{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab --no-import-all inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Kernel PCA exploration" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] } ], "source": [ "import os\n", "import sys\n", "\n", "import pandas as pd\n", "from sklearn.decomposition import KernelPCA, PCA\n", "from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import Imputer, StandardScaler\n", "\n", "# Load the \"autoreload\" extension\n", "%load_ext autoreload\n", "\n", "# always reload modules marked with \"%aimport\"\n", "%autoreload 1\n", "\n", "# add the 'src' directory as one where we can import modules\n", "src_dir = os.path.join(os.pardir, 'src')\n", "sys.path.append(src_dir)\n", "\n", "# import my method from the source code\n", "%aimport visualization.visualize\n", "from visualization.visualize import biplot, triplot, plot_explained_variance" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "df = pd.read_csv(\"../data/processed/2012.csv\", index_col=0)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "scaler = Pipeline([\n", " ('imp', Imputer(strategy='mean')),\n", " ('scl', StandardScaler())\n", " ])\n", "X = scaler.fit_transform(df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Kernel PCA with radial basis function as kernel" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "kpca = KernelPCA(kernel='rbf', fit_inverse_transform=True)\n", "X_kpca = kpca.fit_transform(X)\n", "X_back = kpca.inverse_transform(X_kpca)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pca = PCA()\n", "X_pca = pca.fit_transform(X)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:11: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:12: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:13: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:26: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:27: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:28: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:35: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:36: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:37: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:44: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:45: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n", "/Users/Arya/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:46: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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D5QkGERERg9LOSOiJ8m4fw+/+eHVLR1sVERHDQjtB6DPAN4B9JJ0H/BD4WEdbFRERw0I7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\n", 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V4UAxM7MiHChmZlaEA8XMzIpwoJiZWREOFDMzK+J/ACMRwV8cVCrlAAAAAElF\nTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot results.\n", "\n", "plt.figure()\n", "# plt.subplot(4, 1, 1, aspect='equal')\n", "plt.title(\"Original space\")\n", "y = df_raw.pid_self# y = X_pca[:, 0] < 0\n", "reds = y == 1\n", "blues = y == -1\n", "greens = y == 0\n", "\n", "plt.plot(X[reds, 0], X[reds, 1], \"r,\")\n", "plt.plot(X[blues, 0], X[blues, 1], \"b,\")\n", "plt.plot(X[greens, 0], X[greens, 1], \"g,\")\n", "\n", "\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")\n", "\n", "# X1, X2 = np.meshgrid(np.linspace(-1.5, 1.5, 50), np.linspace(-1.5, 1.5, 50))\n", "# X_grid = np.array([np.ravel(X1), np.ravel(X2)]).T\n", "# # projection on the first principal component (in the phi space)\n", "# Z_grid = kpca.transform(X_grid)[:, 0].reshape(X1.shape)\n", "# plt.contour(X1, X2, Z_grid, colors='grey', linewidths=1, origin='lower')\n", "\n", "plt.figure() # plt.subplot(4, 1, 2, aspect='equal')\n", "plt.plot(X_pca[reds, 0], X_pca[reds, 1], \"r,\")\n", "plt.plot(X_pca[blues, 0], X_pca[blues, 1], \"b,\")\n", "plt.plot(X_pca[greens, 0], X_pca[greens, 1], \"g,\")\n", "\n", "plt.title(\"Projection by PCA\")\n", "plt.xlabel(\"1st principal component\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 3, aspect='equal')\n", "plt.plot(X_kpca[reds, 0], X_kpca[reds, 1], \"r,\")\n", "plt.plot(X_kpca[blues, 0], X_kpca[blues, 1], \"b,\")\n", "plt.plot(X_kpca[greens, 0], X_kpca[greens, 1], \"g,\")\n", "\n", "plt.title(\"Projection by KPCA\")\n", "plt.xlabel(\"1st principal component in space induced by $\\phi$\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 4, aspect='equal')\n", "plt.plot(X_back[reds, 0], X_back[reds, 1], \"r,\")\n", "plt.plot(X_back[blues, 0], X_back[blues, 1], \"b,\")\n", "plt.plot(X_back[greens, 0], X_back[greens, 1], \"g,\")\n", "\n", "plt.title(\"Original space after inverse transform\")\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(5914, 5914)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_kpca.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Kernel PCA with cubic polynomial as kernel" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "poly = KernelPCA(kernel='poly', fit_inverse_transform=True, gamma=10)\n", "X_poly = poly.fit_transform(X)\n", "X_pback = poly.inverse_transform(X_poly)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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K1P6mJ/1Z9SO0bVJE3vYH/3uE0ndt0tooMcuStR1ELVdpXdwu3sMqHvEc65nnVTDEY7Qj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\njQH4OMlLsXjx075VyWdhyU3yplhc1LN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m0a+YxtFVUKDm8g0RORH4AbA5EEqPNyrYRGQIWAV8S1W/G533sWD7edF1wTn5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\nWqXMadc5DLhUVf+oqk8D3wVeE5T5DlWdwgmHq9W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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot results.\n", "\n", "plt.figure()\n", "# plt.subplot(4, 1, 1, aspect='equal')\n", "plt.title(\"Original space\")\n", "y = X_pca[:, 0] >= 0\n", "reds = y == True\n", "blues = y == False\n", "\n", "plt.plot(X[reds, 0], X[reds, 1], \"r.\")\n", "plt.plot(X[blues, 0], X[blues, 1], \"b.\")\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")\n", "\n", "# X1, X2 = np.meshgrid(np.linspace(-1.5, 1.5, 50), np.linspace(-1.5, 1.5, 50))\n", "# X_grid = np.array([np.ravel(X1), np.ravel(X2)]).T\n", "# # projection on the first principal component (in the phi space)\n", "# Z_grid = kpca.transform(X_grid)[:, 0].reshape(X1.shape)\n", "# plt.contour(X1, X2, Z_grid, colors='grey', linewidths=1, origin='lower')\n", "\n", "plt.figure() # plt.subplot(4, 1, 2, aspect='equal')\n", "plt.plot(X_pca[reds, 0], X_pca[reds, 1], \"r,\")\n", "plt.plot(X_pca[blues, 0], X_pca[blues, 1], \"b,\")\n", "plt.title(\"Projection by PCA\")\n", "plt.xlabel(\"1st principal component\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 3, aspect='equal')\n", "plt.plot(X_poly[reds, 0], X_poly[reds, 1], \"r.\")\n", "plt.plot(X_poly[blues, 0], X_poly[blues, 1], \"b.\")\n", "plt.title(\"Projection by KPCA\")\n", "plt.xlabel(\"1st principal component in space induced by $\\phi$\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 4, aspect='equal')\n", "plt.plot(X_pback[reds, 0], X_pback[reds, 1], \"r.\")\n", "plt.plot(X_pback[blues, 0], X_pback[blues, 1], \"b.\")\n", "plt.title(\"Original space after inverse transform\")\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "poly = KernelPCA(kernel='poly', fit_inverse_transform=True)\n", "X_poly = poly.fit_transform(X)\n", "X_pback = poly.inverse_transform(X_poly)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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K1P6mJ/1Z9SO0bVJE3vYH/3uE0ndt0tooMcuStR1ELVdpXdwu3sMqHvEc65nnVTDEY7Qj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\njQH4OMlLsXjx075VyWdhyU3yplhc1LN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28OCD5RdvZKR83ezZtt8uu8APfhD9Pnu2pTJXHZug8dOmV8LNfnwbRyXbzE03\nwc03lwoNsGJVWQfstNrDLr+Vn9cqScA43G9JRWKCp1ZHkEVwvEpVv9CAY98O7CUib8KEwceBT8a2\nuRI4WUQuw4ziv1PV3zSgLy2Fm+27GYd7cSsUbKwqFKIME62NP+MAUEbJM5Xnyzd99avhpZdqbF7g\n6KPhqqsqD+LPPlu5nfhgCyYc/vZvLZusL1TuuivKCzUWDjjAqv/FhZUTKCMj1p+Pf9zsGH4fP/Up\n61eawTyelh2i0rTVGBy0ql/uprvxRlvv1x5Ocu2thEtt4PJsnXSSxdmEmUfbk0Vw/EREjlTVtfU8\nsKpuE5GTgWuBPLBSVe8XkaXF3y8E1gJHAo8CfwIW17MPrUrSbL+/P3p+22O24SidceTYxmZ2Lt+s\nVqEBNpjuuqsNdFu2lF4YEXjta7PFVKiWT+NGRtJd15wnlZ/e44AD7I2/2j9ny5aofrizzUybZr9d\nfXXUXtwuseOOVpL2sMMsG/BNNyW375wEXCEoV5rWJ2lm0d8flYocGrLv7jo4RGpTe9XiqRVoK7II\njs8CXxKRYWCY4mukqr5mvAcvCqO1sXUXep8VOGm8x2ln7r3X4rL8cTFJs9K6+B0docC28SU53HFH\nyzDr3sznzLHFfzMWgfe+19KQZ+qiJs863Pq0i+1+z+XglluSt4nbV/r67J/q3uz32qvcjXbr1vKS\njc89F5WHdXmm0o53/vlRrQ0otTGkucvGU6f87Gfw1reWrjvqqNoGfeep5ZelDMbyjqCq4FDVCpnW\nAvXEvQi6IN7hYRsD/bRCYJ9dpdH2wKmshDEqeIzubvjnf7Y376uusgH5lFPM7uAPvKrpb+SJ3avQ\nK2d0/uUvk9t0/5xKwsXn97+3wbq/39r01VFJbLdduWoqyQ3X78/mzRbUlyQkkgxovb3lKq0HH4TH\nH7cbbWTEhNWyZZX7msSSJaU11MNsoyPIknJEgGOAN6nqV0XkDcDrVbUOzvABh/+M+2UTnOYhrsLf\nZx94+GH405+a09/s+HaOHNvGYhyfMQMOPzwqm+pPv4aHa4/LmD/f3HRfeMFmCk4Hn8TNN1scxfTp\n6aooZ3zK5coH9aR216wxo3NSCvSjj4a1a6MU6Vu2JPfLn8n4Ncv9nFMbN5YLCWdAc2qp//ov2+41\nrylt0xnRjj/ezn08g34lQ3qgLcmiqvo2MAq8D/gq8BIW8f2OBvZr0uG/CDoNiKsAeu658JWvlNp4\n77qraV2JIzg0AAAgAElEQVStkWigzbGNbobpm3of1JKg8de/hlWr4M47KwexVHJXdYiYEDr9dBtc\nb7mltNhRUnzFCSfAhz5kb93Dw+VtfuADMG+eDcBJAsHn8cctuC+J97/f2tl+e5tV/fa36ed6wAE2\nE9q0yWYLLiPupk1W+W/btkiggP3duNHUZIcdZgWfRkZsFuVmUiKlbr/ORjLeQT/UPO88VLXiAtxZ\n/LvBW3d3tf2auey///7abqxbp7rddqr5vP1dvlz1zDNtvarqggVOH9Kei7BVD+UaXce76tCY2BJf\nn8uVfs7ny7fr6Ykuqn/Re3rsIs+fn9y2iG0zf37pcUC1q0t16VL7p223XfL+WZak/lZali0r7X+h\nUN7e0qW2dHeX9zutD0uXlt589byx69FmoCEA6zXjGJtlxrG1mFdKAURkF2wGEqgjlWKqwNzxnW20\n/VCUPE+xO/eyT7qaav58eP55K2qk3rQrbrROC2Tx3/T9zyLwjndE3kvOYyieJdYZlgqFcpWTqq3z\nZyiOrVth+XJ7Q5850zL0joVa66b/+MeRu2vSvm7GMDCQrdqXm+LWMsuoNptIs6kE2ptqkgWzb1yJ\npfv4J+Ah4KNZJVMzlnacccRZty56WVy3zl4As7wwtu4y+sqynL8p30DE3pjd27M78aVLS9/Cc7no\nQohE33t67M3ff3OOv537v3d3l779nnlmtE8uV3rMri77Ld5m1mWsM5BqyzHHpP82b175zCp+A82e\nHa3L5WzGVcuMIMtsIsw42gZqmHFUTc6jqpcCy4CzgN8AC1T1PxolyAL2EtfXBxdeaMuBB5r9t5IX\nZusjuJiO727/WTsZ58oKNpRt22Zvptu2mUG2t9fefqdMse26uiwXU0+P6eKnTLHCRf/4jxaw9rOf\nwdKlthx/fOQtJWJvuv4sYuvW0lgJF3PgZjPqzSp6e+GrXzV31CSq5bjy2wKzYyxfbn9rxZ1ToWA2\nnyR6esww5r/ZH3ZYNONy7bzudXY9XUTpT35iNhBIT5bmr8uS0NDN6r761ZApt4PIWjr2EeD3bnsR\nma6qFepaBsZD0hjnqoS2P8KU/feBY863VBZJrqV+uHySDm/BgnT1iJ8qww3YqslG7TVrLEBwxx1N\nVZXmlrtlS+Tees01UVZcJ8wqqYGcS5zrSz5vgzqMTaXl2tm2LblO+aGHwsKFdn3WrLG/d9xRHsin\navm5brwx8sjYts3+J489Bv/6r5Eb7uLFkUfb0JDtf8AB5pnmjO+VEhoGr6qOI4s77inA3wP/g+Wq\ncv6Vb29s1yYv7uXXj9NQrV0F3qrstBMWa5A02O69t5U9dZGPU6bYOl/v7udCSkqgNzgIq1dHA6QI\n3HNP6XFUbRp32232u4tXiM8OwNp3uvxvfSuqmLd5s3kqXXRR8om6AXbdOmu7ULCAuN5e89RKEmYQ\nBR0m9aUSPT0mND7zmcjdNqlPu+0GTz0VXX/fZuQi5t33oSGbHTl3X7feeWLl8za7q4f3VaB9qKbL\nwtJ9TM2q+2qFpd1tHOvWlarjO2sZ1QXzn0/Wu3d1mWfS/PnlO/reUO4iJenOly8v9y7KsjgvrKT1\nS5em6+nXrUvfr7vb+p3LRefm9unpSe/LzJn2ey22kVzOrtvMmZW3c/Yaf90xx0QeXWmGNN+2FF+W\nLp24hyPQMKizV9WTwO8aKbwmK36kuMsQ0dtr69onKtyYP98cjuKzosgxSnE2jl1v+THcq3DssbbR\nnDnRW3za2/LwsBUjWbgwetNP0q+ffHL5xXNJCdPUSSL2tn7YYaYTVC1d746f5hnktvdxWWD9uI4N\nG6LAPNdHpx7z23jwQbtwu+1ms62nnrIo87S+q9oxqkXLL1hgMR/Ll5fuv8MOybYdh6utccop8PWv\nN37qG+I+Wp4sguNxYEBErgZeeaJV9RsN69UkwM847VKlu6Sk8eDeZrPLLtWrn+60E3z725ZBwx+/\n3vMeC7w+5cQRto4IXWxl0ej34OTby4PMzjorXX2jaoFz110X2RZcxT+nX3dupz6uwNFhh5X7M++5\nJ7zznXZyCxdaaoxrr41yvey3n2WknTULLrmkPF0x2DHTBNKcOaUJ/r77XeufSwXv+v6Od5ReNFXb\n7qmnbEkr4uQC/LJUIszlzBjf12fBlO7m6uqyoMG0N5UZM0wI+vals8+2AMLRUevDnDmVjx2nkmAI\npWfbgiyCY2Nx6S4ugTrgHFLcuKIaJSX9zndMgJx6an2qnI6XnXe28IpKY9OaNTbmxkt8P/BAMV0R\nD9B/4q0wOhLVo1AtfYOPS0wRG9xffLFUco2OpqfD6OmJ6j987nNm+HYD/TXXRG13d8Pf/V0Uu3Hz\nzWa0PvZYG0ivucaMyvfea4NX3EDvTxeTEoetWmV//Wh230agahdmzhybJVUiKVljLmeSetasbDdK\nLmczHbCby8WyLFpkgiCNjRvtHN2MrrcXLr/cZlIueeGpp1o/oPpMoZpg8FOx15rGPTBhZEly+P8A\nROTVxe9jyH8diOPGyLTSCmAvvHGHmEbjxl2fJOedJIaHy0t8b7998cOsWVxS2JvhYbhkdBE3cLAF\nAhYK5cbnDRtsHz83lY+bnjkVl6NaFGV8wPTdSYeGbCB0A7u76E6wnX56qceWn/H1tNPMC8n3EHOC\npKcnquDnCw4nTDZvrq6XTJrRiNi+vb0m8Pr60mdrro3ly02g3XhjdP5QuWbH6KhlHobSgX7z5khF\nNjxs13XVqtJ6HmMJCJw6tXSWNnVqet8CTSOLV9U+wPeBnYrfnwcWqer9De5bR+PGuP5+c8pxTjeL\nFsEXvgD/8i/2XI61XtBYGY96rLvbJgH+C+zHPubl29uWZ0RhmC5LdCi/MFdPSH4Ldaorf6rT1WXq\nIydU4vtkqUwX73Q8s6RPPl+qmhocLLWjbNlis5rzzy9N7e7+mXPmmIpq2rTkOhp9fek5sCqRz0fJ\nDJ2azs2ANmyIbioonfUMDcEnPwlPPmnX1cV8dHeb4HPb+tc8LkT92aG7/ps2ldfziHu6uf4lVSlz\nbN4c9SGXK30xCLQMWVRVK4DTVPVGABHpAy4C3t3Afk0K3HO1alWkLl6zpnTgraa6bjTVytQ6T9ZP\nfSoyVbz5zeYNO3s2nHde5PqfywGqdI9upS93M/RMKX/zT1NdiVgA3rJlkTury5Lr3niTZhqV9OlJ\nKUf8zLsicNxx5aqUuJ+0827wL4oTiL6x368c6Nt2zjuvVOhk+ScceWS54HSxJps3mxrLzdw2bSq1\n7zzxRPR5aMi2Hxiwa7hyZanw7OqK0r6kxddMnWrCMYnBwahd18a555Z6g/j09UWztEqxIYHmUs3t\nioSEhknrWmlpJ3dcP9NFPq+6557ZPTAbvey9t2XqSMu0ccwxpbnwXGqUdetsmTevdHuXP2/d8nvK\nd3Turt3dUboRVXNh7eoyV1DnCrtunW3nu5j29CS75sb3rYRLcdLdnZ4iI+5+m8tF5xJ32T3zzGSX\n2nw+cs2N3wS5nF24BQvSExOKqO6yS9R2Lqd66KHWZne3rfdTqlTy73buxq6/rh8idjMuW1aa+ybp\nmrljxs/PXZP4b2eeWf1/kHa8QMOgBnfcLILjcuArwIzi8n+Ay7MeoBlLOwmO+HizbFnzBUZ8XDn0\n0OTf/CSq8bE/aZxyY2zqhVi6tFwAxCXrmWeWD3Dz5pV+d4OOH89R8eAxli+PBuKkfvrtxrPt+gJx\n+fJkqStS2pe0mJR166wfWZKUJcWhuPiKJCke39elZPbjR3zBlCZ4ly4tb8ttv3RpaZ9ESoV/PANv\nyGvVVGoRHFlUVccB/w/4cfH7zcV1Y0ZEdgJ+WBRETwAfU9XfJmz3BPAHLGJ9m6rOHc9xW5Eke65T\n9Tz7bPPrboyOJpePyOdNO+FqBy1eHGmbkjQuLiQiVfPgAli2bo08alzcRpJO3Kmwcjlbd/fdUeT3\nypVR5/0O+0b4NM+fFSvMhjEyYp5Ws2aVq6pUo5NavLg8oh3sOKeeatvG64TE7SYQxbTEI7D32COK\naofyi7vTTuZ15ny64/h+32mMjpqXxllnlXt+ud+zZrZ1YsLZbNz/rlCwa+VqoCfZtEIm3fYhq4QB\nXgvskHX7Km2dDXyx+PmLwD+nbPcEsHOt7bfTjCMJ9zKWFEDdCssb31heH2T+/HSVltO+JL3AlxCf\nbrk31HhxEtVyNdSCBdEbstOJucj0QiFSuVRTQ1WbpWR9K47Pivy3eD/SutJsw6+1sXRp8g1x6KHW\nZxHb1n12M6G4Gmz33Wv/h1eacbgoeJFklWHSzCJpFunaSlK1BSYE6jnjEJF3ACuBHYrffwccp6p3\njENeHQ30FT9fAgwAXxhHex2D7+beiuTz8KUvldtCk6LGfW6/3SYF8Rf4VxgchG/EYkrdm6uroe3j\ncl25t+FddzVfYPcWu2hRZHhPMnwnvdHGg/mSZgbVXH4dvteR89iCqG/+MZPesv31rk97713uleVP\nB0dHzZj9N39TOnPxZ2xf+YplD3bXoRoicMghNvvz41fcuff2lro5Oxdp/9okGcDTPKv8jMaBliWL\nquq7wImqejOAiLwHWMX4khz+mar+pvh5E/BnKdspcL2IjADLVXVFWoMisgRYAjB9+vRxdK15OO1G\npdiOiSLuyOO8pz73Ocs84UIWnLdUWvB03BM07qX5CkkR2LlcumdNfPDxBYUfpAfmXeS79bo4kHi7\nzqPHqcBcQsI4WbK9+v7WF19cGptw771RP9MG0b6+0sSLK1ea95VfFzyOamlKejfIx72Y4uH9leju\nLhUaTu3lZ8gFC5h0essbbrB1aQkok/oEkceaO4+gqmpdqk1J8ErGeuvuzLDf9cB9CcvRwIuxbX+b\n0sZuxb+vA+4G5meZRrW6qirJ9lot791ELE6rE69ZJBL1N55Dz6mgkozhIuaZ5a9LzYfnJz10qqWk\n8qVx1620EqdxVY9TUflFotL6Ua+yqarJnlUu0aCvzvE9idz3mTNLDdTz5mXTX/oeTUm1iKtl0Zwx\nI1J5FQq1VRPz1YSV1G9pqsJgHG8a1Nmr6lxgOaZaOhD4NvANYD9gv6wHirX5EPD64ufXAw9l2OcM\n4PNZ2m9lwbF8eelz5oqupXluTsTiu9W6MSvuOOQ8PeP7OkHgktLGHXHSPEQTqTZo1zKwxPXobmD2\nhUa9hURan/0Ll89Hg6/T7/vn5ew2cQkc/+6Wri4TKL4N5dBDS20+/htBXFglva3stluyN1Sal1h8\nu7i9ydkw0mwb8evV6P9JIJF6C44bKyz/nfVAsTbPodQ4fnbCNttTNMYXP68DDs/SfisLjiTXVvdM\nNiOVetwzVLX0xdLZcpMEWz5f7k155pnltuy6jQVZBh6/M/E37mrfGzVgrVtng+m8eTaTSor3SBuQ\nXTxF/OL7HgfxFPVJ/6i4sIr3zd/e9TEp/iK+bbxPy5aVCiM/ZiXLjCMIjaZRV8HRiAWYCtyAVRa8\nHtipuH4asLb4eY+ieupu4H7gy1nbb2XBkRSn4Z7JuEv8RCxJs4D4rMiNTfEX56peUvWmVlWGPxDF\nhc6hh5Z6G8XVR2PpWxa1WZKQqqSn7O6O4ivS3vDdDCIp5kPEBvtq1y2uP02Lq4nfCPHFj6mJ99Fv\nN64uzPK/DYKlodQiOLJ4Ve0ILMJiLl7ZXlU/U23fNFR1M3BwwvpngCOLnx8H9h3rMVqVHXcsNTyL\nmL1z40Z4zWsmti8zZ5p3lB96MDBgfYmnC3KOPn6OwKbYLdPiHZKIG7F9I/TChVaj3MU/OO+lscQP\nVMr4OjhoxmWX8dV5ibn8Uq6fixdbEkJ3Y+Ry8KEPRSlWHnsMvvc9yxLstlEtTcK4cKF5OPmV/bq7\nzeOsUpoPsEy9roaIf+3iDgdg39My8k6bZsZ/58Hm99Ht71LUX3JJcgzHli2Wd8elgfcN8yHdekuQ\nxatqLXArcC+Q4jsTyIrLwu3KMsyaZVVNL7xw4j0QDzzQ/p51VuSx6mK1XB/j6Yma9qzGBw7fpTUL\ncTdaKJXeLjX6WPIjpaUCjxddcV5iL75oF39kxLy4brjBzueSSyKPrgsuKC0G5Scwmz8ffvGLqL9T\np1rurlWrSjP0qto2F10U5YgaGLCBvZIQiV+3pBxf06aVb9vdbYLuiCPsjeTOO6PzdlluK+Ulcx5j\nqpZb68oro+sTggNbiiyCY4qqntbwnkwCnLutH5zrR4a7dRNBLme57/r6IiHmnllVG7PipS6aSj0G\nDn8QPOus0hNevHjsJ5yWCtz12Q2ehxxis4KTTooSJTpBc/rpNrCvXm3b+G//q1eXHu+ZZ6L085s2\nRf7RSTeQc93dssWEiztfV+AqPjuKuzOnJY5cuzb6ns/D/vtbpkuI3kCi8o9RzY6pUyMfbif0nNvu\ncceVzrpGR63f/f0mWPP5KBtoSH7YXKrpsoDPAcdj3k87uSWrLqwZS6vaOCrZQCdycc44lby4Jtx+\nUY16u2rWsz3fOOVHm8cjoZ0dwb/wXV3lyb7i/YkbnVx7WeqS53Lp2/jJERcsiIzoSc4DaZHfrk65\ni1b381P5EfP5vB3D3XhdXeWOAsuWJd+Yvp3Hj4oP1BXqnKtqGPOC+jLgXmkUM14HMjI4aLaDfN6e\nBqdaT3pJbDSqpRoNh+tPS5ZByBqxXa/2sta9HhyMqv1BVJjK4dcUP+WUaLrpjFsuyNDVHnEzKj9N\nvJt9nHOO2Tr8f6C7gZJuplwuGn6TcInI4snIhoZslpNU0z1eUwOiWc3QkM2A/PxUqlGxmauuirZ1\nAX5+Ia1vfCOaUbz73ZYrzO2/enUIDmwhsgiOvwX2VNXnG92ZTsVXzxcKVof7uecsQtwvjdBIurrK\nhUXcSF8oRGXAW1ITUG8jS1p7tRhi/focfv0OZxR3KiS3jZPMfhoPKI0gLxSi+hX5vLW5aJEJE9ev\nfD4qwVsowL77Wl4X9w91Nc2ThEY1gaJqKqJCcXhwKiX/mjhj+223ldb62HXXcluS87hYsaL0GHfe\nGR3DL6QlYulVbr89Ot7s2Wb4V7V9Nm60axyER3OoNiUBrgNelXUK0wpLq6mq4nnmmqGeSsqqPXNm\nqbdlI0MZ2orxxIv4aif3z87lSqPXq7mbZklHvnx55NbqPrv6HS7y3u9DXNWV5abp6kqu1TGWxITu\nmvjtu8BMdz5J19H/zaWOjwczBuoCdVZV/RG4S0RuBF7JzazjcMedLCRVy4y/5E2UuirJc/Lxx83G\nmtXBZtJQKQlfnCSVl1M7+UbxM86w7Supv9wMaHDQPKySXFpdsse0mceSJZGr8oIFpeVk3SzG3XSu\nfxAZ9/2b0c2S4jdx/JocV6yykOQi7av8XO4uvxqgv8+sWdGx3D6nn15a7dFX/QXvqqaRRXCsKS6B\nGohrO9zM/sUXSz0r3/teyxN39dXJdodGsnVrcuLZamRV/7cttdpT4iqvuODxVVJZLpifIHHVqlK3\n21cKuHuZc/3B3iX4dJ5K/j/Xqbuc224+Dx/8oNketKhC8zP55nLmyqsa1Sb33zKquUgnPQTTp1uy\nxqS3Ffc5vs/KldE5FgrJpWwDE0pVwaGql4hIN/CW4qqHVHWCh7j2I+49umGDPTNvfnOpveHmm+35\nPe00uPXW7ElL60Elr8ZKnpiV1P8dI1TGY0+pRfCkXbB4AF480Mb3snAUCuW2CP8f5ALttm2LbAm7\n7loq5E45xbaZMqU0V76rTe4EUTyw0RXe8oVkPL7lpJOsz85uk0T8wVm9OuqDSFTcviNusjammi4L\nS274a+BnwE3Ar8iYpbZZSyvYOHzVt/OcdOrZJLVzV5epcifKBlIopLvcVvIMraT+nzTJTeuV+iLr\nBYunE3G2Ad+1108qVsk+k2aTidsZ/IyV7oaJZ7lNSm8Sr/meZltJSkUS70N3t7nwJtWTr/f/IlB3\nG8fXgUNV9SEAEXkL8O/A/g2QYx2Dr224805Yvz56yXNLXJ18zjnpdS1qoVJ9jO5ue9lz9XaSHFMq\nxdpVUv9PiuDeeqa+yHLB0qLPFy2yCHDnSqtq/9RZsyrbZ9JmQ3GX4FwuSh/guw2D3dTO5uB7aKmW\nRs5v3hzdjH50ftxuA6XX1M16NmwwNVo+D8cfX25DCWlImkYWwdHlhAaAqj4sIl0N7FPHcO+9VsPH\nBSjH3V99waEKjz5an+OmCY3XvAaOOso+f+YzpXV3Kqno/bGnkhamFpty21JP6ZjlgiVFnzt10MBA\nclIxPwK9lkJU8f4k5bcaHCy1OcRvZF//6QpjufY+8hErIuVwMS9J8RzuoQH764pTJV0bl98qtUpY\noO5Um5JgZWMvxlRWfcBFwMqsU5pmLK2iqvLTpLvs2L6Hpiu90Kg6HIVC9VTtWcsiZNUINEVzMJEH\nbUQE+1hrkFRyBR5r/6r1Jx41Pn9+VLwllyst7uK3l6SHnT+//DyS6pFAsl41nqk3RJSPC+pcj6MH\nOA34cXH5HNCT9QDNWJopOHxXfP/+dzaFeHbtuMt+PZd586w/u++e/HtczVzpnFrWdtGMzk20dKyW\nst3/rZYYlLH2xcVtFArJaU9c2hK/v0l1PPyCLnEbR9weklY6cunS5KJRgZqpt+DYHsh73/O0eEBg\nswSHP4a5eC83s/DLHMSf80bNOFwdjbRZhxMs1Wj0WDQuWrpzTaDRgtTVDhEpLRBVaSq7bl3y25Gf\n1yt+jKVLS2/ctODCln6raS9qERxZbBw3AIcALxW/b4dFk797nFqyjsNXuYLZ8+IJV9Nc/oeGqAuz\nZ1t706ZF8VS+zcPFT3V1mQo7i0q4pW0XLd25JlDvnF5Q6jI8MBClUVFNTl/i6oD4KUf83902PT3p\n/6/p0+EDH4ArrrB9R0ZK82W5c2vE+QaqU02yAHdlWddKS6vMOOJFzvzt4mrgpJQgY1lmzmxMhdSW\n9nqsZ+da+kTrQFoFvkrbxzPY+jfcMceUziYKhfTqfm76vWxZtmqJvh97tYy9gXFDnVVVtwD7ed/3\nBwazHqAZS7NtHC5tUCV7pksp5NRJcZvIWJf588s1N50+FtaNTld7jMWYnFRy1/fw8Evwgtky0o6d\n5SaM2yxcbEqlfFmBulCL4MiiqjoV+A8ReQYQYFfgL8czyxGRjwJnADOBeaq6PmW7w4FvYnaVi1X1\na+M57kTgvCRHRpIzZPvBtKOjcOKJ5sHoMlSPl5tusvby+Uhb0NTKfe1EIwNRJjqkPul4/f2lN1qW\nc4yrAmfPhv/+b/utp8dcft0ND3DNNVFwULwP1c7bpajXolorny+P3XApnOPp67PQMWkNWoAs0gXo\nAvYpLl1ZpVKF9mYCbwUGgLkp2+SBx7C6H93A3cDeWdpvtjtutdm28150DiONMIzPn995L8wNp1Gu\nttVULLWqj7IcN8lNt6en9CbJ6r7qClAdc0wUUe57fCR5No3lWsZdfeOeVL5HV6VMvNWuSXd3/a51\nB0GdZxyo5aa6r47C6gEAqVxkex7wqKo+Xtz2MuBo4Jf16kej8O11GzdanjgXo7Rhg5WTPvHE6MVp\nPMkN07Lr/vznY29z0lJPQ6sf1ezXmoi/5Q8OwkEHRd4RK1eOf6aTNHOC0roh73hHNu8IV+/YTZMd\nIyNRtS9XL913UOjvt4IzUBpNXompUyNje09PedLE/v7IMD8yUjqVr9a2f01GRqxE7SWXhGjzMZJJ\ncDSJ3YAnve9PAe9M21hElgBLAKa7DKFNxM+QvWpVFAi7cqUlB3XlkyG5yFIWKtXqUS0fn8IsPQP1\n0uv5A5VqVH87LU+LY+vW8QuONE+zeFR4lmP4kes+uZy1624sF2U+daoN6BddFG3r12FPwwkol+4k\n3r94xDqUZu6tJgDcNUlKVR8eiJppmOAQkesxe0icL6vqFfU+nqquAFYAzJ07N2EonVj8gXrxYnvB\ncS9KLuGn6vhTqbvnWQTe+Eb49a/t+5Qp0XgRUvo0gUrpOyBKex73x+7qGr9LcdrMqdbZlKt37GsG\ncrkodxWU55j6v/83mtk4RKrXIvYFVNL2vh0F7OFxN3+WGU1aqvrJ7r49RlIFh4jsV2lHVb2zyu+H\njLVTRZ4G3uB93724ruVJKkMwZUqyfXGsJKUI+sEP7HN8bJgUyQdbjbTBO0mK33ijDWiQXAxprMeP\nt1PLbCqeXBFMqLm05vGkiEND8C//kpwoLW2A9t+ukmZJab+7ehwON/up1L47dz9VfZh+j5lKM46v\nF/9OAeZixmkB3g6sBxp9xW8H9hKRN2EC4+PAJxt8zLoQH6g3bIBjj4VNm+z3b34zyks31my4Lnmp\nq8fjJy+NPwshRq5JJA3USVL89NNbYwCLB/rFVVSjo6XJBuOzJX/bfN4yau66a2SrcLMsp8M96KDo\nprzxxtLkjFAuYJ0gdrVJhobKb37/XCrVJWmF693OVLOeY/mpZnnf9wH+M6v1PaXND2M2iyHgf4Br\ni+unAWu97Y4EHsa8q76ctf1W8qryU4/EPZ/G6lGVz1sMVa1xXCGWowVoxViRpOAjv863i9lI6m/c\nTdDdoAsWlNblcIVoXBtLl5bus2BB6XXxk7il1RXJmowxBDRlgjp7Vb1VVe/1BM19IjJznMLqcuDy\nhPXPFIWF+74WWDueYzWDJK+qpJlFoXj1s9g5Zs6Et77VXuDmzImKwXV32/dqM+/wktUitFqKDPdm\n7ozGELn/+W/4aYXpN28uvbld+dmrroJrr7VZxMknR3YPZ49w02/Hww+XzsSgel2RpFlGmuqrUmXE\nQM1kERz3iMjFwL8Vvx8D3NO4LnUGvlfVJZeUezNCpC4+4QS4++70tgoFOPDAaMYfr9h58sn2OTwP\nbUIrSXGnkvINZs79b9Gi5IL08QHa17mqRsWahoZKS79CZI/YuLG0zbe8BX71q9K3oU2b4Jln7EHJ\n4jbsbDJOfeUL6HjNj3iZ20BtVJuSYDaOz2EzhMuLn6dkndI0Y2m2qsrhx38demjpzDyXi9KNVEo1\nMlX6nW0AABxfSURBVHt2FEDY01OqFXBpS/yKoiELQ6AmfNWZnzqkUqGWuKpt+fKojkb8Zl62LFJ5\n5XL23bUTD+bzHxg/WDFLsN+ZZ5bXMUjL9VNJ9TaJoZ65qtpxaQXB4Wef7umx58V/Lt36pOSGvu2j\nUubqefNC3rdAHcga4a6ani8qydbh0qYn2Tj848aPk1RrIK0eh38Ofhr2pJTt69aV124Pb1qvUIvg\nqKqqEpEDsLxSb8RTbanqHnWf/nQQZ58dOZskeSpqcSZ/++3l+6qnNXDR5e6zz7RpsGRJlD7dd1hp\nFRV6oA3wVWfxmylOmove5s2lN66fNt2lVR8dLS3xWq2ErV9rYNUqU19t2GDf427Lvb2mnjrpJDuO\nO3b8YTjjDLj5ZmtbpHpgYiCZapIFeBA4AngdMNUtWSVTM5ZmzziqqZ+qLf6++bylCNpzz+QZR1La\nozAD6SCa6QmUlP/fzSDifapUUyCeJyuL6ileayCXK52yp+XZ8vuc9jD4qrWkvk5SzyvqnFb9F1kb\na5Wl2YLjzDPHLjScsKikvvKfpbhwqJR5ehI/E+1JM98C4sfOosaqdIONpcSr34eurvJyspVcdJcv\nt7etpGP6D4lrK9T7qLs77o0icg4Wz/HK3FGrRI5PJuKzYX82PxZ8JxSHFrUAIuaa++CDyTnz0jQJ\nIe1IG9LMkP/4sVevrt4XX/UUfyiSEiH6JOlXfdflqVMtpYnvquu3EU8q6fu453Kl26flrYqfYy1J\nFCcZWQSHSyw411unwPvq3532I2lABjjuuMhV/eqro/s4n7e/ScIhCyIwf36p56L//KSFCYS0I21I\nM0P+48deuNBsA1n6kvaWkha/kjXKe9as9NQs8ey3PnvsEdlVXJsub9XKlbZ9/Bzz+dKcVuFNq4Sq\ngkNVD5qIjrQr8QG5v7/0xeqGG+CIIyyN+siI3Y/nnWf1bq68sjRJIZTaF5MoFOyZqZRuJ8nmGNKO\ntCHNDBZMOnY1w7kj7S0lzRie9a2mUvyLf4PHZxx/93flgmpgIPlBcufo10MIb1plVBQcIvLnWHrz\nX6jqS976w1X1vxrduXYgPiBD+TNw223RS9DwsAmNF14o9ZJ6+9srBwGCCZfjjkvPSVWJVgtYnrTU\n6vLWzGDB+LGr9cWd29Sptb2ljOWtJimBoX+D33tvlPdqyZLS/eKzGz/IMR65G960kkkzfgCfAR4C\n1gBPAEd7v92Z1YjSjGWijeOVHDmWLRubgXynnUq9q5z9bpLZ6zqLTnZ5SzKm1+KJUYvnRpbrmNae\nb6RPqjI41j51ANTDqwq4F3h18fMMLCPuZ4vfN2Q9QDOWZntV+fdbUoBflsUF3IZKlx1EJZe3ViXr\n4DmR57ZgQfSgpCVATHPDjbssxiPM600bCZ9aBEclVVVOi+opVX1CRPqA/xSRN2Lp1QMx/Nmzm/1O\nm1ZbG3vuaSrZJUtgwYKgWuoo2s3QVIsrXi3ntmJFuRopSYWXtG7FClizJmpLpPxYSTYTsKRuccP5\ntm2lhvN6klSYJy1ZZLuRJlGA/wZmx9YVgH5gJKtkasbSjBlH2ktOPBNCpSVLXFSgzWmjN9CaZxFZ\nzm358tKb3iVsiz88aQ9UPOmbSLYo2HguK39ZsCBbjYJa/3f+9XOJ5VpYTUmdZhyLgJIakKq6DVgk\nIssbIsXamEqOJOefbxlwXVXMffeFu+4q3X+33eA//qP9X0QCVaiXsXsi8srUOkNKOze/r6tXl/62\nerW9hSfNEJIeqIUL4brrov1Vy2cMaZ4gPT1RqhFXRbBQgJ/8JEr7vmqVFZWqpTBUGnFPr5GR5OCr\nNiRVcKjqUxV+u6Ux3WltKj2rU6favaFaXvnyRz8qzTr9xBPlbb/jHQ3teqCTmKhoznq44q1YEamI\nenosiM8f+BcuNBfYJAGVtG7JEnjsMTjnnMh3fdWq5NxVlYQJRG63y7334LRBfSxp2eMBjH4RnVZX\nU1Yj69SknZZGqKoqOXL4GZsLBZt9JyULTVtyuShbbgvOYAOtRrsY2detK68D4NcZWL68dNuk/Fdp\n6xYsqD2FSRJxg3mlHFjV0rJXU2W1uJqSkFa9/oKj0rMa/23p0ux2jXgOqgUL6t71QKfRLm69cbtC\nV9f43HP983b2gqyp2tOO4YRBvNxt2vZJadnXrbOH3hXOaeX/SQVqERxZUo7UHRH5KJaqfSYwT1XX\np2z3BPAHYATYpqpzk7abCCqpe/v6LCJ8dLS2lCK5XKRqdVx1lWki2lj9GWg07RLN2dcX2RVyOTP2\nZenr4CAcdFD0sDmbg68uchQK5q3kgvZqUeG59tyDO2+erT/rrPSUDC4te7wkrV96twNsGNVoiuAA\n7gM+AmQxsh+kqs83uD9VSXpW/UBZlzJExMoG9PSU3ksipelEcjlT186ZE6UjAdumw++5QD1opfKz\naYxVwPX3lxazccbveHJCsL+bN9vnWhOyjaUuefycBgasj/7DXSi0vw2jCk0RHKr6AIBIe4WD+M+q\nb/NzJZdVzTljwwY47DB46CF45BHbJi44VGH69MiNPV5/JhDoCOop4PzkhH4CwnjW26TU0EnCK0kI\nxA3gCxeWx17Ez8mvuS4Cixe3vlAfL1l1Wo1YgAFgboXffwXcBdwBLKnS1hIsun399OnT66X2SyRu\n8xOJSirH64JXMoj7atksbuSBQMvRCIPvunXl9cizHjep+FRSjEjavr4B3Bkgq9Un9wtDtal9Q7U2\nG0cjhcL1mEoqvvg5r6oJjt2Kf18H3A3Mz3LsRgcApsUSOftaUtGl+DJ7duU4p0Cg5WnkzVsvgZTk\nuVKpz2l5gqp5brW4x1QWahEcDVNVqeohdWjj6eLfZ0XkcmAecNN4262FpFmus/n5qlawGe4LL0BX\nV/UiTnffberUY48NdTICbUoji7yMRcWV9rBWS18dP048OjdeCCrpeJOMZhnHqyIi22P5sv5Q/Hwo\n8A8T2Yc0Jw2nGj3jjNJYJoBbboFvf9vsHJs2WQr1rVtLU6iDCZzhYdtGJP3eDAQaxnijzyc691al\n/lZ7WP0BvlK69IGByFNFBI4+2ryt4jm0fDtLoWAPtCsINRmKPmWdmtRzAT4MPIWVov0f4Nri+mnA\n2uLnPTD11N3A/cCXs7ZfL1WVr5JysUs+69aZTSM+q505M7JXOPvFggWq8+fbb11dUdbbnh5ru6ur\nNB4qEGgo9VIzTZSKplp/qz2sWftcLdLXxWvE65/XIxixydAKqqpKqOrlwOUJ658Bjix+fhzYd4K7\nVsLUqdFMYXTUvvv09pqL+dlnl1bze+ABW1asgE98An74Q3sZUY1mF0cdBbvuakXGXA4r51UYCDSc\neqmZJsotuFp/qz2sPpX6nOZC7GY0cf20iM0ytOhSmctVPnaHkGt2B1qZzZvtPgD7mzSw9/bC5ZeX\nFhlzjI7CpZfa/eTuNTejvfpqi+Ho7rbYo6CmCkwoTs3ULjdftf5meViz0ttrdRF8oXHGGaXxGiKm\nonrHO+Bb37J60C6R4amn2j4dTMvaOFoBZwSvpsJdsQJ+9rPa2h4ZsXvbz4HmkoJ2uno00AK0S/S5\no1p/sz6steJmGkND9iaYy5nAOPJIM2DecYeVqT32WBMqo6PZkyC2MUFwVCDLs7ViBXz607W1KxIF\n+rk2JyLZaSBQQjtEn/uMRcVUjbhnVHx/Py2JCMydaylOBgYsP5BTnYE9vE7AXH+9pSbp0Ic5CI4q\nxO9VP83Ihg2Wyr8SCxaYi+5NnhPx0UfDsmXl92ZwyQ20NRNRI6QStQpC3xMrzTPKJaJzRsq777Z9\n4x5lixbZcsYZJjQ6pO5GGkFw1EB81prE/Plw663R/XfEEZZOxJHLmXeffy+1W0XRQKCMSgkGxytQ\nsu5f63H8Nza/YE68Ettxx1nNDmcAHxgwG0hcz9zXV54EsUMf5iA4asCftSZRKMDXvhZt69Lf+Nvn\n8+X3UrupmwOBMtKmzeMtOpV1//FW6IvPOPyHdNGi5NiPND3zJHiYg+CoAXefpc04XN3773yn9H7J\nklm63dTNgUAJadPm8ephs+4/luOkVQWMu+EODJhdI57sMO24vkdWhxIERw3EK0Fu2GDeVA88kG2f\nDn4BCUx20m708ephs+4/1uMklZh1ZJnFTFI9cxAcNZJkLO/rs7QiXV02q622TyDQkSTd6PV4czr2\nWPsbryte7+PEyTKLmaRvhqJ+FGSHMHfuXF2/PrGoYENws9kXX7T8aAsXJgcEBgItT7M9o+J9aaaf\nerOPP8GIyB2ascpqmHHUgd5eiwH60pfsu0t8WIvwaKXnNTBJaaWB0o/WnijX1vhD2OjZRBs/9EFw\n1IHBQTjnnNJ1q1dnFxyt9LwGJjGtElCUFK3daPtBpey6jbgGaXXV24SQq6pGBgetlr1LRePut8ce\nK91u4cLsbSY9r4HAhNMq+at8v/dcDg45pPFvU416COMDhsPVVVeN6qq3EWHGkRGXgv/ii+3e6uqy\ne8vdb76pqKsLZs3K3vYkdcwItBqtYuiNPxATkfOp2kM4FrVSB6sSguDIgPv/v/xytG542ATJokV2\nT/jZlkdGapvlt8rzGgi0hAtgMx6ISsccqwCopPpbtAhWrjR3zHw+Ok6zr31GguDIgPv/J+Hut7PP\nhjVrbF21cgBp7bTJPRMINJ5mPBBpxxyr7afSLKa319pxlQQvusii09tkVhJsHBlw/3+X7t9lt3Ux\nG729ln+qXuUAAoFACzFW2497q/zqV5MFQm8vTJ9uKSfazMAZZhwZcP///n6rEb7rrlEskp8ttxHl\nAAKBQJMZj+qs2sypTQ2cTREcInIOcBQwDDwGLFbVFxO2Oxz4JpAHLlbVr01oR2P4ec7mzCmtV9/d\nDaecEgUAtsFsMxCYHNQjXqJeqrOJjhVpEE2JHBeRQ4H/VtVtIvLPAKr6hdg2eeBh4P3AU8DtwCdU\n9ZfV2q9n5Lj7P2/caGrIkRFTVYmUJjrM5WwmOzracQ4UgUD7Ug/PpnoF6mXpSxODAls+clxVr/O+\n3gr8RcJm84BHVfVxABG5DDgaqCo46oX/f87no8zLo6Pl9epdueEOr98SCLQX4w1qrKdLbbW+tJH7\nbisYx48DrklYvxvwpPf9qeK6RERkiYisF5H1zz33XF065v+fR0Zg8WKLRRKJtsnlrHTsBReYjaPZ\nsVOBQMBjvEGN9QwMrNaXNooEbtiMQ0SuB3ZN+OnLqnpFcZsvA9uAS8d7PFVdAawAU1WNtz1Irg4J\nlkp9aMg+i0SG8lmz2k5VGQh0NuO1IdTTeF2tL21kKG9adlwR+Wvg08DBqvqnhN97gTNU9bDi99MB\nVPWsam3X08axYoXlnfIz3n74w1HMBlhd8XnzgsAIBDqSibQ7tImNo1nG8cOBbwAHqmqiXklECphx\n/GDgacw4/klVvb9a+/USHGkqxxNOgAsvjLZzgZ8trpYMBAKBVGoRHM2ycZwP7AD8VETuEpELAURk\nmoisBVDVbcDJwLXAA8CPsgiNepKmcly0yPJRgdk4Rkdtm6GhllZLBgKBQF1ollfVninrnwGO9L6v\nBdZOVL/iVFI5Opdc3y13LKlGAoG2oxXrSNTap1Y8hzYiRI5XIM2WNTBgMwznmusIqUYCHU8ruozW\n2qdWPIc2oxXccVuGpNT5vb1w+unRfTU4aMGA+bwtXV2RG25Xl/0WT70fCHQMregyWmufsmyfVkcj\nAIQZxytkDep02xQKcPzxkYtuf79lSW6zJJeBQG1MhMtorWqkWvuUpfZGmJFUJAiOIlkCTP1twBJb\nxtVXza66GQg0lImow13roF1rn/ztp06NZhz+w9wKJXRbmCA4imR5aam0TRvF7gQC46ORtTLGOmjX\n2ie3bZKQCg9zVYLgKJLlpaXSNm2a5DIQaC0mctBOE1LhYa5K0yLHG0k9I8d9ggdfIDABTNSDFmwZ\nJbR8dtx2JNxjgcAEMVFlY9ttZtFCb65BcGQk2MsCgQ6kGbXNx0KLvbmGOI6MjDc7cyAQCIyZFouf\nCTOOjLTbrDYQCHQQLebpFQRHDbTLrDYQCHQYLfbmGgRHIBAItAMt9OYabByBQCAQqIkgOAKBQCBQ\nE0FwBAKBwESzYgUcdpj9rRcTmNE32DgCgUBgIlmxAj79aft83XX2d8mS8bU5wXEeYcbhEVLwBwKB\nhrN6deXvY2GC4zyaMuMQkXOAo4Bh4DFgsaq+mLDdE8AfgBFgW9Y8KmOhxQIzA4FAp7JwYTTTcN/H\nywTHeTRLVfVT4HRV3SYi/wycDnwhZduDVPX5RncopBQJBAITglNLrV5tQmO8aiqY8DiPpggOVfXE\nLbcCf9GMfvi0WGBmIBDoZJYsqY/A8JnAOI9WMI4fB/ww5TcFrheREWC5qqa6IIjIEmAJwPTp02vu\nRIsFZgYCgUDL0rB6HCJyPbBrwk9fVtUritt8GZgLfEQTOiIiu6nq0yLyOky9dYqq3lTt2I2qxxEI\nBAKdSkvU41DVQyr9LiJ/DXwQODhJaBTbeLr491kRuRyYB1QVHIFAIBBoHE1xxxWRw4FlwIdU9U8p\n22wvIju4z8ChwH0T18tAIBAIJNGsOI7zgR2An4rIXSJyIYCITBORtcVt/gz4uYjcDdwGXK2q/9Wc\n7gYCgUDA0Syvqj1T1j8DHFn8/Diw70T2KxAIBALVCZHjgUAgEKiJIDgCgUAgUBMNc8dtJiLyHPDr\n4tedgYZHnk8g4Xxal046Fwjn0+rU+3zeqKq7ZNmwIwWHj4isb2SOq4kmnE/r0knnAuF8Wp1mnk9Q\nVQUCgUCgJoLgCAQCgUBNTAbBUccSWy1BOJ/WpZPOBcL5tDpNO5+Ot3EEAoFAoL5MhhlHIBAIBOpI\nEByBQCAQqIlJIThE5BwReVBE7hGRy0Vkx2b3aayIyEdF5H4RGRWRtnUtFJHDReQhEXlURL7Y7P6M\nBxFZKSLPikhHJOEUkTeIyI0i8svivfbZZvdpPIjIFBG5TUTuLp7P/2t2n8aLiORFZIOI/KQZx58U\nggOr5bGPqr4deBgrVduu3Ad8hDZOLy8ieeAC4Ahgb+ATIrJ3c3s1Lr4HHN7sTtSRbcDfqurewLuA\nk9r8/zMEvE9V9wVmA4eLyLua3Kfx8lnggWYdfFIIDlW9TlW3Fb/eCuzezP6MB1V9QFUfanY/xsk8\n4FFVfVxVh4HLgKOb3KcxUywu9kKz+1EvVPU3qnpn8fMfsAFqt+b2auyo8VLxa1dxaVuvIBHZHfgA\ncHGz+jApBEeM44Brmt2JSc5uwJPe96do44GpkxGRGcAc4Bf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ZVXX7GqJUjEqx84DMS6Phq1WnncoKQFvuMtEbgL8A2znk/78F8HXjnIMBvNL7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot results.\n", "\n", "plt.figure()\n", "# plt.subplot(4, 1, 1, aspect='equal')\n", "plt.title(\"Original space\")\n", "y = X_pca[:, 0] >= 0\n", "reds = y == True\n", "blues = y == False\n", "\n", "plt.plot(X[reds, 0], X[reds, 1], \"r.\")\n", "plt.plot(X[blues, 0], X[blues, 1], \"b.\")\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")\n", "\n", "# X1, X2 = np.meshgrid(np.linspace(-1.5, 1.5, 50), np.linspace(-1.5, 1.5, 50))\n", "# X_grid = np.array([np.ravel(X1), np.ravel(X2)]).T\n", "# # projection on the first principal component (in the phi space)\n", "# Z_grid = kpca.transform(X_grid)[:, 0].reshape(X1.shape)\n", "# plt.contour(X1, X2, Z_grid, colors='grey', linewidths=1, origin='lower')\n", "\n", "plt.figure() # plt.subplot(4, 1, 2, aspect='equal')\n", "plt.plot(X_pca[reds, 0], X_pca[reds, 1], \"r,\")\n", "plt.plot(X_pca[blues, 0], X_pca[blues, 1], \"b,\")\n", "plt.title(\"Projection by PCA\")\n", "plt.xlabel(\"1st principal component\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 3, aspect='equal')\n", "plt.plot(X_poly[reds, 0], X_poly[reds, 1], \"r.\")\n", "plt.plot(X_poly[blues, 0], X_poly[blues, 1], \"b.\")\n", "plt.title(\"Projection by KPCA\")\n", "plt.xlabel(\"1st principal component in space induced by $\\phi$\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 4, aspect='equal')\n", "plt.plot(X_pback[reds, 0], X_pback[reds, 1], \"r.\")\n", "plt.plot(X_pback[blues, 0], X_pback[blues, 1], \"b.\")\n", "plt.title(\"Original space after inverse transform\")\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $k$-Means clustering" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.cluster import KMeans" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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campfin_limcorppid_selfspsrvpr_ssselfdefsppr_selfinspre_selfgun_controlguarpr_selfimmig_policyaidblack_selfenvjob_self...dem_veteranbudget_rdefctaxbudget_rdefmilpatriot_amidentmilln_milltaxbudget_rdef250kfairjob_opinimmigpo_jobswiretap_warrantpostvote_presvtwho
00.0266800.4959750.4448780.2405050.4375320.3185050.4003900.2161810.3769780.403827...0.0905110.2997430.2394970.1398680.273106-0.2518500.3324190.1247180.0751670.541318
1-0.044652-0.830064-0.744547-0.402509-0.732253-0.533050-0.670092-0.361800-0.630910-0.675845...-0.151478-0.501649-0.400821-0.234083-0.4570700.421496-0.556337-0.208727-0.125800-0.905950
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2 rows × 31 columns

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" ], "text/plain": [ " campfin_limcorp pid_self spsrvpr_ssself defsppr_self inspre_self \\\n", "0 0.026680 0.495975 0.444878 0.240505 0.437532 \n", "1 -0.044652 -0.830064 -0.744547 -0.402509 -0.732253 \n", "\n", " gun_control guarpr_self immig_policy aidblack_self envjob_self \\\n", "0 0.318505 0.400390 0.216181 0.376978 0.403827 \n", "1 -0.533050 -0.670092 -0.361800 -0.630910 -0.675845 \n", "\n", " ... dem_veteran budget_rdefctax budget_rdefmil \\\n", "0 ... 0.090511 0.299743 0.239497 \n", "1 ... -0.151478 -0.501649 -0.400821 \n", "\n", " patriot_amident milln_milltax budget_rdef250k fairjob_opin \\\n", "0 0.139868 0.273106 -0.251850 0.332419 \n", "1 -0.234083 -0.457070 0.421496 -0.556337 \n", "\n", " immigpo_jobs wiretap_warrant postvote_presvtwho \n", "0 0.124718 0.075167 0.541318 \n", "1 -0.208727 -0.125800 -0.905950 \n", "\n", "[2 rows x 31 columns]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kmeans = KMeans(n_clusters=2, random_state=0, n_jobs=-1).fit(X)\n", "pd.DataFrame(kmeans.cluster_centers_, columns=df.columns)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IFwM4g+QpAH6+PLj1Hzv1uAZeA6Ip0rZ5Cau/NhFN3o6lafLjNbexVseKcmp9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\nyP1sLNJFs6Iks4i8synzHCzSGyeuUrZ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gjJ+WJ580dU8lF91czoIIa31axyvbt9kmugzy+fRcVwDvepflsnrjG6MIcbBZ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\nT0x3mpxyd+uUKXZ1qJbWvrz22uK8008+Wdr2298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VYuMBmZd63RerTjeRFYCm1GWiC4C/Bus55PcHAVxm1NkHwN7e95MBPB7R1ioA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "# plt.subplot(4, 1, 1, aspect='equal')\n", "plt.title(\"Original space\")\n", "y = X_pca[:, 0] >= 0\n", "reds = kmeans.labels_ == 0\n", "blues = kmeans.labels_ == 1\n", "\n", "plt.plot(X[reds, 0], X[reds, 1], \"r.\")\n", "plt.plot(X[blues, 0], X[blues, 1], \"b.\")\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")\n", "\n", "# X1, X2 = np.meshgrid(np.linspace(-1.5, 1.5, 50), np.linspace(-1.5, 1.5, 50))\n", "# X_grid = np.array([np.ravel(X1), np.ravel(X2)]).T\n", "# # projection on the first principal component (in the phi space)\n", "# Z_grid = kpca.transform(X_grid)[:, 0].reshape(X1.shape)\n", "# plt.contour(X1, X2, Z_grid, colors='grey', linewidths=1, origin='lower')\n", "\n", "plt.figure() # plt.subplot(4, 1, 2, aspect='equal')\n", "plt.plot(X_pca[reds, 0], X_pca[reds, 1], \"r,\")\n", "plt.plot(X_pca[blues, 0], X_pca[blues, 1], \"b,\")\n", "plt.title(\"Projection by PCA\")\n", "plt.xlabel(\"1st principal component\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 3, aspect='equal')\n", "plt.plot(X_poly[reds, 0], X_poly[reds, 1], \"r.\")\n", "plt.plot(X_poly[blues, 0], X_poly[blues, 1], \"b.\")\n", "plt.title(\"Projection by KPCA\")\n", "plt.xlabel(\"1st principal component in space induced by $\\phi$\")\n", "plt.ylabel(\"2nd component\")\n", "\n", "plt.figure() # plt.subplot(4, 1, 4, aspect='equal')\n", "plt.plot(X_pback[reds, 0], X_pback[reds, 1], \"r.\")\n", "plt.plot(X_pback[blues, 0], X_pback[blues, 1], \"b.\")\n", "plt.title(\"Original space after inverse transform\")\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " 1.0 2361\n", " 0.0 1845\n", "-1.0 1389\n", "Name: pid_self, dtype: int64" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.pid_self.value_counts()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " 1.0 2274\n", "-1.0 1539\n", " 0.0 107\n", "Name: postvote_presvtwho, dtype: int64" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.postvote_presvtwho.value_counts()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "data": [ { "marker": { "opacity": 0.2, "size": 2 }, "mode": "markers", "name": "cumulative explained variance", "type": "scatter3d", "x": [ -1.867678248265026, -3.9758431053835506, -2.4144450766480783, -2.385191196208743, -3.0508535797067764, -0.36090625950629396, -1.306463816839479, -0.7237247235171365, -3.0846460879644817, 1.8096809008520756, 1.5370904999753021, 1.2405386195281807, -0.4120299993493803, 0.07296566347715633, 6.509653484985083, 3.2545359682732955, 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