{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Practical Lab Machine Learning Sheet 2\n", "### Authors: Yannick Burchart, Christoph Smoch" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.1" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "def func_f(beta, y, X, b):\n", " return (X @ X.T) @ (beta*y) + b * np.ones(len(y))\n", "\n", "def OneStep(i, j, beta, y, X, b, C):\n", " f = func_f(beta, y, X, b)\n", " delta = y[i] * ((f[j] - y[j]) - (f[i] - y[i]))\n", " s = y[i] * y[j]\n", " chi = np.linalg.norm(X[i] - X[j])**2\n", " gamma = s * beta[i] + beta[j]\n", " if s == 1:\n", " L = max(0, gamma - C)\n", " H = min(gamma, C)\n", " else:\n", " L = max(0, - gamma)\n", " H = min(C, C - gamma)\n", " if chi > 0:\n", " beta[i] = min(max(beta[i] + delta / chi, L), H)\n", " elif delta > 0:\n", " beta[i] = L\n", " else:\n", " beta[i] = H\n", " beta[j] = gamma - s * beta[i]\n", " f = func_f(beta, y, X, b)\n", " b = b - 0.5 * (f[i] - y[i] + f[j] - y[j])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.2" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = np.zeros((40, 2))\n", "X[:20] = np.random.exponential([4, 4], (20, 2))\n", "X[20:40] = np.random.exponential([0.5, 0.5], (20, 2))\n", "y = np.ones(40)\n", "y[:20] = -1 * np.ones(20)\n", "\n", "import matplotlib.pyplot as plt\n", "plt.scatter(X[:20, 0], X[:20, 1], label = '-1')\n", "plt.scatter(X[20:40, 0], X[20:40, 1], label = '1')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2.3 a)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "def SMO(X, y, max_iter, C):\n", " n = X.shape[0]\n", " beta = np.zeros(X.shape[0])\n", " b = 0\n", " iter = 0\n", " while iter < max_iter:\n", " i = 0\n", " j = 0\n", " while i == j:\n", " i, j = np.random.randint(0, n, 2)\n", " OneStep(i, j, beta, y, X, b, C)\n", " iter += 1\n", " f = func_f(beta, y, X, b)\n", " med = np.median(((beta > 0) * (f - y))[np.nonzero((beta > 0) * (f - y))])\n", " #print(med)\n", " #print(b)\n", " b = b - med\n", " return beta, b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2.3 b)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of Support Vectors for C = 0.01 : 30\n", "Number of Margin Defining Vectors for C = 0.01 : 2\n", "Number of Support Vectors for C = 1 : 12\n", "Number of Margin Defining Vectors for C = 1 : 3\n", "Number of Support Vectors for C = 100 : 20\n", "Number of Margin Defining Vectors for C = 100 : 16\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#SMO(X, y, 10000, 0.1)\n", "def f_func_plot(beta, y, X, x_1, x_2, b):\n", " summe = 0\n", " for i in range(len(y)):\n", " summe += y[i]*beta[i]*(X[i, 0]*x_1 + X[i, 1]*x_2)\n", " summe += b\n", " return summe\n", "delta = 0.01\n", "x_1 = np.arange(min(X[:, 0])- 2,max(X[:, 0] + 1), delta)\n", "x_2 = np.arange(min(X[:, 1]) - 2,max(X[:, 1] + 1), delta)\n", "X_1, X_2 = np.meshgrid(x_1, x_2)\n", "\n", "C = 0.01\n", "\n", "fig, ax = plt.subplots()\n", "beta, b = SMO(X, y, 10000, C)\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "ax.contourf(X_1, X_2, f_func_plot(beta, y, X, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(X[:20, 0], X[:20, 1], label='-1')\n", "ax.scatter(X[20:40, 0], X[20:40, 1], label='1')\n", "supVec = X[np.nonzero(beta > 0)]\n", "margDefVec = X[np.nonzero(np.logical_and(beta > 0, beta < C))]\n", "ax.scatter(supVec[:, 0], supVec[:, 1], label= 'Support Vectors', marker = '+')\n", "ax.scatter(margDefVec[:, 0], margDefVec[:, 1], label= 'Marge Defining Vectors', marker = 'x')\n", "ax.legend()\n", "\n", "C = 1\n", "\n", "fig, ax = plt.subplots()\n", "beta, b = SMO(X, y, 10000, C)\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "ax.contourf(X_1, X_2, f_func_plot(beta, y, X, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(X[:20, 0], X[:20, 1], label='-1')\n", "ax.scatter(X[20:40, 0], X[20:40, 1], label='1')\n", "supVec = X[np.nonzero(beta > 0)]\n", "margDefVec = X[np.nonzero(np.logical_and(beta > 0, beta < C))]\n", "ax.scatter(supVec[:, 0], supVec[:, 1], label= 'Support Vectors', marker = '+')\n", "ax.scatter(margDefVec[:, 0], margDefVec[:, 1], label= 'Marge Defining Vectors', marker = 'x')\n", "ax.legend()\n", "\n", "C = 100\n", "\n", "fig, ax = plt.subplots()\n", "beta, b = SMO(X, y, 10000, C)\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "ax.contourf(X_1, X_2, f_func_plot(beta, y, X, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(X[:20, 0], X[:20, 1], label='-1')\n", "ax.scatter(X[20:40, 0], X[20:40, 1], label='1')\n", "supVec = X[np.nonzero(beta > 0)]\n", "margDefVec = X[np.nonzero(np.logical_and(beta > 0, beta < C))]\n", "ax.scatter(supVec[:, 0], supVec[:, 1], label= 'Support Vectors', marker = '+')\n", "ax.scatter(margDefVec[:, 0], margDefVec[:, 1], label= 'Marge Defining Vectors', marker = 'x')\n", "ax.legend()" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Linear least squares:\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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04yer1OMP9Gzs56lVb7Br914Adu3ey1Or3qBnY3/CLRNJP/X+s0XBH1i5dhMD+w8MKhvYf4CVazcl1CKRbFH4Z4eCP1Ds6ddaLiIHU/hng4I/MG7MqLrKRaQyhX/6KfgD82ZNY2Tb4NMxsm0E82ZNS6hFItml8E83zeoJFGfvaFaPSDQ04ye9FPwlZkyfpKAXiZjW+EkfDfWISOw09JMuCn4RaQqFf3oo+EWkaRT+6aDgF5GmWtw3Vy8ACVPwi0giFP7JUfCLSGIU/skIHfxm9qaZvWRmq82su8J2M7NvmtkGM1trZnPCHlNEWofCv/mi6vF/3N1PcveuCtsuAGYEX4uA70R0TBFpEQr/5mrGUM8C4Lte8BxwuJlNacJxRSRDFP7NE0XwO/CYmb1gZosqbD8aKF3buDcoG8TMFplZt5l1v7d9awTNEpGs0Yyf5ogi+E9z9zkUhnSuMrMzyrZbhef4QQXud7l7l7t3je2YGEGzRCSrFP7xCr1Wj7tvDr73mdkSYC7wdEmVXqB0ictOYHPY4+adbhMprU5r/MQnVI/fzMaa2fjiY+A8YF1ZtWXAnwSzez4G7HD3LWGOm3e6TaTkhXr+8Qg71HMk8IyZrQGeB37m7o+a2RVmdkVQZznwOrABuBv4i5DHzD3dJlLyROEfvVBDPe7+OjC7QvmdJY8duCrMcWQw3SZS8kbDPtHSJ3czSLeJlDzSjJ/oKPgzSLeJlDxT+Ien4M+gGdMnceYpx77fwx83ZhRnnnKsZvVIbij8w9GtFyOQxNRK3SZS8k7j/o1Tjz8kTa0USY56/o1R8IekqZUiyVL410/BH5KmVookTzN+6qPgD0lTK0XSQ+FfGwV/SJpaKZIuCv/hKfhD0tRKkfRR+A9N0zkjoKmVIumj6Z7VqccvIi1LPf/K1OMvMXPTUuavv5XD9mxh5+gpPDnzGtZPW5B0s0QkhGL4q/f/AfX4AzM3LeXCNTcwYc9mDGfCns1cuOYGZm5amnTTRCQC6v1/QMEfmL/+Vtr37xlU1r5/D/PX35pQi0Qkagr/AgV/4LA9lW8KVq1cRLJJ4a8x/vftHD2FCXsOvhXwztFTIjuG7pMrkg55n/HTcI/fzKaZ2b+a2Xoze9nM/rJCnflmtsPMVgdfN4ZrbnyenHkN+9pGDyrb1zaaJ2dew8xNS7nysdP5ytKPcOVjpzc07q/F3ETSJc89/zA9/gHgr939xeCG6y+Y2Qp3/3VZvX9z94tCHKcpirN3ymf1AFy45ob3x/+LF31Ln1OLoRZza8Vev97dSBbkdcZPw8Hv7luALcHjd81sPXA0UB78mbF+2oKDwvzKx06vetG3nuDP02JuxXc3xRe64rsbILLw1wuLRClvQz+RjPGb2THAycDKCptPNbM1wGbgGnd/OYpjNktUF33HjRlVMeTjXswtiYCM+91NM15YJH/yFP6hZ/WY2Tjgx8CX3X1n2eYXgenuPhv4FvDIEPtZZGbdZtb93vatYZsVmWoXd+u96JvEYm5JXVeI+92N7oEgccnLuH+oHr+ZtVMI/Qfd/Sfl20tfCNx9uZn9o5lNcveDksfd7wLuAug84SQP0656DdUrfnLmNYPG+OGDi771KO4vbO+7nh58UtcV4n53k6dhM2m+PPT8Gw5+MzPgXmC9u99epc5RwNvu7mY2l8I7jPR05xl+2KDaRd9GlnKodzG38pD/gymH89qb/TUPcSQVkPNmTRt0TiHadzdJDZtJfrR6+Ifp8Z8GfAF4ycxWB2V/C/wBgLvfCXwauNLMBoA9wEJ3b2pvfji19IorXfSNW6UXpF//pu+gekP14JMKyKje3VQT9wuLCLT2jJ8ws3qeAWyYOncAdzR6jGZI67BBpRekaqq1NcmAjHOp6rhfWERKtWLvP/ef3B03ZhRn/e4J/mbkPzPV+tnsk7h54DM8cehZibarnheeaj34Vg5I3QNBmqnVwj/3wf+lzpf54433MMYKQdtp/Sxuv4fvdx7JNk6O9dhDLQNdbZim3HA9eAWkSDRaKfxzv0jbZ9/5p/dDv2iM7eWz7/xTrMcdbhnoatM/T/jwZN3mUSQhrTLdM5U9/qPa32vasZJalXOoZaDXT1vQ0sM0IlnWCj3/VAY/fHAlPe5X2GasyllJLS84GqYRSaesz/hJ/VBP3Cd2qFU54xTVJ4JFJDlZHfpJffBDvOG/ftoCls/+OjtGT8UxdoyeyvLZX4993n5SLzilejb28/2f/jt3PryS7//037VEtEgDshj+lrLPUwHQNXuGdy//xkHlzTzBzVjcLIqbuzfazvIPiEHh4rEuFos0JulhH+v8xAvu3lVL3dSO8Vdy3eTnmxL+PRv7Oaz7ezw64gdMPaSfzQOTuK17IT18IdK1dcJ+IjjMKpV5uz+ASNyydNE3E0M9peI+sTM3LeXW1Wdze9sddI7oZ4RB54h+bmq7k4mrH6xrX3Gvjhlmlcq0fmK5XhqukjTJyrBP5oIfCuEfxwtAcW59B7uwssUoRtkA1/l9de0v7uWDw4R3tU/7ZmmhM93OUtJocd/c1L8AZDL4i6IO/0pz60t12K669hd3rzpMeCdxf4CoaV1+SbM0h3+mgx+iDf+oP7QVd686THjPmD6JM085NtOfAm6V4SppXWkN/0xd3K0mqou+1T7MVbSn/fC69hf36phhP92b9Q+IaV1+yYI0XvRtieCHaMK/0t22igasnRUfvRGofRpmM5ZdyHp4h6F1+SUr0hb+mR/qKRX2xA7+MBccsLb3v7f5Puavv5VzVt940OJqF7/415yz+saK+7x4xK/41SFf4o1DP8+vDvkSF4/4Vag2ygdaYbhK8iNNwz6Z+gBXPeo9yTM3LeX81Tcw6kB5b98wPjhHXvZzafmyObcN6vkXZwmV36+3GZ8MFpH0iqP3X88HuFqqx1+qnhM7c9NS/suL/51DDuzBoOxrcMhXCv1i+fz1tw4qG2oFzjzQHHuRypLu/YcKfjM738xeNbMNZnZdhe2HmNnDwfaVZnZMmOPVq9bwP/elr0XyClg+K+iwKheKq5W3Es2xFxlakuHfcN6ZWRvwbeAC4ATgUjM7oaza5cB2d/8I8A/ATY0er1G1hP/off8RybHKV9Z0a6tYr1p5K9Ece5HhJRX+YTq6c4EN7v66u+8FfgCUD1wvAB4IHv8IONus/DOx8WvG1fRKK2ua769Yt1p5K9Ece5HaJBH+YYL/aKC0+9YblFWs4+4DwA5gYohjNmyo8N/T3hFq3w4VL9juHD21Yv1q5a2kFZaEEGmWZod/mOCv1HMvv/JZS51CRbNFZtZtZt3vbN0RolnVVVvjZ8VH/wcD1n5QI2ud77Rz9NSKs3TSsOZ+UlphSQiRZmrmGj9hgr8XKP0r7gTKr1q+X8fMRgITgG2Vdubud7l7l7t3fWjihBDNGl55+K+ftoCfnXzToJuxLJtzO8vm3H5QcJcbsPaqQZ7UTV7SQHPsRRrTjPBveB5/EOSvAWcDbwGrgM+5+8slda4CPuruV5jZQuBT7v6Z4fYdxTz+WtRygks/pbunfQJtB/Yyav9uoLCEw4qP3piLIBeR5qr32mQ98/hDfYDLzC4E/g/QBtzn7l83s68B3e6+zMwOBb4HnEyhp7/Q3V8fbr/NCn5Ifj6tiEg19YR/04I/Ls0MflD4i0h61Rr++uRundK0eJKISKk4OqYK/kBcd/USEQkr6hk/Cv4yCn8RSauowl/BX4HCX0TSKorwV/BXofAXkbQKG/4K/iEo/EUkrcKEv4J/GAp/EUmrRsO/Ze65G6di+Gu+v4ikTSO5pB5/HdT7F5FWoOCvk8JfRLJOwd8Ahb+IZJmCv0EKfxHJKgV/CAp/EckiBX9IWuNHRLJGwR8Rhb+IZIWCP0IKfxHJglTeiMXM3gE2JnDoSUB/AsetRVrbpnbVL61tS2u7IL1tS1O7prv7h2qpmMrgT4qZddd6B5tmS2vb1K76pbVtaW0XpLdtaW3XcDTUIyKSMwp+EZGcUfAPdlfSDRhCWtumdtUvrW1La7sgvW1La7uGpDF+EZGcUY9fRCRnchn8Zna+mb1qZhvM7LoK2w8xs4eD7SvN7JgmtGmamf2rma03s5fN7C8r1JlvZjvMbHXwdWPc7So59ptm9lJw3O4K283Mvhmcs7VmNqcJbTq+5FysNrOdZvblsjpNO2dmdp+Z9ZnZupKyI8xshZn1BN87qjz3sqBOj5ld1oR23WJmrwS/qyVmdniV5w75e4+pbV81s7dKfmcXVnnukH/HMbTr4ZI2vWlmq6s8N9ZzFgl3z9UX0Ab8BjgOGAWsAU4oq/MXwJ3B44XAw01o1xRgTvB4PPBahXbNB/4lofP2JjBpiO0XAj8HDPgYsDKB3+tvKcxlTuScAWcAc4B1JWU3A9cFj68DbqrwvCOA14PvHcHjjpjbdR4wMnh8U6V21fJ7j6ltXwWuqeH3PeTfcdTtKtt+G3BjEucsiq889vjnAhvc/XV33wv8AFhQVmcB8EDw+EfA2WZmcTbK3be4+4vB43eB9cDRcR4zYguA73rBc8DhZjalicc/G/iNuyfxwT8A3P1pYFtZcen/pQeASyo89Y+AFe6+zd23AyuA8+Nsl7s/5u4DwY/PAZ1RHa8eVc5ZLWr5O46lXUEWfAZ4KKrjNVseg/9oYFPJz70cHLDv1wn+OHYAE5vSOiAYWjoZWFlh86lmtsbMfm5mf9isNgEOPGZmL5jZogrbazmvcVpI9T/EpM4ZwJHuvgUKL+7A5Ap1kj53X6Twbq2S4X7vcbk6GIa6r8rwWJLn7HTgbXfvqbI9qXNWszwGf6Wee/nUplrqxMLMxgE/Br7s7jvLNr9IYShjNvAt4JFmtClwmrvPAS4ArjKzM8q2J3nORgEXAz+ssDnJc1arJM/dDcAA8GCVKsP93uPwHeDDwEnAFgrDKuUSO2fApQzd20/inNUlj8HfC0wr+bkT2FytjpmNBCbQ2NvRuphZO4XQf9Ddf1K+3d13uvuu4PFyoN3MJsXdruB4m4PvfcASCm+1S9VyXuNyAfCiu79dviHJcxZ4uzjkFXzvq1AnkXMXXES+CPi8B4PT5Wr4vUfO3d929/3ufgC4u8oxkzpnI4FPAQ9Xq5PEOatXHoN/FTDDzI4NeooLgWVldZYBxZkVnwaeqPaHEZVg3PBeYL27316lzlHFaw1mNpfC729rnO0KjjXWzMYXH1O4MLiurNoy4E+C2T0fA3YUhziaoGoPLKlzVqL0/9JlwNIKdX4BnGdmHcGwxnlBWWzM7HzgK8DF7r67Sp1afu9xtK302tAnqxyzlr/jOJwDvOLuvZU2JnXO6pb01eUkvijMQHmNwqyAG4Kyr1H4IwA4lMKwwQbgeeC4JrTpP1N4q7oWWB18XQhcAVwR1LkaeJnCDIbngP/UpPN1XHDMNcHxi+estG0GfDs4py8BXU1q2xgKQT6hpCyRc0bhxWcLsI9Cj/RyCteGfgn0BN+PCOp2AfeUPPeLwf+3DcCfNaFdGyiMkRf/rxVnsU0Flg/1e29C274X/B9aSyHMp5S3Lfj5oL/jONsVlN9f/L9VUrep5yyKL31yV0QkZ/I41CMikmsKfhGRnFHwi4jkjIJfRCRnFPwiIjmj4BcRyRkFv4hIzij4RURy5v8DkYgTVoy2IDoAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def LLS(X, y):\n", " X_1 = np.transpose(X) @ X\n", " a = np.linalg.solve(X_1, np.transpose(X) @ y)\n", " return a\n", "k = np.ones((40, 1))\n", "X_new = np.concatenate((k, X), axis = 1)\n", "alpha = LLS(X_new, y)\n", "def z(x_1, x_2, alpha):\n", " return alpha[0] + alpha[1]*x_1 + alpha[2]*x_2 - 0.5\n", "print(\"Linear least squares:\")\n", "fig, ax = plt.subplots()\n", "ax.contourf(X_1, X_2, z(X_1, X_2, alpha),1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(X[:20, 0], X[:20, 1], label='-1')\n", "ax.scatter(X[20:40, 0], X[20:40, 1], label='1')\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.4" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Accuracy of LLS: \n", "0.556\n", "Accuracy of SVM with C = 0.01 :\n", "0.9115\n", "Accuracy of SVM with C = 1 :\n", "0.887\n", "Accuracy of SVM with C = 100 :\n", "0.845\n" ] } ], "source": [ "X = np.zeros((2000, 2))\n", "X[:1000] = np.random.exponential([4, 4], (1000, 2))\n", "X[1000:2000] = np.random.exponential([0.5, 0.5], (1000, 2))\n", "y = np.ones(2000)\n", "y[:1000] = -1 * np.ones(1000)\n", "\n", "print(\"Accuracy of LLS: \")\n", "k = np.ones((2000, 1))\n", "X_new = np.concatenate((k, X), axis = 1)\n", "alpha = LLS(X_new, y)\n", "C_LLS = np.zeros((2, 2))\n", "C_LLS[0, 0] = np.sum(z(X[:1000, 0], X[:1000, 1], alpha) < 0)\n", "C_LLS[0, 1] = np.sum(z(X[:1000, 0], X[:1000, 1], alpha) > 0)\n", "C_LLS[1, 0] = np.sum(z(X[1000:2000, 0], X[1000:2000, 1], alpha) < 0)\n", "C_LLS[1, 1] = np.sum(z(X[1000:2000, 0], X[1000:2000, 1], alpha) > 0)\n", "accuracy = np.trace(C_LLS)/2000\n", "print(accuracy)\n", "\n", "def func_f_2(beta, y, X, b, x):\n", " return (x @ X.T) @ (beta*y) + b * np.ones(x.shape[0])\n", "\n", "\n", "C = 0.01\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "beta, b = SMO(X, y, 1000, C)\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:1000]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:1000]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) > 0)\n", "accuracy = np.trace(C_SVM_1)/2000\n", "print(accuracy)\n", "\n", "C = 1\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "beta, b = SMO(X, y, 1000, C)\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:1000]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:1000]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) > 0)\n", "accuracy = np.trace(C_SVM_1)/2000\n", "print(accuracy)\n", "\n", "C = 100\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "beta, b = SMO(X, y, 1000, C)\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:1000]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:1000]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) > 0)\n", "accuracy = np.trace(C_SVM_1)/2000\n", "print(accuracy)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.5" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "def SMO_KKT(X, y, max_iter, C):\n", " n = X.shape[0]\n", " beta = np.zeros(X.shape[0])\n", " b = 0\n", " iter = 0\n", " while iter < max_iter:\n", " f = func_f(beta, y, X, b)\n", " for i in range(n):\n", " KKT = (C - beta[i]) * max(0, 1 - y[i] * f[i]) + beta[i] * max(0, y[i] * f[i] - 1)\n", " if KKT > 0:\n", " j = np.random.randint(0, n)\n", " if sum(np.logical_and(beta > 0, beta < C)) > 0: \n", " while i == j and (beta[j] < 0 or beta[j] > C):\n", " j = np.random.randint(0, n)\n", " else:\n", " while i == j:\n", " j = np.random.randint(0,n)\n", " break\n", " if KKT == 0:\n", " med = np.median(((beta > 0) * (f - y))[np.nonzero((beta > 0) * (f - y))])\n", " b = b - med\n", " break\n", " return beta, b\n", " \n", " OneStep(i, j, beta, y, X, b, C)\n", " iter += 1\n", " if iter == max_iter:\n", " f = func_f(beta, y, X, b)\n", " med = np.median(((beta > 0) * (f - y))[np.nonzero((beta > 0) * (f - y))])\n", " b = b - med\n", " return beta, b" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Accuracy of SVM with C = 0.01 :\n", "0.775\n", "Number of Support Vectors for C = 0.01 : 25\n", "Number of Margin Defining Vectors for C = 0.01 : 9\n", "Accuracy of SVM with C = 1 :\n", "0.95\n", "Number of Support Vectors for C = 1 : 27\n", "Number of Margin Defining Vectors for C = 1 : 22\n", "Accuracy of SVM with C = 100 :\n", "0.725\n", "Number of Support Vectors for C = 100 : 37\n", "Number of Margin Defining Vectors for C = 100 : 37\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = np.zeros((40, 2))\n", "X[:20] = np.random.exponential([4, 4], (20, 2))\n", "X[20:40] = np.random.exponential([0.5, 0.5], (20, 2))\n", "y = np.ones(40)\n", "y[:20] = -1 * np.ones(20)\n", "\n", "delta = 0.01\n", "x_1 = np.arange(min(X[:, 0])- 2,max(X[:, 0] + 1), delta)\n", "x_2 = np.arange(min(X[:, 1]) - 2,max(X[:, 1] + 1), delta)\n", "X_1, X_2 = np.meshgrid(x_1, x_2)\n", "\n", "C = 0.01\n", "\n", "fig, ax = plt.subplots()\n", "beta, b = SMO_KKT(X, y, 10000, C)\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:20]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:20]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[20:40]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[20:40]) > 0)\n", "accuracy = np.trace(C_SVM_1)/40\n", "print(accuracy)\n", "\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "ax.contourf(X_1, X_2, f_func_plot(beta, y, X, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(X[:20, 0], X[:20, 1], label='-1')\n", "ax.scatter(X[20:40, 0], X[20:40, 1], label='1')\n", "supVec = X[np.nonzero(beta > 0)]\n", "margDefVec = X[np.nonzero(np.logical_and(beta > 0, beta < C))]\n", "ax.scatter(supVec[:, 0], supVec[:, 1], label= 'Support Vectors', marker = '+')\n", "ax.scatter(margDefVec[:, 0], margDefVec[:, 1], label= 'Marge Defining Vectors', marker = 'x')\n", "ax.legend()\n", "\n", "C = 1\n", "\n", "fig, ax = plt.subplots()\n", "beta, b = SMO_KKT(X, y, 10000, C)\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:20]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:20]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[20:40]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[20:40]) > 0)\n", "accuracy = np.trace(C_SVM_1)/40\n", "print(accuracy)\n", "\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "ax.contourf(X_1, X_2, f_func_plot(beta, y, X, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(X[:20, 0], X[:20, 1], label='-1')\n", "ax.scatter(X[20:40, 0], X[20:40, 1], label='1')\n", "supVec = X[np.nonzero(beta > 0)]\n", "margDefVec = X[np.nonzero(np.logical_and(beta > 0, beta < C))]\n", "ax.scatter(supVec[:, 0], supVec[:, 1], label= 'Support Vectors', marker = '+')\n", "ax.scatter(margDefVec[:, 0], margDefVec[:, 1], label= 'Marge Defining Vectors', marker = 'x')\n", "ax.legend()\n", "\n", "C = 100\n", "\n", "fig, ax = plt.subplots()\n", "beta, b = SMO_KKT(X, y, 10000, C)\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:20]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:20]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[20:40]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[20:40]) > 0)\n", "accuracy = np.trace(C_SVM_1)/40\n", "print(accuracy)\n", "\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "ax.contourf(X_1, X_2, f_func_plot(beta, y, X, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(X[:20, 0], X[:20, 1], label='-1')\n", "ax.scatter(X[20:40, 0], X[20:40, 1], label='1')\n", "supVec = X[np.nonzero(beta > 0)]\n", "margDefVec = X[np.nonzero(np.logical_and(beta > 0, beta < C))]\n", "ax.scatter(supVec[:, 0], supVec[:, 1], label= 'Support Vectors', marker = '+')\n", "ax.scatter(margDefVec[:, 0], margDefVec[:, 1], label= 'Marge Defining Vectors', marker = 'x')\n", "ax.legend()" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Accuracy of SVM with C = 0.01 :\n", "0.919\n", "Number of Support Vectors for C = 0.01 : 148\n", "Number of Margin Defining Vectors for C = 0.01 : 13\n", "Accuracy of SVM with C = 1 :\n", "0.891\n", "Number of Support Vectors for C = 1 : 65\n", "Number of Margin Defining Vectors for C = 1 : 44\n", "Accuracy of SVM with C = 100 :\n", "0.7775\n", "Number of Support Vectors for C = 100 : 256\n", "Number of Margin Defining Vectors for C = 100 : 256\n" ] } ], "source": [ "X = np.zeros((2000, 2))\n", "X[:1000] = np.random.exponential([4, 4], (1000, 2))\n", "X[1000:2000] = np.random.exponential([0.5, 0.5], (1000, 2))\n", "y = np.ones(2000)\n", "y[:1000] = -1 * np.ones(1000)\n", "\n", "C = 0.01\n", "\n", "beta, b = SMO_KKT(X, y, 1000, C)\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:1000]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:1000]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) > 0)\n", "accuracy = np.trace(C_SVM_1)/2000\n", "print(accuracy)\n", "\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "\n", "C = 1\n", "\n", "beta, b = SMO_KKT(X, y, 1000, C)\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:1000]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:1000]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) > 0)\n", "accuracy = np.trace(C_SVM_1)/2000\n", "print(accuracy)\n", "\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))\n", "\n", "C = 100\n", "\n", "beta, b = SMO_KKT(X, y, 1000, C)\n", "print(\"Accuracy of SVM with C = \" + str(C) + \" :\")\n", "C_SVM_1 = np.zeros((2, 2))\n", "C_SVM_1[0, 0] = np.sum(func_f_2(beta, y, X, b, X[:1000]) < 0)\n", "C_SVM_1[0, 1] = np.sum(func_f_2(beta, y, X, b, X[:1000]) > 0)\n", "C_SVM_1[1, 0] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) < 0)\n", "C_SVM_1[1, 1] = np.sum(func_f_2(beta, y, X, b, X[1000:2000]) > 0)\n", "accuracy = np.trace(C_SVM_1)/2000\n", "print(accuracy)\n", "\n", "num_SV = np.sum(beta > 0)\n", "num_MDV = np.sum(np.logical_and(beta > 0, beta < C))\n", "print(\"Number of Support Vectors for C = \" + str(C) + \" : \" + str(num_SV))\n", "print(\"Number of Margin Defining Vectors for C = \" + str(C) + \" : \" + str(num_MDV))" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C=0.1\n", "SVM KK:\n", "130 ms ± 1.62 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "SVM:\n", "35.4 ms ± 474 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "C=1\n", "SVM KK:\n", "124 ms ± 753 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "SVM:\n", "36 ms ± 268 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "C=100\n", "SVM KK:\n", "125 ms ± 541 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "SVM:\n", "35.7 ms ± 143 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" ] } ], "source": [ "#Runtime:\n", "X = np.zeros((40, 2))\n", "X[:20] = np.random.exponential([4, 4], (20, 2))\n", "X[20:40] = np.random.exponential([0.5, 0.5], (20, 2))\n", "y = np.ones(40)\n", "y[:20] = -1 * np.ones(20)\n", "\n", "print('C=0.1')\n", "C=0.1\n", "print('SVM KK:')\n", "%timeit SMO_KKT(X, y, 1000, C)\n", "print('SVM:')\n", "%timeit SMO(X, y, 1000, C)\n", "\n", "print('C=1')\n", "C=1\n", "print('SVM KK:')\n", "%timeit SMO_KKT(X, y, 1000, C)\n", "print('SVM:')\n", "%timeit SMO(X, y, 1000, C)\n", "\n", "print('C=100')\n", "C=100\n", "print('SVM KK:')\n", "%timeit SMO_KKT(X, y, 1000, C)\n", "print('SVM:')\n", "%timeit SMO(X, y, 1000, C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.6" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linalg as LA\n", "\n", "X=2*np.random.rand(2,50)-1\n", "L_X=np.zeros(50)-1\n", "Y=[]\n", "count=0\n", "while len(Y)!=50 and count<200:\n", " temp=4*np.random.rand(2,)-2\n", " if LA.norm(temp)>1:\n", " Y.append(temp)\n", "\n", "Y=np.array(Y).T\n", "L_Y=np.ones(50)\n", "\n", "plt.axis([-4,4,-4,4])\n", "plt.scatter(X[0],X[1],label='-1')\n", "plt.scatter(Y[0],Y[1],label='1')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Z=np.concatenate((X,Y),axis=1)\n", "L=np.concatenate((L_X,L_Y))\n", "\n", "Z=np.reshape(Z,(2,-1)).T\n", "\n", "C=10\n", "\n", "delta = 0.01\n", "x_1 = np.arange(min(Z[:, 0])- 2,max(Z[:, 0] + 1), delta)\n", "x_2 = np.arange(min(Z[:, 1]) - 2,max(Z[:, 1] + 1), delta)\n", "X_1, X_2 = np.meshgrid(x_1, x_2)\n", "\n", "beta,b = SMO_KKT(Z,L,10000,C)\n", "\n", "fig, ax = plt.subplots()\n", "ax.contourf(X_1, X_2, f_func_plot(beta, L, Z, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(Z[:50, 0], Z[:50, 1], label='-1')\n", "ax.scatter(Z[50:, 0], Z[50:, 1], label='1')\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "W=[]\n", "for z in Z:\n", " W.append([z[0],z[1],z[0]**2+z[1]**2])\n", "\n", "W=np.array(W)\n", "\n", "C=10\n", "\n", "beta,b = SMO_KKT(W,L,10000,C)\n", "\n", "def f_func_plot2(beta, y, X, x_1, x_2, b):\n", " summe = 0\n", " for i in range(len(y)):\n", " summe += y[i]*beta[i]*(X[i, 0]*x_1 + X[i, 1]*x_2+X[i,2]*(x_1**2+x_2**2))\n", " summe += b\n", " return summe\n", "\n", "fig, ax = plt.subplots()\n", "ax.contourf(X_1, X_2, f_func_plot2(beta, L, W, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(Z[:50, 0], Z[:50, 1], label='-1')\n", "ax.scatter(Z[50:, 0], Z[50:, 1], label='1')\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.7" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "def gaussian(t,x,sigma):\n", " return np.exp(-LA.norm(t-x)**2/(2*sigma**2))\n", "\n", "def OneStep_gaussian(i, j, beta, y, X, b, C,sigma):\n", " f = func_f(beta, y, X, b)\n", " delta = y[i] * ((f[j] - y[j]) - (f[i] - y[i]))\n", " s = y[i] * y[j]\n", " chi = gaussian(X[i],X[i],sigma)+gaussian(X[j],X[j],sigma)-2*gaussian(X[i],X[j],sigma)\n", " gamma = s * beta[i] + beta[j]\n", " if s == 1:\n", " L = max(0, gamma - C)\n", " H = min(gamma, C)\n", " else:\n", " L = max(0, - gamma)\n", " H = min(C, C - gamma)\n", " if chi > 0:\n", " beta[i] = min(max(beta[i] + delta / chi, L), H)\n", " elif delta > 0:\n", " beta[i] = L\n", " else:\n", " beta[i] = H\n", " beta[j] = gamma - s * beta[i]\n", " f = func_f(beta, y, X, b)\n", " b = b - 0.5 * (f[i] - y[i] + f[j] - y[j])\n", "\n", "def SMO_KKT_gaussian(X, y, max_iter, C,sigma):\n", " n = X.shape[0]\n", " beta = np.zeros(X.shape[0])\n", " b = 0\n", " iter = 0\n", " while iter < max_iter:\n", " f = func_f(beta, y, X, b)\n", " for i in range(n):\n", " KKT = (C - beta[i]) * max(0, 1 - y[i] * f[i]) + beta[i] * max(0, y[i] * f[i] - 1)\n", " if KKT > 0:\n", " j = np.random.randint(0, n)\n", " if sum(np.logical_and(beta > 0, beta < C)) > 0: \n", " while i == j and (beta[j] < 0 or beta[j] > C):\n", " j = np.random.randint(0, n)\n", " else:\n", " while i == j:\n", " j = np.random.randint(0,n)\n", " break\n", " if KKT == 0:\n", " med = np.median(((beta > 0) * (f - y))[np.nonzero((beta > 0) * (f - y))])\n", " b = b - med\n", " break\n", " return beta, b\n", " \n", " OneStep_gaussian(i, j, beta, y, X, b, C,sigma)\n", " iter += 1\n", " if iter == max_iter:\n", " f = func_f(beta, y, X, b)\n", " med = np.median(((beta > 0) * (f - y))[np.nonzero((beta > 0) * (f - y))])\n", " b = b - med\n", " return beta, b" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "C=10\n", "sigma=1\n", "\n", "beta,b = SMO_KKT_gaussian(W,L,10000,C,sigma)\n", "\n", "def f_func_plot3(beta, y, X, x_1, x_2, b):\n", " summe = 0\n", " for i in range(len(y)):\n", " summe += y[i]*beta[i]*(gaussian(X[i,0],X[i,1]))\n", " summe += b\n", " return summe\n", "\n", "fig, ax = plt.subplots()\n", "ax.contourf(X_1, X_2, f_func_plot2(beta, L, W, X_1, X_2, b), 1, colors=['moccasin', 'skyblue'])\n", "ax.scatter(Z[:50, 0], Z[:50, 1], label='-1')\n", "ax.scatter(Z[50:, 0], Z[50:, 1], label='1')\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 2.8" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "#Load MNIST Data\n", "import numpy as np\n", "import os\n", "import gzip\n", "from urllib.request import urlretrieve\n", "\n", "def download(filename , source='http://yann.lecun.com/exdb/mnist/'):\n", " print(\"Downloading %s\" % filename)\n", " urlretrieve(source + filename , filename)\n", "\n", "def load_mnist_images(filename):\n", " if not os.path.exists(filename):\n", " download(filename)\n", " with gzip.open(filename , 'rb') as f:\n", " data = np.frombuffer(f.read(), np.uint8 , offset=16)\n", " data = data.reshape(-1, 28, 28)\n", " return data / np.float32(256)\n", "\n", "def load_mnist_labels(filename):\n", " if not os.path.exists(filename):\n", " download(filename)\n", " with gzip.open(filename , 'rb') as f:\n", " data = np.frombuffer(f.read(), np.uint8 , offset=8)\n", " return data\n", "\n", "X_train = load_mnist_images('train-images-idx3-ubyte.gz')\n", "y_train = load_mnist_labels('train-labels-idx1-ubyte.gz')\n", "X_test = load_mnist_images('t10k-images-idx3-ubyte.gz')\n", "y_test = load_mnist_labels('t10k-labels-idx1-ubyte.gz')" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "for gamma=0.1:\n", "Model with rank: 1\n", "Mean validation score: 0.654 (std: 0.019)\n", "Parameters: {'C': 10}\n", "\n", "Model with rank: 1\n", "Mean validation score: 0.654 (std: 0.019)\n", "Parameters: {'C': 100}\n", "\n", "Model with rank: 3\n", "Mean validation score: 0.620 (std: 0.022)\n", "Parameters: {'C': 1}\n", "\n", "for gamma=0.01:\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\yanni\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n", " DeprecationWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Model with rank: 1\n", "Mean validation score: 0.900 (std: 0.036)\n", "Parameters: {'C': 10}\n", "\n", "Model with rank: 1\n", "Mean validation score: 0.900 (std: 0.036)\n", "Parameters: {'C': 100}\n", "\n", "Model with rank: 3\n", "Mean validation score: 0.882 (std: 0.029)\n", "Parameters: {'C': 1}\n", "\n", "for gamma=0.001:\n", "Model with rank: 1\n", "Mean validation score: 0.882 (std: 0.027)\n", "Parameters: {'C': 100}\n", "\n", "Model with rank: 2\n", "Mean validation score: 0.876 (std: 0.033)\n", "Parameters: {'C': 10}\n", "\n", "Model with rank: 3\n", "Mean validation score: 0.740 (std: 0.022)\n", "Parameters: {'C': 1}\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\yanni\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n", " DeprecationWarning)\n" ] } ], "source": [ "from sklearn import svm, datasets\n", "from sklearn.model_selection import GridSearchCV\n", "\n", "ss=500\n", "\n", "rand=np.arange(ss)\n", "\n", "np.random.shuffle(rand)\n", "\n", "A=X_train[rand]\n", "B=y_train[rand]\n", "\n", "A=np.reshape(A,(ss,-1))\n", "\n", "g=0.1\n", "\n", "print('for gamma=0.1:')\n", "\n", "parameters = {'C':[1, 10,100]}\n", "svc = svm.SVC(gamma=g)\n", "clf = GridSearchCV(svc, parameters, cv=5)\n", "clf.fit(A,B)\n", "clf.get_params(clf)\n", "\n", "def report(results, n_top=3):\n", " for i in range(1, n_top + 1):\n", " candidates = np.flatnonzero(results['rank_test_score'] == i)\n", " for candidate in candidates:\n", " print(\"Model with rank: {0}\".format(i))\n", " print(\"Mean validation score: {0:.3f} (std: {1:.3f})\".format(\n", " results['mean_test_score'][candidate],\n", " results['std_test_score'][candidate]))\n", " print(\"Parameters: {0}\".format(results['params'][candidate]))\n", " print(\"\")\n", "\n", "\n", "report(clf.cv_results_)\n", "\n", "\n", "g=0.01\n", "\n", "print('for gamma=0.01:')\n", "\n", "parameters = {'C':[1, 10,100]}\n", "svc = svm.SVC(gamma=g)\n", "clf = GridSearchCV(svc, parameters, cv=5)\n", "clf.fit(A,B)\n", "clf.get_params(clf)\n", "\n", "def report(results, n_top=3):\n", " for i in range(1, n_top + 1):\n", " candidates = np.flatnonzero(results['rank_test_score'] == i)\n", " for candidate in candidates:\n", " print(\"Model with rank: {0}\".format(i))\n", " print(\"Mean validation score: {0:.3f} (std: {1:.3f})\".format(\n", " results['mean_test_score'][candidate],\n", " results['std_test_score'][candidate]))\n", " print(\"Parameters: {0}\".format(results['params'][candidate]))\n", " print(\"\")\n", "\n", "\n", "report(clf.cv_results_)\n", "\n", "\n", "g=0.001\n", "\n", "print('for gamma=0.001:')\n", "\n", "parameters = {'C':[1, 10,100]}\n", "svc = svm.SVC(gamma=g)\n", "clf = GridSearchCV(svc, parameters, cv=5,scoring='accuracy')\n", "clf.fit(A,B)\n", "clf.get_params(clf)\n", "\n", "def report(results, n_top=3):\n", " for i in range(1, n_top + 1):\n", " candidates = np.flatnonzero(results['rank_test_score'] == i)\n", " for candidate in candidates:\n", " print(\"Model with rank: {0}\".format(i))\n", " print(\"Mean validation score: {0:.3f} (std: {1:.3f})\".format(\n", " results['mean_test_score'][candidate],\n", " results['std_test_score'][candidate]))\n", " print(\"Parameters: {0}\".format(results['params'][candidate]))\n", " print(\"\")\n", "\n", "\n", "report(clf.cv_results_)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 883 3 11 2 6 32 20 11 2 10]\n", " [ 0 1129 2 1 0 0 1 0 1 1]\n", " [ 14 197 713 19 29 3 5 15 15 22]\n", " [ 9 58 35 828 1 13 1 7 4 54]\n", " [ 1 26 2 0 593 0 12 0 0 348]\n", " [ 33 83 17 279 26 226 11 8 8 201]\n", " [ 17 54 67 1 102 44 669 0 0 4]\n", " [ 2 88 15 0 8 0 0 567 2 346]\n", " [ 23 123 22 153 8 7 9 8 392 229]\n", " [ 11 18 7 11 50 1 0 13 0 898]]\n", "0.6898\n" ] } ], "source": [ "from sklearn.metrics import confusion_matrix\n", "from sklearn.metrics import accuracy_score\n", "\n", "X_test=np.reshape(X_test,(len(X_test),-1))\n", "\n", "svc = svm.SVC(gamma=g)\n", "svc.fit(A,B)\n", "prediction = svc.predict(X_test)\n", "\n", "print(confusion_matrix(y_test, prediction))\n", "print(accuracy_score(y_test, prediction))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }