{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PR02: Linear discriminants - part 1" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from sklearn import datasets\n", "from sklearn import metrics\n", "\n", "from matplotlib import pylab as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate a binary classification problem" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "X0, y0 = datasets.make_classification(1000, n_features=2, weights=[0.4,0.6],\n", " n_informative=2, n_redundant=0, \n", " n_clusters_per_class=1, flip_y=0.01,\n", " shuffle=True)\n", "y0[y0 == 0] = -1" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the data points - just to see how the classes look like\n", "plt.scatter(X0[:,0], X0[:,1], c=y0, cmap=plt.cm.Paired)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Perceptron" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, try your own implementation of the Perceptron algorithm. For example, fill in the gaps below:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# naive implementation of a Perceptron\n", "\n", "# train a perceptron\n", "def perc(X, y, theta=0.5, eta=0.1):\n", " n, d = X.shape # n samples, d variables\n", " a = np.ones(d+1) # a = [1,....,1]\n", " Z = np.zeros((n, d+1))\n", " \n", " for i in np.arange(n):\n", " Z[i, 0] = y[i]\n", " Z[i, 1:(d+1)] = y[i] * X[i,:]\n", "\n", " k = 0\n", " grad = 2*theta\n", " while np.abs(grad) > theta:\n", " grad_v = np.zeros(d+1)\n", " for i in np.arange(n):\n", " if np.dot(a, Z[i,:]) < 0:\n", " # i-th sample is misclassified\n", " a += eta*Z[i,:]\n", " k += 1\n", " grad_v += Z[i,:]\n", " print(\"Coefficient update {:d}\".format(k))\n", " grad = eta * np.linalg.norm(grad_v) # norm\n", " \n", " return a\n", "\n", "\n", " \n", " return a\n", "\n", "\n", "# use a trained model to classify a new dataset\n", "def perc_clsf(X, a):\n", " d = a[0]\n", " d += np.dot(X, a[1:])\n", " c = np.ones(X.shape[0], dtype=np.int)\n", " c[d < 0] = -1\n", "\n", " return c\n", "\n", "\n", "# show separation boundary\n", "def plot_clsf_reg(X, y, a):\n", " xmn, xmx = X[:,0].min() - 1, X[:,0].max() + 1\n", " ymn, ymx = X[:,1].min() - 1, X[:,1].max() + 1\n", " \n", " xx, yy = np.meshgrid(np.arange(xmn,xmx,0.02), np.arange(ymn,ymx,0.02))\n", " Z = perc_clsf(np.c_[xx.ravel(),yy.ravel()], a)\n", "\n", " # for plotting, convert to 0, 1:\n", " Z = (Z + 1) / 2\n", " Z = Z.reshape(xx.shape)\n", " \n", " plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)\n", "\n", " # add the points with \n", " plt.scatter(X[:,0], X[:,1], c=y, cmap=plt.cm.Paired)\n", " plt.xlim(xx.min(), xx.max())\n", " plt.ylim(yy.min(), yy.max())\n", "\n", " plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And apply it to the data generated above or to the classical IRIS dataset:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coefficient update 1\n", "Coefficient update 2\n", "Coefficient update 3\n", "Coefficient update 4\n", "Coefficient update 5\n", "Error rate: 0.333333\n" ] }, { "data": { "image/png": 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vE9PMLPU7Xk4HrHXkGlNZZf0UqeqAiDwEvBrYPel476Ri/wp8wufrtwPbIbdwWLnBLlaKciY6QndskKy4tKTr6JhoIare3z4Xl8N1vZyJjqBAPBthw2gb9W5xG/3SdB2HAPVY2jd/8aLjEdch7bgFxwV8O3i94lk/uox4NsJYKDXnM1cVOHnNDRy96ZVk4nUs2/cM6376Y2IjQ2WVj44MlVWPMXOplNEybUA6n9gTwCuZkrxFZKWqduc/vRXYG3iki9iRRB+nY8PnZpD2OMP0R8fYMtThuQTB7sZuxiclzYlQmt1NJ9g61EF8yi5IDg7RbJhkaNKf3vlfu82pOIPRiYLjDkJTOkFvbLTwuAoxnydur3j2NHVz+fAKjib6GQ2ncrv5qXDRWDAdxdN5/nW/x4kXvTS3RRtwYttLOH351bz4Mx8lMl68q5Nf+WV7n+Tk1TeUXI8xc6mUZpmVwM9E5Gng1+Ta3H8sIh8TkVvzZf5cRPaIyFPAnwPvqEy4i09KMvTEhs4ldgAEMuJyKlr8hDjqJAsS6dnykBv94lU+GfLoOIVcYp9yXNFcYp9y3BXKjqcr3s/mkVVcNdjJ5qFVXDu4htZ0g9dtCEyyoYnj173sXEIG0HCYTDxB14tfVnL5dCLBiW0vLbkeY+ZaKaNlngaKNiVU1Y9Mev1h4MPBhmYAxkIpRKVonXQVZSgyQUeysHx/xOeJMT+Ucarpynu1r/st4TubeKIaJjpHjXQjq9bgZNJkI4V9DW40ysD6TfDQfSWV10gUssVDNv3qMWau2QzVeS7qhn3bwr2aQeqyPptPq/e+qNOVL/d4EPFUWmywv2ByzlmSzRLvPV1yea/EPl09xsw1G5Ywz9W5URLZCKNeHY8TxRtdLM3U46jgokW/FFaPLfUs77dbUswNF+1ZKgjxbIjxkMdSwAHEU2kNp45T33OCkRWr0fD5f/6SzbD6V8UzMP3KO9kM8b4zjC1fWbCHp7hZz3ouhOs47HnTuziz+RrUcYj3nWHzd/+V5uNHAqnf1DZ7cl8ANo6soCkTR/IdlxE3xIaR5dS53k/FVwyvIqRybs9TFFaNt7A0U+9Zfkm6eK9UB6E+Ey06LgqXjLZXNJ5K2/qVz9Lywn4kk8ZJJYkOD3LFt7fTcOpEWeXVCYFMns2luKEw4gYzw/bxP/sIp7e8KPdLxXGYaG3jifd8mNG29kDqN7XN9lBdQNKSJSsuMTeMlDCRadxJkZIsjdkYjs/v8ZRk2NXcVfLep6KwaqKFzoklFYlnLqXqGsjG4sQHepESfg4mlx9e0cmO9/23wuQOoErLoee45kufmlVsQytXV7R+s3DZHqo1KKKhstqpE26UxAxlxkKpsvY+VYHh8ETF4plL0bERGBuZuaBH+TObtngXEmFk5ZpZx1bp+k3tq/7jk6mqqBsue+9T31mti0hj9zHvE6pEhwbmff2m9tmTexUoSndskFOxIbKiNGfirB5f6ps0/cpH3RD7608xGMk/SbsO60eX05wt/fm4zo1Sl4kyEk4WdZwmMmHGw+mC5J/rOF0Ye5+qCEdv+k26bryFbCzOkgPPsuH+H5Do7535i2fQ9tzThJITZGPxoqaTi//vnez6w/fRd+lmcByig/1s/t4XaTlysOR4pqt//f+9kyMveVVRPfGBPs/6/Y773YdK3jczd6zNvQoO1p2mLzp6fmKSQkgdtg51ejZz+JUPqRRuPJ0/feVQh2/nppfn63roi44W1OOocMXwKo4m+hmMjAFCxHW4eKyN5sx8alzx9+wb30HPldeen2iUzRJOjnP9pz9KdGR41vWPtbTyxJ/+NenG/Cgh12X9A3dx/EUvZaK17XxSzv+MLdu7i74Nl5ccj1/9o8tXer6vJc/vpfeyLSUf97tupe+bmR1rc5+nkpKhNzpa2IEpufVXTsYGWT2xtOTyWcFzSd4X6s6weWRVyfH0R8c8Z6KeiY6wcbSdDC6uuEQ0VFLH6Xww0dRCz5ZtBXuBEgrhRmIcu/7lrH/wnllfo26gl5f+04eYaGwhXd9A/ckuhjvWcvDVv1P4tC0CqpzZtLVg2ORM8XjVn2pq4dG//B9F7ysbiXH6iqshFC7puN915+K+mblhyX2OjU/TgTkSTpZV3rNdXHJfE2Q8YRyYuqHHPDe6ohPJZCBS+BeMG4kwtHZ9oNeKDw8QH861g/ddOnXB1Lypo17KiGdy/X7vSyMRz4lVfsf9rjuX981U1sL6ia0BsWk6MOPZ4jb36cp7UoiUsWRuufEsFPH+M2jI4z5kM9T1nKzYdRv9JhipnmuemU08/u/LZ2y973Hv61brvpng2ZP7HEu4UeozMUbCE0UdlSuTxTM8c+WjDHt0eIoqbu6TAmvHl9AV7+dUfsGxxnScteOthF2H3U3Hc+305MasrxtrLSuehaL+9Emajh1icM363NNrnpPNsvqX/16x6y7bvxtnYgw3Xlf0tF5/souxtpUlx5OKxvj1n3+E5JJlQG4W7ca7vuHzvjIkTh5ntHNdYdOPm6Wx+xgjK9eUdN1q3TcTPHtyr4JLR9pZkspN+xeFeDbMxpEVvqNlwu6UTlYFUWXT0EqibujcrE9RWDveyunoKCfig2QcFze/s9GexuM82Xz0fAes5JpeXqjvpX28sax4Foot3/g8bXt2Ipk0ks1Qd/okV33lM9T19lT0uksP7S88oIqTSXPFt7eXFc8vP/y/c4ldBETQUJjn3vgOOn757571jK3oKJoxSzjC2ofuL+u61bpvJlg2WqaKXHLJ12tN9rOSTpqnmo57ziBdOdHM6omlZMiScVzibsS3/LlmnKlNMJobQnnN0NqS4lmIsuEwbjhCZKLy2/eNtyzlsb/4WGGHJCDpNKt/8RM2PHBXSfGcuvwq9vz+ezxnqEaG+nnpJ/6moJ5yy5diLu+bKZ2NllkAHBzPfUQnG3fSJXR4hs493fuV91vCFyG3q1KJ8SxEoUyGUGZu9gEdXb7Kt8NzaPXFJcdzenPRKts5IqQbmorqKbd8KebyvpngWbPMPBdzI7g+HZ4Jj+V0pyvvSckt6mUCUdfbU7B65FmSydBwsqvkepYefM77hCphj12eyi1val8p2+zFgZ8DsXz5O1T1o1PKxICvAdcCvcCbVfVw4NEuMC5KV7yPnvwWeQ2ZOOvGWom7Ec/jXhOPEm6EpkyMoXCyoKnFb6/RhBuhwbMDNp/fPfZEXTO6lKPx3pLiuaD7EApz8Ddv5cSLfgM3GqP5yAEu/dG3fVdhzETjPPmuDzC8+iIAQhPjXPaDr7Bs3+6K1hPv7/Msv/zZXSW/17reHlpeeJ6Biy4paJqRbIb2Jx/l4b/+n6Sbzk9K2nDv9+l8/Oee8ZDNQihU1NSy4f98n+df/Tsll7/0R9/xjNXv+1J3pqes+1yual13sZmxzV1EBKhX1RERiQCPAO9X1UcnlfmvwBZV/VMReQvw26r65unqXQxt7vvrTzEQGT+flPNL6Tam4wxFJoqObxnsJOax6XUWlyOTNpiuy0a5aKyVhmzc87o7m44UbmCdv0xdOsxYJFN0vDmdKCuecj3zX95N76VX4kbzyc51CaWSvPgz/0B8sL+o/CN//QlSTS1FMzxbDu1jaPXFs66n+dA+hj3qcVLJ3GzQKeWv/cLHae46XPL7zUai7H/9mzl11fW4oRAN3cfYePe32PnHf5kbgTKl/sYjBxhdtbYoHsmkydQ3lhz/li99iqff9QGy8cS58msfuo/1D97tGaff96X5yAEGLtpY8n0uV7WuWysCa3PXXPY/u3ReJP8x9TfCG4B/yL++A/iciIhWq7d2Hphw0oWJHXIzSzU3eqVoRqgqJ2ODrJ1oLaorRG7a/0Vjy1ByidfPYGi8MLHn60cpTOyTjpcbTznGl7TSu/HKwg5Gx8ENhzl2wy1ccv8PCsr3r9tQmJDh3AzPgYsvBXFmXc/gRZcWDhd0HNxwpHgdl3z5fb/1Vq77wsdLfs+hdIrLfvh1Nt31DdQJ4WQznLzy2sLEPqn+4bUbCo87DtlwGHzi8Y4/zJkrr+Vl//0DZEMhstEE0XH/FS/9vi/ZcJi+DZfn/gKYUr/XfS5Xta67GJXU5i4iIRHZBfSQ2yD7sSlFOoBjAKqaAQaB2WWFBW4i37FZxCcvq8CYxx6nhV8q0yZ2OL8cb6nXnU08pRhtW5nrYJxafzjCcMfaouP9F230rkimrrUwi3o8Zot6tZOfLT/Rutz73AxEFSebe+/TLeHrKewzDNU3/vP3IZTNTpvYwf/74nddv/tcrmpddzEqKbmralZVrwI6getEZOoc65K68ETkNhHZISI7+lKzTxzzWbzMjk1RqJu689EFaPRpqil3T9Sg4qk7c8qngzFN44mjRcdbDh/wrshnhmdQ9ZD1GRWiSrwvtyeqklsxsahICcdb9+3xj8dLJu1fvoz74Mfv++J33cn1+73fSl/XlKesBlVVHRCRh4BXA7snneoCVgNdIhIGmoE+j6/fDmyHXJv7Bca8IMTdCM3pOIOR8fMzPydtX1fQ4am5p/IVqdkvpducSRB2HTIebe4N6SijkVRRPA2ZGMOTZ6gGGE9d32mWHNhL//rLCtpSnWyWTo+9Rpe+sI/IyDDphuK25sZjhxjuvOj8n+6qiOtOU89QbhjglHqajh1iaEo9TjaLMz5Opr6hqPz6++5g32+9le5rb8QNR2g6fpiNd3+Lup5uDrzmd0s+LplMLrFNqb++6wijq1YXxuO6OMkRMnXF8TQdPcjIlDZ6v/tZ7vcllM3SdOx5BtdsKKp/1eMPe96Hsn6pXMB1y3lf5rwZn9xFpE1EWvKvE8Arganjru4B3p5//bvATxdze/tZl4wuZ3myCSe/f2hDJsblwytzn0+WX4UxKFuHOklkI+dmrjoqrB9t47LRlZ7xbBxp9zweC2iG6hXf/v9ZteNhnFQSXJfmo4e4Zvv/JDFQ9PsfgIbuo4VPpyJIJk1o6jop554evZ8ir//U31Pffezc024oOcHm72wnPHVSTr6eutMnPK975JbXc2LbTbklcB2HodUXs/NP/oqn3v5nPsff53n8mts/QXh0+PzTt7pcfP8PiI0Ne8Zz9b9+0jP+q7/8qbLupx+/78uWr33O8/iB173J832Nt5TXAlvudct9XyanlNEyW4CvAiFyvwy+p6ofE5GPATtU9Z78cMmvA1eTe2J/i6oemq7exTBaZjJFEYQJJ83TPjNIVySbWDsebFeFi+u5X+nZeEo9HhSPkZgFxpa28fj7P1o0w5NMOteZGiqcPSuZNB2PPsSl935/2uu65P7x+tUvmUyuqWFK/X7X9Y/Hu56pcWbJ/UD5x1NY/mz8U810P0vlV8/Z46XGGfR1TbEgR8s8TS5pTz3+kUmvJ4A3lRvkYnI2YU5MM4N0rIylekvltxG1XwKv9HrtM9U+tqzdc4YnYZ8lbcMRRlaunvG6Z++CX/0aDnuvoOhzXf94vOuZGufZ1O8fT2F5vz+xg/puzdTfXmqcQV/XXDiboTrH/Dpag+rAXOjqT3eX3eHWlF9m13VCZKf+Uiixfs8RHNNc1z8e73r84vSP53x5P6W836CUEmdQ8czl+6pltrbMHIu7EVrSCQYj4wXb5jkqrFjAS+wGJdHfy9Ln93Bm45aiDs+mo88zsH7T+THequC6rPz1wzz7xrdzast1aMih/lQ3m+76Os3HXvCsv3XfM0WTaJxMmsZjLxTVL65Lywv76N9wWVE8zYeLj0s2Q/ORQwxs8IhzxyOecXrHk6HTZ4ndTDTG/t96S0nvNyj+9y1T1v2fTjXeVy2zJ/cq2DC6nPaJJkKugyg0ZeJcPrwqkNmgtSATnTKcUwTEYbhzbdGkHo1E2fPmP+HUlhflJgk5IUZXdvLkuz7I2NI2z/o3f/eLrP7lg4THRpFMhiUHn2Pb7f/ESMcaz/rTDY2e8WTjPnGu9onz9/7IM86LHrjbM5740IBn/M/8/nvKer9B8btv+2/9L4HEU633Vassm1SBg7BmYilrpuyXamCsdTlDa9YXdUi6oRBMneGZN7JqdeGMTUBDIbpuvIVLf/zdovJONsv6B+5i/QN3nTvWu+EyMol67/pXFtfvOk7hcMqS4lzjGeeJ61/GpT/+bkE8fsYy6pUnAAAST0lEQVRalzO4dgM6te17mvcbFK/7FlQ81Xxftcqe3M28Mta6HPGaUDR1tMpZ08w4HWnvKPm6g/nleEutH78ZrRWO0+/+lFtPUIKKZ769r1pgyd1csGwkSjpRH+AIfWg4dQL1mIru2+HpN2MznaL56LSjcQvib33+2bLqJ+09sqkScU7me3/KrCcoQcUz395XLbBmGVO2TCzBc7/9h5y+fCsgxAd62fTDr7Pkhf0zfu1M4oN9LNv7FD1XXA3O5A7MDKHhQVItSz1WVTzI8LoNBcdVHDof/VlZ8cf6z5zf1m5S/Uv372bg4o25yTsArks4k6b5hb30brqiOM6RIVLNS4rr2fcMA+s3FdQTyqR94/S7P227n+D05qtnVU9Qgopnvr2vWmBP7qZsT73tvZy+fCsajqDhMOPL2nnq7X/G2AUusDXVRGNT4Zo3IrjisPWrn6XlwLPguqBKZHiQrV/+dC6xU1ieUIjuq68vK/4rv/4vnvVv+cbnWfvQvUSHB3GSEyx77mm2ff7jpBMJzzjDw4NFM11Jp9lw/w8864kND5Z1fy77wVcCqScoQcUz397XQmd7qJqyjLat4Nfv/bvzT1dnZbN0PP5zNv7o23Na/8FbXseRV9xa3J6timTSvPyj76tI/NPVAwqhcNHxIO6PMaXOULUnd1OW8SXLEK8Zm6EQY8tXzHn9Axdd6l2RiOekm6Din64ez/mVAd0fY0plyd2UpeFkl2fHl5NO0ey3zO4M0vEEE00taIn1Ty6/8olfeVeqSmh8vOhwufX78atH0t4zV2dzfxabUu6/mZl1qJqyxIcGaN/1GKe2vmhSx1cWJ5Wi89GHyqornajj2Te9i74NlyGqREZH2HTn13zrb9/1GE+97X1F5clmcs0gUzowL/vev5UVv1/9rQeKR9L41RNKJVm6fw9nNl816/uz2Pj9e/C6/2Zm1uZuyqYiHLvxFXTdcAuZeJzW/Xu4+IG7SAz0llXPjnf/NcMdawuaT5xUkm1f+Dh9Gy4vqn/Pm//Ys3yst4fx9o7CCULpFC/+l3+kvqe75Pj96n/R5/+/suqJD/YFcn8WG79/D373f7Eqtc3dkrupipHlK9nxX//Ws0Ny1Y5H2HT3N0suL+RmMpZST1DxmGDZ/S+ddaiaeS3Z0urbITm+rHhI5XTlPR9PfOoJKh4TLLv/wbPkvgilGhoZa11e8j6Y5ZYvRUP3MVyfjs2WQ/uLrutXXnxmik6uJ6h4/Iy0r6R3/WW4TmV+nCpx/+eb2dx/423GDlURWQ18DVhBbkOY7ar6mSllbgbuBs6uzXmnqn4s2FDNbKXqG9jzlj9hYO0GJOsSSie57M6vsey5pwMpX47Y8CArnnqM7mtuLFxiN5Nh+TM7ePKP/qLouu27HuPktYXlnUyG5Xse59SWSR2b2Syh5AQdj/1HWfGs2vFIbn/QEusZbWvniXf/DZlE3bl41j10Lxc/eM+F3JIilbz/882F3H8zvVK22VsJrFTVnSLSCDwB/GdVfXZSmZuBv1LV15d6YWtzn3u/fu/fMdLe4dGB+U80nDo+6/Llevy9f8fIis6CxbYklSTR38t46/Ki68b7exlraz8/3R9wUimuvf3jDK2+mGM3vYJMvI7Wfc9w8b//iJjPkrl+VIQT215Scj0P/cNnc9vOTX6iVuWKb97O8mefLOvaXip9/+ebcu//YhXkNnvdQHf+9bCI7AU6ABuftICMrOhgtG1F0cQeNxTm2I23cNkPvz6r8hcSz1jbiqJVFDUcZmxZu8dSuvnjTvESu1035OLp+PXDs4pJVOn49cMl1dOz+erixJ538FW/PevkXun7Px+Vc//NzMpqJBSRdeT2U33M4/QNIvKUiNwnIpt9vv42EdkhIjv6UsHvF2r8JZuW+HZYTSxdNuvygcXj+CyZ67eUbkDxlGt0+SrvEyLFm3tcgErff1P7Sk7uItIA/AD4gKoOTTm9E1irqluBzwKeuw6o6nZV3aaq25ZGbY/EudR44oj3zMxUiiXP7511+cDi8VtKN5Xy3DQ5qHjK1fbsTu8TqjQGsC1cpe+/qX0lJXcRiZBL7N9U1TunnlfVIVUdyb++F4iIiD1ezCPRkWFW7PxlbsXDs1RxMmk6Hv+5Z/mORx/CSSXPHZNMhvDEmGf5C4mn7Zkdhasn5vca7Xj850XXjUyMscrjeFDxlKvhVDcNx48Wx6/KxgDGZFf6/pvaV8poGQG+BOxV1U/6lFkBnFJVFZHryP3SsOl484gCA2um7DYkQjYcZmJJK5HusaKv2XDf92noPpbr4ErUsWzvU6z7j/uITBSXLZcLnLry2qJ43GiM5sMHaDr2QvF1R4a9jwcQz4XY9vl/ZP8bfp+TV1+PGwpTf+o4m7//JeoCmolayftval8po2VeAjwMPEPuZxLgb4E1AKp6u4i8D3gPkAHGgQ+q6i+nq9dGy8yt4ZWdPHHbh3BjUzZ1zmZZ8eSjXH7nV+c0nlNXXsuet9zmuVRvoreHGz7593MajzELRZCjZR7Bcw3TgjKfAz5XenhmrqUaW5DJTTJnhUIkW+Z+o+6xZT7L34qQrmuY22CMqUE2Q3UeGndSjIQmcPFIxheo8fhhz/XNnVSKpft3AzC6rJ3BzovI+m3+HKDlu3d4n1Cl6cjCWhp3Lu+bMaWyf43zSFIy7G84xUQonVsMC1g31kpbavZD66KjI6x+5EGO3fgK3FhuBqBk0kTGhmndt5vH3/f3jC1bnnu6F+HSu7/Fyl2Pzvq6fupPn6Kh6wgjnWsLl+pVZdPd36rYdYM00byEp//wfXN634wplSX3eUJRnms8yYSTLmgEO1zXSyIbpSEb8//iEl38k7to7D7KsRtfQbqunmXP7mLNwz9h57s/lNv/dNJY8n3/+fepP91N0/Ejs76uFwUysVhu9M7Z64pAOkWqsYn4UH9FrhsUBXa98wNzft+MKZU1y8wTY6EUKSdT1LvhopyKTZ1WcGEEWL57J9du/19c/+l/YMMDd5Fc0kqyeUnxjNBwhK4bbgnkul5GVq0h7XFdKnzdoIysWlOV+2ZMqSy5zxNpySJeA5eEXNKvkFR9Y+HY97Mch2RTS81dNygLPX5T+6xZZp5oyMZwPcYkiQot6bqKXbep6wWfjtYkrRVcfbBa1z3LBU5feS3Jxhban36c2MjwtOUVGFnZSSZeR+PxI1WP35iZWHKfJ8IaomO8mROJQdz8I7yoEHVDLE/OvkPVT2R8jLU/u5cjN7/m3FKrTjpFNL8Ea61dF6B/3QZ2veuD53ZvOvC632P5rse44vtf9iw/vqSVp97xfiaacsNJNRRiw//5XtXiN6YUltznkY7kEuqyMU7GB8mIy9JUHe3JZkIVbj276KF7aew+xrEbbyFd10Dbnp2s/tVDhCdNfa+V67rArj/6IOqECiZQ9Vz1Yo6/sI+OHb8oKH+243R8aVvBHq0HXvd7XP2lT1blvhlTCkvu88ySTB1LRirXDONn2b5nWLbvmZq/7qmrry9K7Gcdvvm1Rcl9uGMtqcbmws23yXecXv9yNn//y1W5b8bMxDpUzaIy0ewzG1eEbDxRdDhd1+DbcZpqbAo4OmOCY8ndLCornvSZYKRKy8Hnig43HTvk23G6bO9TQYdnTGAsuZtFJTHYlxvNkp8NC+T2bs1mPGfGRibGuegnd+eW3s0/wTupJPGBPlZNacIxZj6xNnez6Gz9+r9w5KZXcuylryIbjdFy8Dk23f0NomMjnuXXPvITGk8cpeuGW0jXN9C2eyerdjxCyGdjEWPmA0vuZlFa+4sHWfuLB0suv/TQPpYe2lfBiIwJljXLGGNMDZoxuYvIahH5mYjsFZE9IvJ+jzIiIv8sIgdE5GkRuaYy4ZpKURH6Lt5Iz+ZrSNXbeurGLHSlNMtkgL9U1Z0i0gg8ISI/UdVnJ5V5DXBJ/uPFwBfy/zcLwMjylex611+Qzc+01FCIdT/9Mev+4/4qR2aMuVAzPrmrareq7sy/Hgb2Ah1Tir0B+JrmPAq0iMjKwKM1gVMRnnrn+0k1NJGNJ8jGE7iRKIdf/jr6L95Y7fCMMReorDZ3EVkHXA08NuVUB3Bs0uddFP8CMPPQUOdFZGIJzxmYx6/7jSpFZYyZrZKTu4g0AD8APqCqUxcY99pjtWgBWxG5TUR2iMiOvpQNI5sPMlM3zD7LcUgn5n4ZBGNMMEpK7iISIZfYv6mqd3oU6QJWT/q8EzgxtZCqblfVbaq6bWk0eiHxmoA1Hz2IOsX/DJxUkvZnnqhCRMaYIJQyWkaALwF7VfWTPsXuAd6WHzVzPTCoqt0BxmkqJJxKcsmPv5ObgZnNAuAkJ6g/dcJ/qr4xZt4rZbTMTcAfAs+IyK78sb8F1gCo6u3AvcBrgQPAGPDO4EM1ldKx4xc0HT/K8eteRqqhkbY9T9L+zK9x8sneGLPwzJjcVfURvNvUJ5dR4L1BBWXmXmP3MTbd/Y1qh2GMCYjNUDXGmBpkyd0YY2qQJXdjjKlBltyNMaYGWXI3xpgaZMndGGNqkCV3Y4ypQZbcjTGmBllyN8aYGmTJ3RhjapAld2OMqUGW3I0xpgZZcjfGmBpkyd0YY2qQJXdjjKlBltyNMaYGlbLN3pdFpEdEdvucv1lEBkVkV/7jI8GHaYwxphylbLP3FeBzwNemKfOwqr4+kIiMMcbM2oxP7qr6c6BvDmIxxhgTkKDa3G8QkadE5D4R2RxQncYYYy5QKc0yM9kJrFXVERF5LXAXcIlXQRG5DbgNoDMeD+DSxhhjvMz6yV1Vh1R1JP/6XiAiIst8ym5X1W2qum1pNDrbSxtjjPEx6+QuIitERPKvr8vX2Tvbeo0xxly4GZtlROTbwM3AMhHpAj4KRABU9Xbgd4H3iEgGGAfeoqpasYiNMcbMaMbkrqpvneH858gNlTTGGDNP2AxVY4ypQZbcjTGmBllyN8aYGmTJ3RhjapAld2OMqUGW3I0xpgZZcjfGmBpkyd0YY2qQJXdjjKlBltyNMaYGWXI3xpgaZMndGGNqkCV3Y4ypQZbcjTGmBllyN8aYGmTJ3RhjatCMyV1EviwiPSKy2+e8iMg/i8gBEXlaRK4JPkxjjDHlKOXJ/SvAq6c5/xrgkvzHbcAXZh+WMcaY2Zgxuavqz4G+aYq8Afia5jwKtIjIyqACNMYYU74g2tw7gGOTPu/KHzPGGFMlM26QXQLxOKaeBUVuI9d0AzCy4v779gVw/UpbBpypdhBzyN5vbbP3u/CtLaVQEMm9C1g96fNO4IRXQVXdDmwP4JpzRkR2qOq2ascxV+z91jZ7v4tHEM0y9wBvy4+auR4YVNXuAOo1xhhzgWZ8cheRbwM3A8tEpAv4KBABUNXbgXuB1wIHgDHgnZUK1hhjTGlmTO6q+tYZzivw3sAimn8WVDNSAOz91jZ7v4uE5HKzMcaYWmLLDxhjTA2y5D4DEQmJyJMi8uNqx1JpInJYRJ4RkV0isqPa8VSaiLSIyB0i8pyI7BWRG6odU6WIyMb89/Xsx5CIfKDacVWSiPyFiOwRkd0i8m0RiVc7prlkzTIzEJEPAtuAJlV9fbXjqSQROQxsU9VaGxfsSUS+Cjysql8UkShQp6oD1Y6r0kQkBBwHXqyqR6odTyWISAfwCHC5qo6LyPeAe1X1K9WNbO7Yk/s0RKQTeB3wxWrHYoIlIk3AbwBfAlDV1GJI7HmvAA7WamKfJAwkRCQM1OEz/6ZWWXKf3qeBDwFutQOZIwo8ICJP5GcT17KLgdPAv+Wb3b4oIvXVDmqOvAX4drWDqCRVPQ78b+Ao0E1u/s0D1Y1qblly9yEirwd6VPWJascyh25S1WvIrfT5XhH5jWoHVEFh4BrgC6p6NTAK/E11Q6q8fPPTrcD3qx1LJYnIEnKLGl4ErALqReQPqhvV3LLk7u8m4NZ8O/R3gFtE5BvVDamyVPVE/v89wA+B66obUUV1AV2q+lj+8zvIJfta9xpgp6qeqnYgFfZK4AVVPa2qaeBO4MYqxzSnLLn7UNUPq2qnqq4j92fsT1W1Zn/zi0i9iDSefQ28CvDcoKUWqOpJ4JiIbMwfegXwbBVDmitvpcabZPKOAteLSJ2ICLnv794qxzSnglg4zNSGduCHuZ8DwsC3VPX+6oZUcX8GfDPfVHGIGl86Q0TqgN8E3l3tWCpNVR8TkTuAnUAGeJJFNlvVhkIaY0wNsmYZY4ypQZbcjTGmBllyN8aYGmTJ3RhjapAld2OMqUGW3I0xpgZZcjfGmBpkyd0YY2rQ/wNt+DQiIfljNwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ 0.7 -0.92 0.16]\n" ] } ], "source": [ "iris = datasets.load_iris()\n", "X = iris.data[:, :2] # we only take the first two features. We could\n", " # avoid this ugly slicing by using a two-dim dataset\n", "y = iris.target\n", "# Just 2 classes...\n", "y[y > 0] = -1\n", "y[y == 0] = 1\n", "\n", "a = perc(X, y)\n", "yy = perc_clsf(X, a) # get the predicted labels...\n", "# ...and compare y to yy (error rate):\n", "print(\"Error rate: {:f}\".format(np.sum(y != yy) / float(yy.size)))\n", "\n", "# TODO: try\n", "#a = perc(X, y, 0.1)\n", "#a = perc(X, y, 0.05)\n", "\n", "plot_clsf_reg (X, y, a)\n", "print(a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the professional way:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import Perceptron" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Have a look at [http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Perceptron.html] for documentation of the class. Identify the parameters discussed during the lecture." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error rate: 0.195000\n", "[[2.42439397 1.38266523]]\n", "[0.]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/vlad/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/stochastic_gradient.py:128: FutureWarning: max_iter and tol parameters have been added in in 0.19. If both are left unset, they default to max_iter=5 and tol=None. If tol is not None, max_iter defaults to max_iter=1000. From 0.21, default max_iter will be 1000, and default tol will be 1e-3.\n", " \"and default tol will be 1e-3.\" % type(self), FutureWarning)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clsf = Perceptron() # create a default Perceptron classifier. TODO: try different initial parameters\n", "clsf.fit(X0, y0) # train the classifier\n", "yy = clsf.predict(X0) # make predictions. NOTE: usually you predict a new set of points\n", "print(\"Error rate: {:f}\".format(np.sum(y0 != yy) / float(yy.size)))\n", "print(clsf.coef_)\n", "print(clsf.intercept_)\n", "w = np.hstack((clsf.intercept_, clsf.coef_[0,] ))\n", "\n", "plot_clsf_reg (X0, y0, w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### TODO/HOMEWORK\n", "- use numpy.random.shuffle() function, to shuffle your dataset and then re-train the classifier. Does the solution change?\n", "- random partition your data into a \"train set\" and a \"test set\" (e.g. using numpy.random.choice()). Then train a classifier on the \"train set\" and apply it to the \"test set\". How does the test error rate compare with the train error rate?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fisher linear discriminant\n", "- FDA (Fisher discriminant analysis) is LDA (linear discriminant analysis) for 2 classes\n", "- check the documentation for LDA: http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html\n", "- repeat the training/testing/plotting steps from above, but in the case of LDA. \n", "- go through the example below (taken from scikit-learn http://scikit-learn.org/stable/auto_examples/classification/plot_lda_qda.html) and try to understand the principles (not the details):" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/vlad/anaconda3/lib/python3.6/site-packages/sklearn/utils/deprecation.py:77: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n", "/Users/vlad/anaconda3/lib/python3.6/site-packages/sklearn/utils/deprecation.py:77: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n", "/Users/vlad/anaconda3/lib/python3.6/site-packages/sklearn/utils/deprecation.py:77: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n", "/Users/vlad/anaconda3/lib/python3.6/site-packages/sklearn/utils/deprecation.py:77: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import linalg\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "from matplotlib import colors\n", "\n", "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n", "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n", "\n", "# #############################################################################\n", "# Colormap\n", "cmap = colors.LinearSegmentedColormap(\n", " 'red_blue_classes',\n", " {'red': [(0, 1, 1), (1, 0.7, 0.7)],\n", " 'green': [(0, 0.7, 0.7), (1, 0.7, 0.7)],\n", " 'blue': [(0, 0.7, 0.7), (1, 1, 1)]})\n", "plt.cm.register_cmap(cmap=cmap)\n", "\n", "\n", "# #############################################################################\n", "# Generate datasets\n", "def dataset_fixed_cov():\n", " '''Generate 2 Gaussians samples with the same covariance matrix'''\n", " n, dim = 300, 2\n", " np.random.seed(0)\n", " C = np.array([[0., -0.23], [0.83, .23]])\n", " X = np.r_[np.dot(np.random.randn(n, dim), C),\n", " np.dot(np.random.randn(n, dim), C) + np.array([1, 1])]\n", " y = np.hstack((np.zeros(n), np.ones(n)))\n", " return X, y\n", "\n", "\n", "def dataset_cov():\n", " '''Generate 2 Gaussians samples with different covariance matrices'''\n", " n, dim = 300, 2\n", " np.random.seed(0)\n", " C = np.array([[0., -1.], [2.5, .7]]) * 2.\n", " X = np.r_[np.dot(np.random.randn(n, dim), C),\n", " np.dot(np.random.randn(n, dim), C.T) + np.array([1, 4])]\n", " y = np.hstack((np.zeros(n), np.ones(n)))\n", " return X, y\n", "\n", "\n", "# #############################################################################\n", "# Plot functions\n", "def plot_data(lda, X, y, y_pred, fig_index):\n", " splot = plt.subplot(2, 2, fig_index)\n", " if fig_index == 1:\n", " plt.title('Linear Discriminant Analysis')\n", " plt.ylabel('Data with\\n fixed covariance')\n", " elif fig_index == 2:\n", " plt.title('Quadratic Discriminant Analysis')\n", " elif fig_index == 3:\n", " plt.ylabel('Data with\\n varying covariances')\n", "\n", " tp = (y == y_pred) # True Positive\n", " tp0, tp1 = tp[y == 0], tp[y == 1]\n", " X0, X1 = X[y == 0], X[y == 1]\n", " X0_tp, X0_fp = X0[tp0], X0[~tp0]\n", " X1_tp, X1_fp = X1[tp1], X1[~tp1]\n", "\n", " alpha = 0.5\n", "\n", " # class 0: dots\n", " plt.plot(X0_tp[:, 0], X0_tp[:, 1], 'o', alpha=alpha,\n", " color='red', markeredgecolor='k')\n", " plt.plot(X0_fp[:, 0], X0_fp[:, 1], '*', alpha=alpha,\n", " color='#990000', markeredgecolor='k') # dark red\n", "\n", " # class 1: dots\n", " plt.plot(X1_tp[:, 0], X1_tp[:, 1], 'o', alpha=alpha,\n", " color='blue', markeredgecolor='k')\n", " plt.plot(X1_fp[:, 0], X1_fp[:, 1], '*', alpha=alpha,\n", " color='#000099', markeredgecolor='k') # dark blue\n", "\n", " # class 0 and 1 : areas\n", " nx, ny = 200, 100\n", " x_min, x_max = plt.xlim()\n", " y_min, y_max = plt.ylim()\n", " xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n", " np.linspace(y_min, y_max, ny))\n", " Z = lda.predict_proba(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z[:, 1].reshape(xx.shape)\n", " plt.pcolormesh(xx, yy, Z, cmap='red_blue_classes',\n", " norm=colors.Normalize(0., 1.))\n", " plt.contour(xx, yy, Z, [0.5], linewidths=2., colors='k')\n", "\n", " # means\n", " plt.plot(lda.means_[0][0], lda.means_[0][1],\n", " 'o', color='black', markersize=10, markeredgecolor='k')\n", " plt.plot(lda.means_[1][0], lda.means_[1][1],\n", " 'o', color='black', markersize=10, markeredgecolor='k')\n", "\n", " return splot\n", "\n", "\n", "def plot_ellipse(splot, mean, cov, color):\n", " v, w = linalg.eigh(cov)\n", " u = w[0] / linalg.norm(w[0])\n", " angle = np.arctan(u[1] / u[0])\n", " angle = 180 * angle / np.pi # convert to degrees\n", " # filled Gaussian at 2 standard deviation\n", " ell = mpl.patches.Ellipse(mean, 2 * v[0] ** 0.5, 2 * v[1] ** 0.5,\n", " 180 + angle, facecolor=color,\n", " edgecolor='yellow',\n", " linewidth=2, zorder=2)\n", " ell.set_clip_box(splot.bbox)\n", " ell.set_alpha(0.5)\n", " splot.add_artist(ell)\n", " splot.set_xticks(())\n", " splot.set_yticks(())\n", "\n", "\n", "def plot_lda_cov(lda, splot):\n", " plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')\n", " plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue')\n", "\n", "\n", "def plot_qda_cov(qda, splot):\n", " plot_ellipse(splot, qda.means_[0], qda.covariances_[0], 'red')\n", " plot_ellipse(splot, qda.means_[1], qda.covariances_[1], 'blue')\n", "\n", "for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):\n", " # Linear Discriminant Analysis\n", " lda = LinearDiscriminantAnalysis(solver=\"svd\", store_covariance=True)\n", " y_pred = lda.fit(X, y).predict(X)\n", " splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)\n", " plot_lda_cov(lda, splot)\n", " plt.axis('tight')\n", "\n", " # Quadratic Discriminant Analysis\n", " qda = QuadraticDiscriminantAnalysis(store_covariance=True)\n", " y_pred = qda.fit(X, y).predict(X)\n", " splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)\n", " plot_qda_cov(qda, splot)\n", " plt.axis('tight')\n", "plt.suptitle('Linear Discriminant Analysis vs Quadratic Discriminant'\n", " 'Analysis')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }