2IiIhI3iQHnHnz5iEiIgKLFi2ClZWVanidOnXw7bffar0cKysr+Pn5ITo6Wm14dHQ0AgMDNaYvW7Ys/vzzT1y4cEH1GDVqFGrUqIELFy7gnXfekbopREREJFOSLxPfsGED1qxZg9atW2PUqFGq4XXr1sXly5clLSskJAQffPAB/P39ERAQgDVr1iA+Pl613NDQUNy7dw8bNmyAmZkZateurTZ/hQoVYGNjozGciIiISjbJAefevXvw9vbWGK5UKpGdnS1pWX369MHjx48xZ84cJCQkoHbt2oiKioKnpycAICEhAfHx8VJLJCIiohJO8imqt956K9/ehrdt24YGDRpILmDMmDG4desWMjMzERsbi2bNmqnGRURE4NixYwXOO2vWLFy4cEHyOomIiEjeJB/BmTlzJj744APcu3cPSqUSO3bswJUrV7Bhwwbs3bvXEDUSERERSSL5CE7nzp0RGRmJqKgoKBQKzJgxA3FxcdizZw/atm1riBqJiIiIJJF0BCcnJwfz5s3D0KFDcfz4cUPVRERERFQoko7gWFhYYPHixZJ6LCYiIiIqapJPUbVp0+a1DX+JiIiIjE1yI+Pg4GCEhobir7/+gp+fH0qVKqU2XsrdxImIiIgMQXLAGT16NABgyZIlGuOk3E2ciIiIyFAkBxylUmmIOoiIiIj0RlIbnJycHFhYWOCvv/4yVD1EREREhSb5KipPT0+ehiIiIiKTJvkqqs8//xyhoaFITk42RD1EREREhSa5Dc7y5ctx/fp1uLu7w9PTU+MqqnPnzumtOCIiIiJdSA443bp1M0AZRERERPqj0802iYiIiEyZ5ICTJzY2FnFxcVAoFKhVqxYaNGigz7qIiIiIdCY54CQlJaFv3744duwYHBwcIIRASkoKWrZsiS1btqB8+fKGqJOIiIhIa5Kvovr444+RmpqKv//+G8nJyXjy5An++usvpKamYty4cYaokYiIiEgSyUdwDhw4gJ9//hm+vr6qYbVq1cLKlSsRFBSk1+KIiIiIdCH5CI5SqYSlpaXGcEtLS97GgYiIiEyC5IDTqlUrjB8/Hvfv31cNu3fvHiZOnIjWrVvrtTgiIiIiXUgOOF9//TXS0tJQpUoVVKtWDd7e3vDy8kJaWhpWrFhhiBqJiIiIJJHcBsfDwwPnzp1DdHQ0Ll++DCEEatWqhTZt2hiiPiIiIiLJdO4Hp23btmjbtq0+ayEiIiLSC61PUR05cgS1atVCamqqxriUlBS89dZbOHHihF6LIyIiItKF1gFn6dKlGDFiBMqWLasxzt7eHiNHjsSSJUv0WhwRERGRLrQOOBcvXkT79u0LHB8UFITY2Fi9FEVERERUGFoHnAcPHuTb/00eCwsLPHz4UC9FERERERWG1gGnYsWK+PPPPwsc/8cff8DNzU0vRREREREVhtYBp0OHDpgxYwaeP3+uMS4jIwMzZ85Ep06d9FocERERkS60vkz8888/x44dO1C9enV89NFHqFGjBhQKBeLi4rBy5Urk5uZi2rRphqyViIiISCtaBxwXFxecOnUKo0ePRmhoKIQQAACFQoF27dohLCwMLi4uBiuUiIiISFuSOvrz9PREVFQUnjx5guvXr0MIAR8fH5QrV85Q9RERERFJplNPxuXKlUPDhg31XQsRERGRXki+2SYRERGRqWPAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItkxesAJCwuDl5cXbGxs4OfnhxMnThQ47Y4dO9C2bVuUL18eZcuWRUBAAA4ePFiE1RIREVFxYNSAExkZiQkTJmDatGk4f/48mjZtiuDgYMTHx+c7/S+//IK2bdsiKioKsbGxaNmyJTp37ozz588XceVERERkyowacJYsWYJhw4Zh+PDh8PX1xdKlS+Hh4YHw8PB8p1+6dCmmTJmChg0bwsfHB/Pnz4ePjw/27NlTxJUTERGRKTNawMnKykJsbCyCgoLUhgcFBeHUqVNaLUOpVCItLQ2Ojo4FTpOZmYnU1FS1BxEREcmb0QLOo0ePkJubCxcXF7XhLi4uSExM1GoZ//3vf/Hs2TP07t27wGkWLFgAe3t71cPDw6NQdRMREZHpM3ojY4VCofZcCKExLD+bN2/GrFmzEBkZiQoVKhQ4XWhoKFJSUlSPO3fuFLpmIiIiMm0Wxlqxs7MzzM3NNY7WJCUlaRzVeVVkZCSGDRuGbdu2oU2bNq+d1traGtbW1oWul4iIiIoPox3BsbKygp+fH6Kjo9WGR0dHIzAwsMD5Nm/ejMGDB+OHH35Ax44dDV0mERERFUNGO4IDACEhIfjggw/g7++PgIAArFmzBvHx8Rg1ahSAF6eX7t27hw0bNgB4EW4GDhyIZcuWoXHjxqqjP7a2trC3tzfadhAREZFpMWrA6dOnDx4/fow5c+YgISEBtWvXRlRUFDw9PQEACQkJan3irF69Gjk5ORg7dizGjh2rGj5o0CBEREQUdflERERkoowacABgzJgxGDNmTL7jXg0tx44dM3xBREREVOwZ/SoqIiIiIn1jwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISIiItlhwCEiIiLZMXrACQsLg5eXF2xsbODn54cTJ068dvrjx4/Dz88PNjY2qFq1KlatWlVElRIREVFxYdSAExkZiQkTJmDatGk4f/48mjZtiuDgYMTHx+c7/c2bN9GhQwc0bdoU58+fx9SpUzFu3Dj8+OOPRVw5ERERmTKjBpwlS5Zg2LBhGD58OHx9fbF06VJ4eHggPDw83+lXrVqFypUrY+nSpfD19cXw4cMxdOhQfPnll0VcOREREZkyC2OtOCsrC7Gxsfjss8/UhgcFBeHUqVP5znP69GkEBQWpDWvXrh3Wrl2L7OxsWFpaasyTmZmJzMxM1fOUlBQAQGpq6isFPQMyBf43ErDKfcMGGHh6uazDFGvSYZ707HTkZuT+b/JU5Fjm6HX6olqHMj0dT3P/fx6znNfPY+jpi2od6Vk5UGamq+bJsXr9T5+hp5fLOkyxpqJYhynWVBTrMHZNefttIcQb15s3oVHcu3dPABC//vqr2vB58+aJ6tWr5zuPj4+PmDdvntqwX3/9VQAQ9+/fz3eemTNnCgB88MEHH3zwwYcMHnfu3NEqZxjtCE4ehUKh9lwIoTHsTdPnNzxPaGgoQkJCVM+VSiWSk5Ph5OT02vUQERGR6RBCIC0tDe7u7lpNb7SA4+zsDHNzcyQmJqoNT0pKgouLS77zuLq65ju9hYUFnJyc8p3H2toa1tbWasMcHBx0L5yIiIiMwt7eXutpjdbI2MrKCn5+foiOjlYbHh0djcDAwHznCQgI0Jj+0KFD8Pf3z7f9DREREZVMRr2KKiQkBN9++y3WrVuHuLg4TJw4EfHx8Rg1ahSAF6eXBg4cqJp+1KhRuH37NkJCQhAXF4d169Zh7dq1mDx5srE2gYiIiEyQUdvg9OnTB48fP8acOXOQkJCA2rVrIyoqCp6engCAhIQEtT5xvLy8EBUVhYkTJ2LlypVwd3fH8uXL0bNnT2NtAhEREZkghRDaXm9FREREVDwY/VYNRERERPrGgENERESyw4BDREREssOAQ0RERLLDgENERESyw4BDRCRjvFCWSiqj34vKmB4/fow//vgD9erVg6OjIx49eoS1a9ciMzMT7733Hnx9fdWmz8jIwObNm3Hy5EkkJCTA3NwcXl5e6NatG1q3bm2krdDN3bt34eDggNKlS6sNz87OxunTp9GsWTPVsD179iAmJgbt27dHQEAAjhw5gi+//BJKpRI9evTAhx9+qJr2v//9L3r16qXqy8hQtdvY2MDZ2RkAcOLECaxatQrx8fHw9PTE2LFjERAQYLD169OzZ8/www8/4NSpU0hMTIRCoYCLiwuaNGmCfv36oVSpUlov68GDB1i9ejVmzJjxxmmrVq2KgwcPwsfH57XTZWdnY9++fbh27Rrc3NzQvXt3STWR8VlbW+PixYsav2dFKSEhAeHh4fn+dg4ePBjm5uaFWv7du3cRHh6u8T0KDAzEqFGj4OHhoactoeKkxPaD8/vvvyMoKAipqalwcHBAdHQ03nvvPVhYWEAIgXv37uHkyZN4++23AQDXr19HmzZt8PTpU1hZWSExMREdOnTAo0ePEBMTgx49euCHH36AhcX/Z0YpwQCQvuPWJUwkJCSga9euiI2NhUKhQP/+/bFy5UpV0Hnw4AHc3d2Rm5sLAFi1ahU+/vhj1KtXD9euXUNYWBhGjx6NPn36wNzcHBs2bMCCBQswfvx4AICZmRnMzMzQsmVLDB8+HN27d4eVlZUO79D/e3XHHRgYiOnTpyM4OBg//fQTevTogU6dOsHX1xdXr17F3r17sWPHDnTq1KnAZWqz49ZHoH1dkLh06RLatm2L9PR0NG/eHC4uLhBCICkpCcePH0epUqVw6NAh1KpVS6t1Xbx4EW+//bbqvQOA5cuX5zttSEgIpkyZAldXVwDAuHHjALx4baOiouDg4ICHDx+idevWuHLlCjw9PXHnzh1UqFABp06dQsWKFVXL0jWkSQnZUv8ZeZM7d+5g5syZWLdundpwqd/ZV+t+3Wfq/PnzcHBwgJeXFwBg48aNCA8PV32/P/roI/Tt21dtmStWrEBMTAw6duyI3r174/vvv8eCBQtU9cyZM0f1m/PyTYVftmzZMgwYMEB1v74lS5aojdf1HwZt37+YmBi0adMGXl5esLW1xW+//Yb+/fsjKysLBw8ehK+vLw4ePIgyZcqoliHlt+3kyZMIDg6Gh4cHgoKC1L5H0dHRuHPnDvbv348mTZpozKuPfzBe9x3PyMhAbGwsHB0dNb7Hz58/x9atW9V664+Li8OZM2cQEBCAmjVr4vLly1i2bBkyMzMxYMAAtGrVKt91aPs79fHHH6N3795o2rTpG7frZYX5/j158gTfffed6nsxaNAgyYFTyj9varS657gMtWnTRgwfPlykpqaKxYsXi0qVKonhw4erxg8bNkx069ZN9Tw4OFiMHDlS5ObmCiGEWLBggQgODhZCCHH16lVRpUoVMXPmTNX04eHhwsLCQvj5+YmyZcuKjRs3ijJlyojhw4eLkSNHCltbW7F06VK1mgICAkRUVJQQQohdu3YJMzMz0aVLF/Hpp5+K7t27C0tLS7Fnzx7V9AqFQpibm4s2bdqILVu2iMzMzDdu98CBA0Xjxo3F2bNnRXR0tPD39xd+fn4iOTlZCCFEYmKiUCgUqul9fX3FmjVrhBBCHDlyRNjY2IiVK1eqxq9fv174+vqq1bR+/XrRtWtXYWlpKZycnMT48ePFn3/++cbaCnLhwgVhZmamel6mTBlx8+ZNIYQQ77zzjli4cKHa9CtWrBANGjRQGxYQECCePHkihBAiKSlJ1KlTR1hZWQkfHx9hY2MjKleuLO7evaua/tq1a8LT01M4OTkJNzc3oVAoRMeOHcU777wjzM3NxXvvvSeys7NV0y9btizfh7m5uQgNDVU9f1mLFi1E3759833fMjMzRb9+/USLFi1Uwy5evPjaR2RkpNrrJMSL96NSpUqiSpUqag+FQiEqVqwoqlSpIry8vNSmf/DggRBCiBEjRoj69euLhIQEIYQQjx49EoGBgWLo0KGq6f/++2/h7u4uHBwcRNeuXcWHH34oRowYIbp27SocHBxExYoVxd9//61W0/3790XDhg2FmZmZMDc3FwMHDhRpaWmq8YmJiWrb8dtvvwl7e3uhUChEuXLlRExMjPDy8hI+Pj7C29tb2NraitjYWI3X8HVe/UwJIf07K/Uz1aBBA3HkyBEhhBDffPONsLW1FePGjRPh4eFiwoQJonTp0mLt2rWq6efMmSPKlCkjevbsKVxdXcXChQuFk5OTmDt3rpg/f74oX768mDFjhtp7V79+fdGiRQu1h0KhEA0bNhQtWrQQLVu21HgtpP7uSH3/mjRpImbNmqV6/v3334t33nlHCCFEcnKyqF+/vhg3bpxaTVJ+2/z9/cWECRMKHD9hwgTh7++vMVzqZ1fqd/zKlSvC09NTKBQKYWZmJpo3by7u379f4Ou0f/9+YWVlJRwdHYWNjY3Yv3+/KF++vGjTpo1o3bq1sLCwEIcPH1bbBqm/U3m1+Pj4iIULF6q+268j9fvn5uYmHj16JIQQ4saNG8LV1VW4urqKtm3bikqVKgl7e3sRFxf3xvW+LL/vqzZKbMApV66cuHTpkhBCiKysLGFmZiZ+++031fhz586JihUrqp7b2dmJq1evqp5nZmYKS0tL1Ru5a9cuUaVKFdV4qcFACOk7bl3ChLu7u9p2Pn/+XHTt2lXUr19fPH78WONLZ2trK27fvq16bmlpqbb8mzdvCjs7O7Wa8naQDx48EP/5z39EzZo1hZmZmWjYsKFYs2aNSE1NVatJ6o7b3t5eXLx4UQghRIUKFVR/57l+/bpaTa/Wpc2OW2qglRok8l7bV3f+L/vzzz+Fra2t2jrMzMyEQqHQeOQNf/VH4MMPPxT169dXfdbzWFhY5Lvul1+n6tWri71796qNP3r0qNrnXGpIE0J6yJb6z4gQQvz000+vfXz11Vcar5UuYV7KZ8rOzk71XWrQoIFYvXq12vo3bdokatWqpXpetWpV8eOPPwohXvzAm5ubi40bN6rG79ixQ3h7e6uez58/X3h5eWnsBAt6r/NI/d2R+v7Z2tqKf/75R/U8NzdXWFpaisTERCGEEIcOHRLu7u5q65Ty22ZjYyMuX75c4PbFxcUJGxsbjeFSP7tSv+PdunUTnTp1Eg8fPhTXrl0TnTt3Fl5eXqrPwKu/tQEBAWLatGlCCCE2b94sypUrJ6ZOnaoaP3XqVNG2bVu1OnX5nfr555/F+PHjhbOzs7C0tBRdunQRe/bsUS3jVVK/fy9/L/r27StatGghnj17JoR4sb/p1KmT6NWrl9o6dPnnTRslNuCUKlVK9aUWQojSpUurfQlv376t9qVwd3dXS6lPnjwRCoVCtbO+ceOGsLa2Vo2XGgyEkL7j1iVMlCpVSi2oCSFEdna26Natm6hbt674448/1D5IlSpVEr/88osQQoh79+4JhUIh9u3bpxp/7NgxUalSpXxretkvv/wiBg0aJEqVKiVKlSqlNk7qjrtLly7is88+E0II0a5dO40jI998843w8fHRWIeUHbfUQCs1SAjx4jO1a9eufMcJIcTOnTvVfvidnZ3F2rVrxa1bt/J97Nu3L98fgZ07dwoPDw+xYsWKN9alUChEUlKSEOLFZ/DVaW7duqXxOZcS0vK2W0rIlvrPSN52FPSZevmz9bLChHltPlNOTk4iJiZGCPHitb1w4YLa9NevX1d7rfKr56+//lI9v3XrlsZvyO+//y6qV68uJk2aJLKysoQQbw44Un93pL5/np6e4uTJk6rn9+/fFwqFQqSnpwshXryurwYQKb9tXl5eYt26dQVu37p16zT+uRBC+mdX6ne8QoUK4o8//lAbNmbMGFG5cmXxzz//aLxOZcuWFdeuXRNCvAiBFhYWavucP//8U7i4uKgtT+rv1Muva1ZWloiMjBTt2rUT5ubmwt3dXUydOlVVQx6p37+X15Ff4D5z5ozaPiNvHqn/vGmjxAacmjVrqr3we/fuVX3hhNB8EwYNGiSaN28u4uLixI0bN0SfPn3U/qs5duyY8PDwUD2XGgyEkL7j1iVM1KlTR2zfvl1jnryQU7lyZbUP0tixY4WPj4+YO3euaNSokRg0aJCoWbOm2L9/vzhw4ICoU6eO2n+pZmZm+daUJyUlRfVfch6pO+5Lly4JJycnMXDgQPHFF1+I0qVLiwEDBoh58+aJgQMHCmtra7F+/Xq1dUjdcUsNtEJICxJCCDFz5kxhb28vFi9eLC5cuCASEhJEYmKiuHDhgli8eLEoV66cmD17tmr6du3aiS+++KLA1/bChQtq/zm/7O7du6JVq1aiffv2IiEh4bUBp0OHDqJ79+6iXLlyqlMXeU6fPq32Iys1pAkhPWRL/Wckr66dO3cWWNf58+c1fjB1CfNSPlMDBgwQw4YNE0II8d5774nPP/9cbfr58+eLOnXqqJ57eXmJ/fv3CyFe/DduZmYmtm7dqhq/b98+tZ1XnrS0NDFw4EDVa2lpafnaHbnU3x2p79/48eNF7dq1xf79+8WRI0dEy5Yt1Y6MHDhwQFSrVk1teVJ+21auXCmsrKzE2LFjxa5du8Tp06fFmTNnxK5du8TYsWOFtbW1CA8P11iWLp9dKd/xMmXKaIQhIYT46KOPVJ+1ggKOEJqf81u3buX7OZfyO1XQ63r79m0xc+ZM4enpqfG9kPr9e/l74e7urhbKhXgRaF/97dT1n7c3KbEBZ9asWWLz5s0Fjp86daro0aOH6vmDBw9E48aNVUmySpUq4ty5c6rx27ZtE8uXL1c9lxoMhJC+49YlTEyZMkUEBQXlO312drbo0qWL2gfp6dOnYvjw4aJ27dpi1KhRIisrSyxevFhYWVkJhUIhWrRooVZDQV+g19Flx339+nXRt29fUaZMGVXSt7S0FIGBgfnu2KTuuKUG2jzaBok8CxcuVJ07NzMzU/234ubmJv7zn/+oTbtjxw7x/fffF7is5ORkERERUeB4pVIp5s+fL1xdXYW5uXm+dQ0ePFjt8fIOVQghJk+eLNq1a6d6LjWkCSE9ZEv9Z0QIITp37iymT59e4GuR32dK6ndW6mfq3r17okqVKqJZs2YiJCRE2NrainfffVeMGDFCNGvWTFhZWakFqmnTpony5cuL4cOHCy8vLxEaGioqV64swsPDxapVq4SHh4eYOHFigdu4efNm4eLiIszMzF77GZT6uyP1/UtLSxO9e/cWFhYWQqFQiMDAQHHjxg3V+IMHD2p8zqT+tm3ZskW88847qnUoFAphYWEh3nnnHREZGZnvMnT57Aqh/Xe8YcOGYsOGDfmue+zYscLBwUHtdapbt64q0Arx4ojNy+1nTpw4oXEkSurv1Jt+n5VKpTh06JDaMKnfP4VCIerUqSMaNGggSpcuLXbs2KG2vOPHj2sccS3MP2+vU2IDzps8e/ZMPH/+XGP41atXNT54+ZEaDPJcv35d9OnTR6sdty5hIjs7W6SkpBQ4PicnR9y6deuNy8nIyNA4/aWrwuy4lUqlSExMFPfv31cdks+P1B231ED7ak1vChKvunHjhjh16pQ4deqU2o+/IcTExIilS5eq2kxI8fTpU5GRkaE2TEpIE0J6yJb6z4gQL/7Tf3lnkd92HDt2TGOYlO+s1M+UEC/+w/70009FrVq1hI2NjbCyshKenp7i/fffF2fPnlWbNicnR8ydO1d06tRJ1S5m8+bNwsPDQzg5OYnBgweLp0+fFriNQghx584dsWvXrjdOJ+UfBm3ev/x2RhkZGWqNkV9Hl982IV6cQrl///4bfw/ySP3s5tHmOz5//nxVe5j8jB49Wu11Cg8P1zjN+bKpU6eqjgDmkfo7VaVKFdXpK21J/f7NmjVL7XHgwAG16SdPniz69u2rNqyw/7wVpMReJm4sz58/R3Z2ttolkfkR/7vMUalUwtnZGZaWlkVUYcn07NkzmJubw8bGRm34tWvXkJmZiZo1a6p1AaCN2NhYnDx5EgMHDkS5cuX0Wa5JunnzJhITEwEArq6uqsuhX5WTk4P09HSULVs23/G5ubm4e/eu1t0fpKenw9zcHNbW1roV/gbafmdfVdBnypRp87uj7/fPFGj72X2VqXzHC/M7VViG/v4VRonuyTgjIwMnT57EpUuXNMY9f/4cGzZsKNT0cXFxWL9+Pa5cuQIAuHz5MiZOnIjx48fjyJEj+daUN8/Vq1fh4uKClJQUjBs3DkOHDs13nrzpL1++rFrH6NGjC5y+KLZb6vS6bEdh1vHy+5G3jt9++01jRxQXF4eTJ0/C0tISFhYWb6zp1W0oVaoULl++jEmTJhntvSiKdeRtd1ZWFgICAlCuXDksWrSowNfJwsIC9+7dK/D9Pn78uMbO8XWfjzNnzhj0x9XGxgZlypTBnTt3MHToUK3nS05OxpgxYwxWlyHk9QPj5uamCjevbreFhUWB4QYA7t+/j9mzZxu0TqnvxZt4eXkhICAAAQEBqnCjzTr8/Pwwfvx4lCtXTu81SeHj44PatWtrhJuiqOnx48cYPXq0Qdeh83ZIPuYjE1L7KCiKPg2kzqPLOgy93VKn12U7imIdcngvimIdpvo5NwSpfXHo2neHqTHF7TbFdZji+22Kr1NRrqPEnqLq3r07cnJysH79evz7778ICQnBX3/9hWPHjqFy5coaPfpKnT4wMBCtWrXC3LlzsWXLFowZMwajR4/GvHnzAADTpk3D2bNncejQIVVNUufRZR2G3m6p0+uyHUWxDjm8FyX5c66L3bt3v3b8jRs3MGnSJNW2S53eVJnidpviOkzx/TbF18mk1qH3qFVMSO2joCj6NJA6jy7rMPR2S51el+0oinXI4b0oinWY6udcF1L7ztGlrx1TZIrbbYrrMMX32xRfJ1NaR4ltg5ORkaFxvnLlypXo0qULmjdvjqtXrxZq+peZmZnBxsYGDg4OqmFlypRBSkqK3ubRdnpDb3dhXidtt6Mo1lEU0xfFa1tSP+e6cHNzw48//gilUpnv49y5c4Wa3lSZ4nab4jpM8f02xdfJlNZRYgNOzZo1ERMTozF8xYoV6Nq1K7p06VKo6atUqYLr16+rnp8+fRqVK1dWPb9z5w7c3NwKNY8u6zD0dkudXpftKIp1yOG9KIp1mOrnXBd+fn6v/SFVKBQQL53Rlzq9qTLF7TbFdZji+22Kr5MpraPEBpzu3btj8+bN+Y77+uuv0a9fP7UXVOr0o0ePVjtf+GoL9/3792vcGVbqPLqsw9DbLXV6XbajKNYhh/eiKNZhqp9zXXzyyScIDAwscLy3tzeOHj2q8/SmyhS32xTXYYrvtym+Tqa0jhLbyJiIiIjkq8QewSEiIiL5YsAhIiIi2WHAISIiItlhwCEiIiLZYcAhIiIi2WHAISKjS0xMxPjx4+Ht7Q0bGxu4uLjg3XffxapVq5Cenm7s8oioGCra+6oTEb3ixo0baNKkCRwcHDB//nzUqVMHOTk5uHr1KtatWwd3d/d8OzEkInodHsEhIqMaM2YMLCwsEBMTg969e8PX1xd16tRBz549sW/fPnTu3BkAkJKSgg8//BAVKlRA2bJl0apVK1y8eFG1nFmzZqF+/fr4/vvvUaVKFdjb26Nv375IS0tTTSOEwKJFi1C1alXY2tqiXr162L59u2r8kydP0L9/f5QvXx62trbw8fHB+vXri+7FICK94REcIjKax48f49ChQ5g/fz5KlSqV7zR53bR37NgRjo6OiIqKgr29PVavXo3WrVvj6tWrcHR0BAD8888/2LVrF/bu3YsnT56gd+/eWLhwoerO459//jl27NiB8PBw+Pj44JdffsGAAQNQvnx5NG/eHNOnT8elS5ewf/9+ODs74/r168jIyCiy14OI9IcBh4iM5vr16xBCoEaNGmrDnZ2d8fz5cwDA2LFj0a5dO/z5559ISkqCtbU1AODLL7/Erl27sH37dnz44YcAAKVSiYiICJQpUwYA8MEHH+Dw4cOYN28enj17hiVLluDIkSMICAgAAFStWhUnT57E6tWr0bx5c8THx6NBgwbw9/cH8OI+WERUPDHgEJHRKRQKtee///47lEol+vfvj8zMTMTGxuLp06dwcnJSmy4jIwP//POP6nmVKlVU4QZ4cZfipKQkAMClS5fw/PlztG3bVm0ZWVlZaNCgAYAX973q2bMnzp07h6CgIHTr1u2198ghItPFgENERuPt7Q2FQoHLly+rDa9atSoAwNbWFsCLIzNubm44duyYxjIcHBxUf1taWqqNUygUUCqVqmUAwL59+1CxYkW16fKOCgUHB+P27dvYt28ffv75Z7Ru3Rpjx47Fl19+qftGEpFRMOAQkdE4OTmhbdu2+Prrr/Hxxx8X2A7n7bffRmJiIiwsLHQ+bVSrVi1YW1sjPj4ezZs3L3C68uXLY/DgwRg8eDCaNm2KTz75hAGHqBhiwCEiowoLC0OTJk3g7++PWbNmoW7dujAzM8PZs2dx+fJl+Pn5oU2bNggICEC3bt3wn//8BzVq1MD9+/cRFRWFbt26qdrMvE6ZMmUwefJkTJw4EUqlEu+++y5SU1Nx6tQplC5dGoMGDcKMGTPg5+eHt956C5mZmdi7dy98fX2L4FUgIn1jwCEio6pWrRrOnz+P+fPnIzQ0FHfv3oW1tTVq1aqFyZMnY8yYMVAoFIiKisK0adMwdOhQPHz4EK6urmjWrBlcXFy0XtcXX3yBChUqYMGCBbhx4wYcHBzw9ttvY+rUqQAAKysrhIaG4tatW7C1tUXTpk2xZcsWQ206ERmQQgghjF0EERERkT6xoz8iIiKSHQYcIiIikh0GHCIiIpIdBhwiIiKSHQYcIiIikh0GHCIiIpIdBhwiIiKSHQYcIiIikh0GHCIiIpIdBhwiIiKSHQYcIiIikp3/A9q9ZbOsKFZeAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linkages=['complete','single','average']\n",
    "HC_methods=[]\n",
    "#Here we'll use linkage function defined in scipy library instead of AgglomerativeClustering\n",
    "#This is because AgglomerativeClustering does not enable the correlation based distance metric\n",
    "for i,l in zip(range(4),linkages):\n",
    "    HC = linkage(y=df, method=l, metric='correlation')\n",
    "    HC_methods.append(HC)\n",
    "    plt.figure(i)\n",
    "    plt.title('%s linkage ' %l)\n",
    "    plt.xlabel('Genes')\n",
    "    plt.ylabel('Correlation-based distance')\n",
    "    dendrogram(HC, labels=df.index, leaf_rotation=90, leaf_font_size=10);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2212ad7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Results dataframe for complete linkage\n",
    "complete = pd.DataFrame(cut_tree(HC_methods[0], n_clusters = 2))\n",
    "complete.index.name = 'patients'\n",
    "complete.rename(columns={0: 'Complete'}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "491c82c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Results dataframe for single linkage\n",
    "single = pd.DataFrame(cut_tree(HC_methods[1], n_clusters = 2))\n",
    "single.index.name = 'patients'\n",
    "single.rename(columns={0: 'Single'}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6a3814de",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Results dataframe for average linkage\n",
    "average = pd.DataFrame(cut_tree(HC_methods[2], n_clusters = 2))\n",
    "average.index.name = 'patients'\n",
    "average.rename(columns={0: 'Average'}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9d283f98",
   "metadata": {},
   "outputs": [],
   "source": [
    "dataframes=[complete,single,average]\n",
    "data=dataframes[0].join(dataframes[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "491eb8aa",
   "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>Complete</th>\n",
       "      <th>Single</th>\n",
       "      <th>Average</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>patients</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
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       "      <th>6</th>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Complete  Single  Average\n",
       "patients                           \n",
       "0                0       0        0\n",
       "1                1       0        0\n",
       "2                0       0        0\n",
       "3                0       0        0\n",
       "4                1       0        1\n",
       "5                0       0        1\n",
       "6                1       0        0\n",
       "7                0       0        1\n",
       "8                1       0        0\n",
       "9                1       0        1\n",
       "10               0       0        1\n",
       "11               0       0        1\n",
       "12               1       0        1\n",
       "13               0       0        1\n",
       "14               0       0        1\n",
       "15               1       0        0\n",
       "16               1       0        1\n",
       "17               1       0        1\n",
       "18               1       1        0\n",
       "19               0       0        0\n",
       "20               1       0        1\n",
       "21               1       0        1\n",
       "22               1       0        1\n",
       "23               1       0        1\n",
       "24               1       0        1\n",
       "25               1       0        1\n",
       "26               1       0        1\n",
       "27               1       0        1\n",
       "28               1       0        1\n",
       "29               1       0        1\n",
       "30               1       0        1\n",
       "31               1       0        1\n",
       "32               1       0        1\n",
       "33               1       0        1\n",
       "34               1       0        1\n",
       "35               1       0        1\n",
       "36               1       0        1\n",
       "37               1       0        1\n",
       "38               1       0        1\n",
       "39               1       0        1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2426cca",
   "metadata": {},
   "source": [
    "Yes, results depend on the type of linkage used."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b34608",
   "metadata": {},
   "source": [
    "### (c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b32a9281",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Genes which differ the most across the two groups are the genes which contribute the most in variance\n",
    "#expalantion. These are the genes which show the high loadings, in absolute values, obtained after PCA\n",
    "pca=PCA()\n",
    "pca_df=pca.fit_transform(df)\n",
    "PVE=pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b3899421",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(15,6))\n",
    "ax = axes[0]\n",
    "ticks = np.arange(pca.n_components_)+1\n",
    "ax.plot(ticks,PVE,marker='o')\n",
    "ax.set_xlabel('Principal Component');\n",
    "ax.set_ylabel('PVE')\n",
    "ax = axes[1]\n",
    "ax.plot(ticks, PVE.cumsum(),marker='o');\n",
    "ax.set_xlabel('Principal Component')\n",
    "ax.set_ylabel('Cumulative PVE');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9295145a",
   "metadata": {},
   "source": [
    "The first principal components shows an elbos in the right side panel of the previous figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "83b2e509",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now let's sort the genes following the first principal component in terms of loadings in abs values\n",
    "df_pc1= pd.DataFrame({'Gene': range(len(df.T)), 'Loadings': pca.components_[0,:]})\n",
    "#Add a column for absolute values of loadings\n",
    "df_pc1['Abs_loadings']=abs(df_pc1['Loadings'])\n",
    "#Sort the data frame in descending order\n",
    "df_pc1_sorted=df_pc1.sort_values(by=['Abs_loadings'], ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8bf6bcf5",
   "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>Gene</th>\n",
       "      <th>Loadings</th>\n",
       "      <th>Abs_loadings</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>599</th>\n",
       "      <td>599</td>\n",
       "      <td>-0.114243</td>\n",
       "      <td>0.114243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>583</th>\n",
       "      <td>583</td>\n",
       "      <td>-0.110398</td>\n",
       "      <td>0.110398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>548</th>\n",
       "      <td>548</td>\n",
       "      <td>-0.108329</td>\n",
       "      <td>0.108329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>539</th>\n",
       "      <td>539</td>\n",
       "      <td>-0.108125</td>\n",
       "      <td>0.108125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>501</td>\n",
       "      <td>-0.107460</td>\n",
       "      <td>0.107460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>581</th>\n",
       "      <td>581</td>\n",
       "      <td>-0.106549</td>\n",
       "      <td>0.106549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>564</th>\n",
       "      <td>564</td>\n",
       "      <td>-0.106271</td>\n",
       "      <td>0.106271</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>567</th>\n",
       "      <td>567</td>\n",
       "      <td>-0.106188</td>\n",
       "      <td>0.106188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>528</th>\n",
       "      <td>528</td>\n",
       "      <td>-0.104163</td>\n",
       "      <td>0.104163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>598</th>\n",
       "      <td>598</td>\n",
       "      <td>-0.103821</td>\n",
       "      <td>0.103821</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Gene  Loadings  Abs_loadings\n",
       "599   599 -0.114243      0.114243\n",
       "583   583 -0.110398      0.110398\n",
       "548   548 -0.108329      0.108329\n",
       "539   539 -0.108125      0.108125\n",
       "501   501 -0.107460      0.107460\n",
       "581   581 -0.106549      0.106549\n",
       "564   564 -0.106271      0.106271\n",
       "567   567 -0.106188      0.106188\n",
       "528   528 -0.104163      0.104163\n",
       "598   598 -0.103821      0.103821"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_pc1_sorted.iloc[:10,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9ef1961",
   "metadata": {},
   "source": [
    "The gene which differs the most across the two groups is gene 599."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e4f4e37",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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