{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Kernels, kernel trick, kernel regression and SVM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This short series of exercises serves as an introduction to the notion of Kernel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1.\n", "\n", "__1.a Non Linear features + Linear classifier__ \n", "\n", "Consider the dataset below. This dataset is not linearly separable. However, as we previously discussed, one can bring the data into another (higher dimensional) space and then learn a separating plane in the new space. What would be good features to add to the model to make the data separable ? \n", "\n", "(Try to think of a (geometric) feature that makes the yellow points different from the purple ones. Look at the axes, what is particular to the yellow prototypes?) " ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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Shk97lpHTh7Lp6LqUGPO24xvpMqEF/q/60uHDJqw7tNIt18xpHHY78aFRBTLd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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from sklearn.datasets import make_moons, make_circles, make_classification\n", "from matplotlib import cm\n", "\n", "\n", "X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,\n", " random_state=0, n_clusters_per_class=1)\n", "\n", "\n", "X,y = make_circles(n_samples = 200, noise=0.2, factor=0.5, random_state=1)\n", "\n", "figure = plt.figure()\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y)\n", "plt.set_cmap('PiYG')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1.b__ Apply your transformation to the data and plot the result in a 3D space. Then learn the separating plane from the minimization of a RSS criterion and plot the plane in the 3D space using the function 'surf' from matplotlib" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put the code here\n", "\n", "import matplotlib.pyplot as plt\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2. Kernels \n", "\n", "Now consider the following two datasets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Example 1. (Scikit Moons DataSet)__ " ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "image/png": 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2IcRiKeXBG2OklINTjR8IPJhqCYuUstbtynEvkjc8lCFfv8zHvb9StMWH5AtG\nZ9ASdzUBu8WORqtBb9TxxoyXfdJe38s07fpoioK4U0iMS2LpzFXsWLGbgiUK0G5Qa8rXKsNT/Zrz\nVL/minMKlYrAFGJKyXV1A6PZSKFSETkhtooKEJgdQz3guJTyJIAQ4hfgGeCgn/FdgFEBuO59QdOu\nj1KzyQNMH/ItG3/fit6oTy6GY2bCX+8QXiw/y75exY6/91CoVATtBraiXM3SuS32fU1cTDyv1H6T\n2Kg4bBY7Go1g7fzNDJszgMbPNvA779FO9Zkx9FtsiaS48AohMAQZeLRj5g7jVVQCwW2n3RZCdAJa\nSin7JH/uDjwspfQx6AohSgFbgOJSSldymxPYDTiBCVLKPzK65t2YdltKyYFNh9m5ci95wkJo0rlh\nll1KE+OSOLj5CEF5gqjaoKJPdbBA4LA7+OH9X1k6cxW2JBt1nqxF/497ULh0wYwnqwAwe+RP/Dr5\nTxw2711eSL5gFlyepZhY7wZnD0cy4YXPOb3/HBIoW70kw398neIV7x7ToMqdS2bTbuf04XNn4Ncb\nSiGZUlLKSCFEWWCNEGKflPJE2olCiH5AP4CSJUvmjLQBwu128/5zk9mxYjfWJBsGo57Z7/zEqF+H\nUrflgxkvkExwqDlL42+FsZ0+YdfqfSmZRDf/sY296w4y5/Dnt1UG835i06LtPkoBPF5HZw6eT3dH\nV7JyMb7aMZHY6DjAY05UUclpAvHKGQmUSPW5eHKbEp0Br3wPUsrI5H9PAmvxPn9IPW6mlLKOlLJO\nRMTdZW/9bfISNi/e7vFGkR5XU1uSnXGdP/Wbyz83OHs40kspALjdEmuSjWVfr0ppk1JycMtR1vy8\nkbPpJJ27X8kTFqLY7nK4/JYSTUve8NB0lYLL6WLh50vpXfV1XijzKjPf/M5vhLeKSlYJxI5hO1BB\nCFEGj0LoDHRNO0gIURkIA/5N1RYGJEkpbUKIcOARYGIAZLpj2Lp0J7OG/6gY3ARwYNPhTEXOZgWX\n08Vvny5h8VcrsCbaqP90bV4c14UCRdI3XZ3adxadTkvaRB12i51DW44BEBsdx7BmY7h4Igqh8cRN\n1G1Zi3d+GZyuieR+osPrrTmx+5RXjIlGq6FMjVJ+D5HjYuL565s1HN52nLI1SvJUv+aEFcrn9xrj\nu37GtmW7Utx0f/9iOZv+2M7MPR8HLChP5f7ltncMUkonMABYARwC5kspDwghxgohUruedgZ+kd6H\nGlWAHUKIPcA/eM4Y/B1a33W43W4+6TPNr1IAsuWc4INun/PdmPlcPnOF2Og4Vn2/nldrv5nhG2Wx\n8oVxKciqN+opU92zKZzU+ysUS7gvAAAgAElEQVTOHorEmmjFEm/FbrGz46/dzP94ccDv427l0Y71\naT+oNQaTHnOoGVOwkZJVijF64TDF8ZdOR/Fi5df5dvR8Nvy2hZ8//J0XK7/OqTQ5s25w+sA5ti7d\n5RW74bQ7ibl4nbXzNmfLPancXwTkqSSlXCalrCilLCelHJ/c9p6UcnGqMaOllG+nmbdZSlldSlkz\n+d97oyJMMpdPXyEpXrmkJnjeIh94pFJAr3n+2EW2LNnp9dBwOV0kxibx1+w16c4t/2AZytYohd7o\n/eavM+ho83ILLIlWdq7YjcvhneTNZrGzdMbKwN3EXY4Qgt7ju/LjmWmM+Ol1Pl3/PjP3fOJV+zk1\n0wbPJSEmIcWEZ7d60oN/1n+G4vjD246jUagHYU20smftrdfzUFG5gZoSIxsxhwbhdrkU+4RGMHrh\nsICbX078dwqdQupmm8XO/o0Z13n4cPkIHu3YAJ1Bh0aroULtskxeO4bwYgU8sRR+sodaMyhuf78Q\nc+ka+zceIubSNfJF5OXh1g9hNBvYtWov16KUK8ftXLkHt9vXO/DQ1mM+xYQAIornVywUpDfqKVIu\ne/NbqdwfqEbhbCRveCg1HqvKnrUHcKZ6y9YZdLzyaa9sydVTqHQEbgUXZJ0hc9HQwXmDGf7DIN6c\n+xoup8urJGiesBCKlS/MmYPnveZodVoaPJ2hB9w9jdPh5JM+01i/4N+UlOUN2tblamQMx3adRGfQ\nYbc6aN23Ka993tsr9YnBZPDJEAuen+uNxH+pqfVENUIL5MGWZPcyU2p1GlrdQrp1FZW0qDuGbGbE\nT29Q/sEyGM1GgvOa0Zv0tH2lBU+/3CJbrlepbnmKlSvsU11Mp9dm6ZpanVaxTvTQ2a8SFGJKMTcZ\nzUbyRoTy4jj/BWruB74bPZ8Nv25JMQPZrQ42/PYvB/49gs1iT6kct2L2P14eXgBPvvg4BpN3bii9\nQUfj5xoqnkFptVomrxtLpXrl0Rt1GIIMFC5TkAkr3r0r8mOp3PncdoBbbnA3BridPnCOK+evUr5W\n6XS9TQJBbHQck3p/xc6/PeUgi5QtxNBvXqFqg8CcZ1w5f5WlM1dy7nAkDzxSmSd7NSE4b+bcMO9V\n2uXvSeL1pEyNLVG5KLMPfp7y2W61894zH7F/02E0Wg3SLSldrSQT/hqZ4c/12uXrOGwOIkqEZ1v5\nVZV7h8wGuKmK4Q7E7XZzev85HDYHmxZt4+85a3E6XDTq8DAvjuuc6aAnS4IFu9WhBknlAC10zyEV\nzgmUCCuUj/kXv/ZpP7XvDKf2naV4paJUrF0uU2tJKdm5ci9/zVmD2+miabfHaNC2DhqNhrir8SyZ\n8Td71h6geMWitBvYihKVimXpvlTuLVTFcJdy8N8jjH32ExJik7Bb7F4PG51eS3jxAszaP1n1Vb/D\nGNhgBIe3HstwnEaroVn3xxg2+7WAXHfqoG9YMeeflJgJU7CRh5+qTf+Pe/BqnbdIivOYtbQ6DTqD\nnrGL3rrlTLYqdz+ZVQzqGcMdRPy1BN5uOY6rF65hS7T5vIE6HS6uX4lj3fx//aygklsMmPKSV5U4\njVaDwaRHb9SltOmNekLyBdNz9HMBueaZQ+dZ/s0ar0A6a6KNrUt38ln/GcTHxKfUdnA53diSbHzS\nZ5pPeVEVlbSoXkl3EGt/2ZRuMByANcHK4W3HaNGzSc4IpZIpKtUpx7SdE5n/8WKO7zpFuQdL8/yw\nZ3DYnfz26RIij12kZuOqPDOwNWEF8wbkmjv/3qNovrIm2ti7/qBPnQ7wnEnEXLqeYRS8yv2Nqhju\nIK5FxSq6LabGaPZU/bpTkK4okHbQFrvvDz+LVyzKkJkv+7QP/ebVbLmeOdSMVqfBkSaERG/weCql\nLfsKIN0SU7BqhlRJH9WUdAdR/dEqmEJM6Y7R6XU079E4hyTyj3Sewx3dAXnlCWR0a2R0M6R9d26L\ndV/RKLkkaFqEVkP711tjTFMVUKfXUrtFTYJDzTkhnspdjKoYchinw8mJPae5dDrKp6/W49WoWr8i\nRvPN+AGhEQgh0Oq1VHioDJ9ueJ/Q/Lmb/lpKJzKmGzgPAnbACq5zyGu9kK7oXJXtfiIkXzBjF72F\nOTQo5csUbOTt7wbSdXgHmnZthN6oxxwahNFspPyDZXhzbmAOvVXubVSvpBxk3YJ/+az/DFwuFy6n\nmzLVSzJ64TCvHDpOh5OlM1ay8PNlJMYlUalOOV4c34UiZQreMbEC0voPMnYIyLRJ+YwQMhBNSL9c\nket+xW5zsGftAdxOFzWaPEBQ8M1d55XzVzmx+zSFSoVTpnopzh6O5JvhP7J/4yHyRoTy/LB2tOjV\n5L43A94vqO6qdxjHd5/ijUfewZaq1oFGq6FEpaJ8vW9yyh+m3ebgzaZjOLH3DNYEKzq9Fq1Oy8hf\nBt8xaSdk0i/IuA8AhQSBQZ3R5B2b4zKpZMyFE5d4+aE3sSZYUzyTTGYjnYY+Tc/Rz+eydPcf0nUZ\nGT8ZbP+AMIG5MyK4L0LoM558i6juqtnI7n/2M7LNB/SvNZSv3/rBb3K01CyashxHmqI8bpeby2eu\ncPy/UyltK2av4fjuUykF4Z0OFzaLnY96TMFhv0OK+uhrKLcLM8JQN2dlUck0P3+4EFuSzctd1Zpk\nY8GkxSTFW3JRsvsP6Y5HXu0A1sUgr4P7EiRMR15/I7dFA1SvpHSxJFiYMfQ7Vv2wAafdQa3Hq1Ht\n0Sr8MuEPbMnZRM8djmTld2uZsfvjdFNdRJ2LVsygqdVqiLl0PeXzmp82KnomSSk5sv0EZaqVYNUP\n6zl94BwVHirH410e8TId5ARCXxVpfARsm7i5azCApgiYnsxRWVQyz8F/jyq6Q2v1Wi4cv0T5B8vk\nglT3J9LyK7jjgdTZl61gW490nkDoMhf5nl2oisEPUkqGtxzP0Z0nU970d67ay86Ve73GOexO4q8l\nsuCTxfSb2MPvenWerMWBTUe8TEkAdpuTinVu/hIYzL6J68DjZnj9Shzdyw/AbnFgS7JhCl7P92Pm\nM3XbhBz3Sxf5piCTfoCkeSBtENQGEdwPIZTlV8l9ipYrzNlDvqVYnXYnBYop14pQySbsO1E0xaJF\nJv6AlDEgwhHm5xH6ijktnWpK8sfRnSc5see0t/nHz3GM0+5k/YIt6a7Xum8z8hXM61UExxRspOPg\np7wCntr0a67oZx4SFsxvn/5JQkxiym7Fmmjj2uXrzBj6bRbuLDAIoUMT3AtNxHI0BdegyTMEoVGu\ndXwrSFc00nEUKdOP61DJPF2Gt/fyeAMwmPTUb1M7YEF3KplEVw5QeomyguVXsC4Hy4/Iq+1xJ8zN\nYeECpBiEEC2FEEeEEMeFEG8r9PcSQlwRQuxO/uqTqq+nEOJY8lfPQMgTCM4eOp8lT42oc9Ec2X7c\nb39wqJlpuyby3NC2lKpanGqNKvPm3AH0Hu9dHrtRh4dp0bMJBpMek9lIUJ4gQsPzMOb3YRzcdNQn\nnYHL6WbLnzuzdnN3MNKdgDumH/JKE2TM88ioh3En/pzbYt3RRJ2LZnTHSTwV3I1n8vZgyoBZWBJ8\nzwyqNqjE8B9ep0DRMPRGHTqDjkfaP8ww1YVVEenYjzumP+6oxz2/k/Y9AVtbmLuASGuw0eB5+7wR\nmOgGHJDwAe7YkTmayuS2vZKEEFrgKNAcOA9sB7qkrt0shOgF1JFSDkgzNz+wA6iD5yeyE6gtpbyW\n3jUD7ZUUfSGGC8cvUaxCkRSTzJHtxxn6xGif6FGhEX6zaNZvU5v3F/voxVsi8vhF9q47SN7wUOq2\nqoVGo+Gp4G4+ZTXB48/+e8zcgFw3t3HH9AP7ZjzxETcIQoRNRRgfzS2x7liS4i30qjiQ2CtxKWdY\neqOe8g+W5vNN4xVfbmwWG5/2m8GG37bgdkvCCuVl4NQ+d4zX252AtG9HxryE5yEtAQEYEWEzEcb6\nAbrGHmTsCHCd8qwvgj0H0YoYEXnHIII63NY1c9IrqR5wXEp5Unr2/b8Az2Ry7pPASillTLIyWAm0\nDIBMmcLpcPLhC5/To9wA3nvmI7qXfY0J3b/A6fDY/cvWLIXeeNN1TGgEQcEmxbKKACf2nAmYbMXK\nF6HVS01p+Exd9Aa9p0pamzo+BXj0Rj3Nuj8WsOvmJtIVraAUACzIRN801Sqw6vv1WBKsXo4NDpuD\nU/vOcshPttdJvb9iw29bsVsdOO1Orpy7yvgun/odfz8i48bhOQO48XOVgBUZ/37AriEMNdFELEUU\n/BdRaAfoH0xntA2Z+H3Arp0RgVAMxYBzqT6fT25LS0chxF4hxK9CiBJZnJstzH1vHpt+34bD5kip\nsLVx4Va+Gz0fIQQT/nqH5j0aYzR7smY+1LQ6k9eNQW9Q9jOOjrzKpN5f4nIq13m+XV6f3pei5QoT\nlMeEMciAKdhIuVql6T3+Hqme5r4K/ny4XZdyVpa7hKM7TyjmRELC6X1nfZqvRcWy+Y/t2K1pnCAs\ndn7+cGF2iXn34Tzqp/1YwE06QpMXIYIQwV2BdPJYycwVggoEOeWV9Cfws5TSJoToD3wLZKk4rRCi\nH9APoGTJkoERatoKHy8hm8XO4mkr6D2+K0EhQQye0Z/BM/p7jXlmQEsWf7Ui5RD4BtItWTd/MwVL\nhmdLwFC+iLzM2j+Z3Wv2E3nsImWql+SBRyrfO1GrutL+OsDQMCcluWsoW6MURrNvzWihERSv5Fvj\nO/r8VfRGnU9MjZQQeUxVvimIfCCvKrTnzba/N2FsjDT3gqQZCr2GHHUFD8SOIRIokepz8eS2FKSU\nV6WUN56is4DamZ2bao2ZUso6Uso6ERERty20lBJLgpK7GFjildtv0GdCN7qP6uQxO6bBlmRn0dS/\nFOcd2X6cQQ1H0tLQmU4Fe/PDuN9wubK2u9BoNDzUrAZPv/Ik1RpVuXeUAiCEEUKGAkGpWnUgghEh\n/f1Nu69p0bMJhiCD1++BVqcFAR90/ZxhTcewb8OhlL6i5QvjtPv+zmm0GqrUr5AjMt8VBPfG+/cQ\nz+fgF7P1sprQ/0HejwE9cMNsHATawojgl7L12l5yBGCN7UAFIUQZ4XFi7wwsTj1ACJE6T3Rb4MZv\n6gqghRAiTAgRBrRIbst2hBBUqltesa9yPeX2G2g0Gp4b6v8YJSnOd8t35tB5hj4xmkNbjuJyuoiN\njueXCQuZOnC24hpSSjb9sY1hTUfz8kPD+H7sAhJj0+YmuvfQBHdDhE0BfT3QloKgTojwxQjtnZNq\n/E4iJF8wX2z+gJpNqiI0Aq1O63npibdy9UIMu//Zz/CW49i61OO5FhxqptOQNphSZV4VwpPOvcvw\n9rl1G3ccIvglML8AmDyHwhjB/Dwi2DeteqDRBLVFhC8Dc3cwNoc8byEKLEZocs6lOCC5koQQrYHP\n8Ki42VLK8UKIscAOKeViIcSHeBSCE4gBXpFSHk6e2xsYkbzUeCnlnIyuFyivpCM7TjD08VE4bA5c\nTjdanQa9Uc8na8dkWHN316q9vN1ynKKH0gMNK/HZxnFebR/1nMKanzb6RJ7qjXp+iZzhkzF1zrs/\ns/CzpSn2Y4NJT3ixAkz/byJBIWnfZFTuVaSUOGwO9EZ9hrtDl8vFoAYjObrjhE9f/iJhzIucmbLm\n8m/WMH/iH8RGx1OtUWX6TOhGqaolfObd70h3oiddhaYwQnNnJLG8HdQkepnk/LGLLPh4Mcf/O0WF\nh8rw7NC2FCuf/tup2+2mS4n+xFz0dS3T6rV8sXm8j2LpW30Ipw+c8xlvDg1i4sr3vHYv16JieaH0\nKyllGW9gNBt46YOutB/0VFZuUeUuZenXK5n77jziouPIUyAPvd7vTJt+zdOd09rUBYfdqdj37bEp\nFC1XODtEVblLUJPoZZLiFYoweEZ/vtw2gTem989QKQBcOHGZpDjlpGMFCocp7jbKVC+p6ObqsDkp\nXKagV9uRbcfRGXz9AmxJdrYu+y9D+VTufpbPXs20wd9yPSoWt1sSeyWO6UO+Zfk3q9OdF5TH/25y\n1Q/rAi2myj3Kfa8YbgVTsFGxni74/8PsMrw9BpN3CLzRbOCJro3IGx7q1Z6vYKhiwj2NVkNE8QK3\nKPWdhXTH4E74xhPRmTQf6c45V7y7ge9Gz/fxerMl2fhu9Px059V+sqbfvujIdONGVVRSUBXDLRBe\nND/lHyytuAO4cOIi+zcd9mnPVzAvz7/5DIXLenYH5jxBtB/U2scVFqBS3fKEF8uPRuv936M36nhm\nQI7F/2Ub0nEEeaU5JHwOlgXIuPHI6FZIl4J7YKbXPIY79n3c1wYiLQvv+hxLVy8oP8T9td/ghXc6\nKv5eGs0GajdXVhpOh5MLJy6l69xgTbJhTVKIl1C5J1EVwy3y7vz/EZLP9zDKYXMyvsunXkEwP477\nlW5lXmXBJ38SdyWefAXz8tnG93npg24e18I0CCH46O93KVO9JMYgA+Y8QQTnNfO/Wa9SvtbdnxpZ\nxr4NMp6b2SUt4L6CTPjkltZzW5Yir3YEy49gW4GMG4u8+hxSpu92fCdTuHRB5fYyyu03sCXZFQ+p\ndQYdj7TzrZWxZMbfdCr4Ev1rDeXZwn35qMcUr+C3iycvM7jxe7TL15N2+XoyrOkYos5eyeLdqNxt\nqIrhFokoXoCwwsr1FxKuJXLuyAUA/luzj58n/IHD6sASbyEp3sL1qFiGt/oAt1vZHAVQsEQ403dN\nYvruj5m4ehQLLs/i8c6PZMu95CTSnQDOIwo9TrCuzPp60gZx7+BRMsk/T5kEzpPIpPTNLncyfT96\nAWOQr+mxz4Ru6c6bN/EPRU85u8XB9StxXm1bluxk+v++IzE2CWuiDYfNwfrftvBpf0+AlTXJxqCG\nIziw6TAupwuX08Xe9QcZ1HDknVM0SiVbUBXDbaBXOCAGTwT0jb4l0//2sRUDXL0YQ++qb7Dht/TT\ndRevUIRKdcr5TcNx1yF8d0g3+27hHh37UIw0xArWZVlf7w7h0Y71Gf7j65SsUhy9UU+JysUY/sPr\nPNapQbrzzh2+oJiyQW/UcWLPaa+2nz5Y6PO7abfYWTf/XxLjkli/4F+sSTYvReN2uUmKt7B50d1V\nWvdORbpjcce+i/tybc9X7Eik218ivZxDLdRzGzzVtxkzhn3v9cclBBQqHUGRsoUASPTjvYSEyKMX\nmdhrKpfPXKHTkKdzQuRcR4ggpKFhcrK81G6VRgh69hYWNJOyU/Dpy6PcfpfwSLt6PNKuXpbmPNCw\nEmcOnvfJ15UUZ2F0+4kUr1CUt74fSPlaZbhyXvlMR6vTEBcdT+Sxi1gTfF9q7BY7F09ezpJcKr5I\n6UJe7QKuM0DyDszyB9K+A8KXZGvt54xQdwy3Qeu+zajzZE2MZiMGkx5zHhN5w0MZ9duwlDGNn22g\nWHjnBtZEG9+Onu+T1OxeRUo7BHUATQHAjCeyNAj0DyJCXvWMccchnSe5mUUlHXRVktdKu2sIQpi7\nKs24p3nuzWcwmg2K5wxOu4vTB87xvyajuHwmCqdDOd5Bq9OScD2BP6YuV+w3mAyUq1kqoHLfl9jW\ngfsCKUoBPN+7LoLtn9ySClB3DLeFVqdl9G/DOP7fKQ5sPkL+ImE8/NRDGFKl6m76wmMs/2YNp/ad\nUc6CiWeXcfHk5Xs+8lTaNiKvD0rV4oag5xDmtgh9DaS0477+FliXphQxkSGD0AT39rumEALCZiJj\neoJM9qqRDjD3QJgez8a7uTMpXLogU7d+yKy3f2TXqr3YkmyktSy5HC5GtZ9EwjVfLyStXkufCd14\n95mJirE6Wr2GIuUKUbuFf7dYlUziPOInY6oVad+JMLXIcZFuoCqGAFD+wTJ+C6kbjHo+WTuaDb9u\n4avBc4lNcwAInje5sELKB9n3CtIdg7z2GpDmYWOZDyGe/DMybqynpCF2uOFuGv85UlMYEdTa79pC\nVw4i1oF9G7ivgaE2Qlsoe27kLqBEpWKM+f1N/pi6nK/f/N4ngt5msXNq7xnFWJl8EaGUrVFKMd8X\nQMESEUxeNxaNRjU23C5SmPx32rcg7dtBXydXEmWq/7s5gN6g54mujzLipzcUa+42bFeX0AJ3tz08\nQ6wrUC6aLcG6DCktYFmEb4F0CzJxWobLC6FFGBsgglrf10ohNZXqlveJhQEwmY0IPw92h92J1Y/L\nK3jcZYNDzQGV835ESieQTo105xHktX7I6CeRuVCLRFUMOchDTavz+rR+hBYIwWg2ojfpeaxTA4bN\nfjW3Rct+3PF4HzbfwAEyIbnfDy7Vb/5WqFyvPFXqV8SQyu1VZ9BRoHh+ChQN8xmv0QhqN69B1QYV\nfZI9gkeh3Asu07mJlBJ3wtfIqHoQPyadkW6PadR1Fnn9jRyT7waqKSkNl89cYevSXej0Whq2q0u+\niMCmum3evTFPdG1E9PkY8uQPwZxObpt7CuMjkDAVH+UgjEhtaYifhrJ3kQDDQ9kv3z2IEIJxS4Yz\nf9Ii/vpmDS6ni8bPNeSFdztxZPtxRrWfiMPmxO1yozfoMAYbeXFcF0xmI69P78dn/WbgsHv6TcEm\nytYoSdMX7o0ysrmFTPox+e/Aj7eiD25w7Ee6ohHa8OwUzYv7PrtqauZNWsR3o+aBEGiEwC0lw+a8\nSpPn1LekQOCOfdtzhiCT/yiEGXTVwLEXj2dG2gIyGhAmRP4FCL1aRCbQnNp3hl8nL+H80QtUa1SF\nDm88RYEiN3cSpw+cY9msVVyPiqNh2zo06vAwOr36Lnk7uKMeAbfSDligbGoFMCHClyF0xW/7+mra\n7Sxyat8ZBtYf4VPq02Ay8PO56ff+GUAOIKUE2z9Iy0JAgqktxL4DxKYZKUCEgPExRMgAz+Gyiso9\ngPtSZfzG3QS9CJYf8HZfBTRFEBFrA3IIrabdziL//LJJMY+9RivYvFiN8gwEQgiE6Qk0YVPRhH2J\n0JUBoZRaQYKmIJp8n6pKQeXeQusn15m2NCLPK6AtxM2SonogCJFvUo57Jqn7wmRcTpdijhkpJS4/\ngUAqt4kmGKSfmtdC9XzJLqSU7NtwiE1/bMNkNtKoQz12/3OATX9sJ1/BUNoPbE3NJg/ktpj3JCJ0\nOPLaALy970yIPMMRmnxQYAnSsggcW0BbEmHujNAWy3k5A1TasyXwOZ7SnrOklBPS9A8B+uA5ebwC\n9JZSnknucwH7koeelVK2zeh6t2JKsibZWDL9b/6Zt4mgYBNPv/Ikj3Wqn6KJD287xtAnxvjkjjGY\n9Hx7fCrhRfNn6XoqmcN9uSHIaN8OfV00BX7MeYHucaSUTOw1lY0Lt2JLsqHRanC73Gi02pQ0Gkaz\nkRfHdabjG21yWdp7E2nbgkyYDM5ToCuNCBmMMDbMkWtn1pR02zsGIYQW+BJoDpwHtgshFkspD6Ya\n9h9QR0qZJIR4BZgIPJ/cZ5FS1rpdOdLDYXcw+NF3OXc4MuUM4cj24+xbf5ABU14CoHK9CjzVrxlL\nZ67EbnWg0WjQ6rX0/aibqhSyE391Exy7kdKNEKq1M5D8t3ofGxduTYnCv1FwKnVuJVuSjdkjfqbl\ni48TnPfur3N8pyGM9RHGOzvzbyD+6uoBx6WUJ6WnOsovwDOpB0gp/5EyJfZ7C3D7x+tZYP2CLZw/\nesHrYNmaaGP5N6u5eOpmMrBXJvfik7Vj6fxWO7qO7MDo34aCFKyY+0+6RUxUbgd/OaJc3PBSks6z\nuOM+wH31BdzX38VtP5pj0t1rrJ2/2W9qltToDTqObD+RAxLdm0jnedzXXsN9qQbuy3Vxx024q+qD\nBEIxFANSV7k/n9zmj5eA1Nm5TEKIHUKILUKIdgGQx4ftf/2n+Meg0WnZv9G72lqlOuV4cVwXkuIt\njO74MV+/9T1fDppN5+L92bV6n88aKreJsQGKv4b6agihx520CBndCpLmgmMbWOdBTFvcsRN856hk\niMGkV6zwlhaXy0We/OlE5qr4RbpjPYWjbKsBK8hYSPoRee3l3BYt0+ToPl0I8QJQB5iUqrlUss2r\nK/CZEELRDUUI0S9Zgey4ciVrkbAFioah0/vWAdAIQb6CvgFs/63Zz9IZK7Fb7NitDiwJVqyJNsZ0\nnHTfZEHNKUSeER7XVG5koDWACEaEjkW645OL8KT1XHKD5QekfVfOCnsP0LxHEwym9NM5azSC8GIF\n/Ob/UrmJdEUjnaeQqZwoZNKvybE6qd1SbWDfhXQcynEZb4VAKIZIIHVa0OLJbV4IIZoBI4G2MlU+\nZSllZPK/J4G1wINKF5FSzpRS1pFS1omIiMiSgK37NkObRjEIAaZgIw81re4z/u+5//jdbu/+50CW\nrq2SPkJXChG+AkL6g6EJBL+ICF+O0FcFe3pFjOxIy585JeY9Q6U65eg6ogMGkx6j2UhQiAmdQYfe\nqCc4rxlTsJFiFYvy4V8jcyV5292CdMfgjumBvNIEebU9Mqoh0rrK0+nci2/OLwAX8lpf3FGP4Y4d\nhXQpOF3cIQTCXXU7UEEIUQaPQuiM5+0/BSHEg8AMoKWUMipVexiQJKW0CSHCgUfwHEwHlGLlizDi\npzeY1OtL3G43bpebAkXDeH/x24o1l50OPy6U4DeHvcqtI7QFECEDFHoy+vW8+4Iz7wS6juhIs+6N\n2b78PwxBBhq2rYNGq2Hf+kNsWLiVnX/vYfBj79K8e2O6jOhAUHA6WUDvU2RMX3AeApzJDhRJyOtD\noMA80FUC1gBpXy4d4E5+/FkWIG2rIXwZQhOao7JnhkC5q7YGPsPjrjpbSjleCDEW2CGlXCyEWAVU\nBy4mTzkrpWwrhGiIR2G48exePpNSfpPR9W418tnpcHL8v1OYgk2Uqlrc7xvR5sXb+aDrZ9iSvM1G\nRrORBZe+JijkPslvlMtIaUNG1b9ZZ8ELAyL/twhD7RyX617E7XYzsP5wTu8/l5Km22DSU+qBEkzd\n+qGaZjsV0nEMebUTvvmONBDUDhEyFBn9JMh0EkMCYIKQgWhC+iId+8C2HkQwmFojtAWzRfYcc1cF\nkFIuA5alaXsv1ffN/BcIaLwAACAASURBVMzbjEdh5Ag6vY7K9dLPuSOlZM8/+3GkymEvhEBv1DFs\n9quqUshBhDBCvmnIa33w9l7SgrmbqhQCyM6/93Du8AWv2g12q4PzRy6wY8Ue6rVStPDen7gvewpJ\n+bxTu8F5zpPsLv/PyLh3wbEHTx4kgW92YSvY1uG2LvUU7cEN6CF+MuT7FGFqmv334gc18jkNi6et\nYOnXq72KmGi0gofb1KbxczkThKJyE2GsDwW3ePIr2XeAthgiqB1CXym3RbunOLrjJNYk33M1a6KN\noztOqIohNfqqfuJvjJ4swoDQV0QUmIeUDs+B87XuINMqBg04tuOtYTzrytghYPgXocmdDACqYkjD\nb5P/9Il+djndbPlzJ3arHYPJ4GemSqCQ7mvIpF/AsQ90lRDmzmiCe0Bwj1Rj4sC+GdCB8RGEUHdy\nt0PBUuGYzEYsCd6HpqZgI4VKZc3Z415HaPIjzd0h6UdumpP0oAn1qTMuhB701T2p5Z3H8N41+Emm\nB4AW7Fshl8rTqobDNMTHKAeySSkV36hUAot0nkNeeRISvgLbKkj8Ghnd0svNz530OzLqEWTscGTs\nMGRUA6RtUy5KfffzaMf66E16r3M3IQR6k55HO9XPRcnuTESeYYi84zxp47UlwNwFUWCRJ99R2rFC\nIPLPAcPDeBLjGUHkB+7cQ31VMaShRuOqiofS4UXzkydMDfjJbmT8hyDjuOnRYQeZiIzzHFlJ51mI\ne8/TLxOTv5KQ11/1xD2o3BIms5HPN46jQu2yHvdVg44KD5Xhsw3vYzIbU8YlXE/k+O5TxF9LyEVp\ncx8hBCLoaTThC9FErEYT+k66hXSEJj+a/HMQBTchIlZAvi885xR+cScHf+YOqikpDX0/eoHd/+zH\nZrHjcrgQGoHBpOf16f1Uv+6cwLYRxS22Yx9S2j2ZJ30K+gBSeHYYQe2zW8J7luIVi/LltgnERscB\nkDf8phuly+Vi2uC5LJu1Gr1Bh8Pm5MleTRgw9SW0Wl+XbxVlPDuKfKApiMRfoKEe8f/2zjtMrqps\n4L/3Tt+SzaZBKImhKR1CQJpgAggCUiNdAcGAiKKgnyIq8gkKiiJ+ghIBRUBKkBJ6bwIBAoYagdAT\nSM8muzt97vv9ce5uZnbu7M7szu7sZs/veebJzC3nvHN3ct973jryckRqt6KwK4YubLTFBsx85Xcc\nNGM/Np88iS8etTt/+PeFTPnS9rUWbXhQ8j9DwLw0jq9iwPX2VY5mF6LxWWjygSFVz6a/aBozokAp\nANx88Z08cO1jZJIZ4msSZFIZHr7+SW745W01knJoIxJEmv9isv6lHggDQQjtDM03o4l7TSLc8sPR\n5AMDL5/t4GYZTLitl0L7dRQmB4Uh+mWckb9F0y+a8FXtGkMeQcbciwQnVDbfmt9C/B+YNqIOIEjz\ntUi4Xwv+DjmOHPsN1qwoNtXVj6zjzpXX1UCidQN145B6zNRTCu8GEkWXf8XL3elYOceg4ds4DTP6\nPJ/t4GYZkkjDdyG8KxD1aijFILQ1MuJ8c0BoCkT2hc4oJDHH1H+jYqWgqWcgfgNGCSU8f0UbumoG\nqn6d5YYXuVyOmy6+naM3nOGrFADiqxMMxYfLwYI4dUjsYKTueCS4Cdo206fOUgLarjBKZICwPgbL\noEIkjIz6K5pdAJm3TSOT0FZ5+wWaLoX0U2jiXpAQEjscCff4EFSEJmZRnL0KkIH0SxAZ3tE4l58+\nk8du+ndRBYB8Jm03wfreqkn6eYoT4QAJQO59cAams55VDBWwZmUrt//hXp6960WaxjRy+FkHsfsh\nO9darHUSCW4Gwc3894lAZG8ksnevxlZVyL4O2YWlZqe4zs3wYtWSFh698emCTOh8RIRwLMSZfzxl\ngCVbxwlsCDmfPhiaAWfg8kmsYiiT9tXtfGun/2HV4hYyKaPR//vCAo7+n0M54WdfrbF0lnLR3GJ0\n5cngflq637TmjBNwHSadTHP3nx/kkRueIhAMcvBp+7HfiXt3Rhh9NH8RoUjIVzGEoiF2O3gnjv3J\nEWy2gy3NXU2k4TR05QsUVmcNmyTOfqqf5IdVDGVyz1UP07J0dadSAFMu4KZf38Eh3z6AEaMaayid\npVx01ZmQ+wD/yKageTVdWLNSBANBLpfjh/tcwLvzPujsavjhmx/z4gPz+NmtZwMwfpNxZFLFSsEJ\nOOxz7J6cc80ZAyrzcEHCO6MjLoTWC0FTQA4iU5GmgW1MNewUQ6I9ya2/vYtHb3wax3H48inTOPys\ngwhHum9e8vx9L5NO+Dw9RUK8Pfe9ssJZVZV5j7/OU7c9RygcYr+v783mkzfp9XexVIbmFnnFynyU\ngoyBuulI7Agk+JmBFm1Aef7el3n/tY+KWt0+f9/LLJj3PpvtMIlxE8YyZf8dmPvgvIJVQzgaYvoP\nDqmF2MMGp+4QNHYg5D4BZ2RNynIPK8WQy+Y4e6+f89H8hZ0/9usvmMVLD7/KJQ/9rFsn2tiNxiAi\nRREYuWyOUesXp8F3RVW59BtX8tRtz5FsTyGOcN/Vj3DCz6ZzzI9sUlZPaOZVtO0ayC2EyOeRupOR\nQIU2V7fNq4rp4z9wRuI0nl0dYQc5rz75RlFNJAB1XV5/+r+d5qGf/PMs/nL2dTx03RNkMzk2/uwG\nnPXnGUzcckBbtg9LRIJQYZRdNRlW4arP3/syC9/5tOAJKJVIM3/O27z5XPcN5o8460DCscJVhRNw\nGL/Jekzatuc/4GtPz+9UCgDqKql4musvmMXSjwdvJ6fBgJt4EF1xAqQegOxr0H4duvwg3Oz7nceo\npnFb/4C7ZFfTgH3lDDT7QeFAwU3xfxYKQ3S//vwKg4pR45t923sGQgGa11vb6jYSi3DWn2cwu/V6\n7m69nqtfv4xtv7DlQIpqATQ1B3f5kbiLt8dddgCavL/f5xxWiuHN594i6fOklM1k+e/z73R77md3\n3ozvXXUadY0x6hpjhGNhNp88iV/dX14LxGfufKGoaiuA4zjMfWBe+V9imKGag9bzMc64jtVaBrQF\nlu+Pu/xINPMW2nIOtF8LutIcm34SXTEdzZn+4Oq2mJVC7HhM1FEHEQiMReq/MaDfq5bscejOvrkH\noXCQ3Q4pDvsNBAK2qnCFqCqanoemnkDd1b0fJzUHXTXDPBCRgNx7aMuPcOOzqiesD8PKlDRuwlgi\ndeGiuOxQJMSYjUb3eP6+x+/FXtN344PXP6KxuYHxm6xX9tzhWBgn4JDLFtYBEsdUsLSUIPeJT5Zz\nHtnX0JVHe7Xu8/+uCppEW/+AZl+B7Pus9S10uSk2zUScJoYDD1//JH84fSZOwDH6UU2U0ZgNRnHB\nHT+0CqAKaPYjdNXJ4K4AHNAM2nAWTsOp/sfnlkHmZZCREJ6CyNraU9r6W4r7Ryeh9XdobHq/5ZAM\nqxXD1GP3KOrxLCJEYmHfJyU/wpEQW+y0aUVKAWDf479AMFSsh11X2b3MuYclTmPpsNIONIN//+c0\nJG+H7NtABpNN2rVAXwpWHYu663610EULPuXy02eSTqTNw5F3yRwRrnzpEiZtO7G2Aq4DqCq66hTI\nLTK1u7QNSEH7/6Gp54qOd1svR5dNNSXkW0437/NMpL45DWAqEPu2vK0OVVEMInKAiLwlIgtE5Mc+\n+yMicou3/3kR+UzevnO97W+JyP7VkKcUjc0N/O7xC9hoi/GEoyFCkRCbbDeRy576ZY9RSX1l4lYb\nM+O3XyMcDRFriFLXGCNaF+Hns86hvqm+X+ceyogzEiJ7YoqMlSKDf/hpmT9vbUXjN1Yu3BDAdV1c\n1yjDR294mmy2+Do5AYc5d7800KKtm2TnQ24ZRQ8gmkDjNxRuSj0J8WsxpeXbzI3eXYKu+uZaU5+z\ngf88Es0rC1N9+mxKErPuuQLYD1gIvCgis1X1zbzDTgFWqepmInIMcAlwtIhsBRwDbA1sADwiIluo\n9vSI2Hs223ES186/nGULV+AEHMZsMKq/pirikDMO4AvTd2Pug/MIhYPscuBk6hpt57GekKbfoC1n\nQvplCs1FHcTAWR/cRV32C/4KoytqCpk1nFYNcQcFSz9ezuXfmsncB19BRNj1KzvRNGYEro9icHOu\nb5TSuoy6a8BdBoGNTG/xauGuMcUY/Raw7qpCGdpv9DGTKrjLjYIJbYU0noW2/JACc5LEoH5Ggcmp\n2lTDx7ALsEBV3wMQkZuBQ4F8xXAo8Avv/W3An8QYxw4FblbVFPC+iCzwxitec1UREWHcxqWbavQn\nzeOa2O9rvSvlMFwRZwQy6h+mu1vLWZ5pqEMBBMCph5GXQvs1picDWQhuCeE9IH49/vWQujCA5Qb6\nm1QixXd2/QktS1o6e5fPufslmsaOIBwr9rGp6rApK6+aRlf/FJL3dTbK0Ybv4NRXqbRHaFuf3s4A\nUYh+qYswa0oM4nSaiSS6PzqiHdouBbfFUwrfROr79yGmGqakDYGP8z4v9Lb5HqOqWWA1MLrMcwEQ\nkRkiMldE5i5btqwKYluGGhLcGBl9E9SfaFojSj2EdweisPI4oxQCm8Lo2Thj7kAazgCnCdPLoTui\nSF4/6aHOU7PmEG9NdCoFMPk2ibYEm03ehGi9eUIWgUhdhCO/f3DFPrOhiq65AJIPYMw3cfNq/aMp\nyFgFxKmHEedh2nZ2OIZjENwYiR1VeHD0y/i393SNgvFw6o5Axj6DjHsRGfciTsPp/V64cMhEJanq\nTGAmmH4MNRbHUiNEIkjjD6Hxh6jbgi6b5jn4PHL/hVUnoWOfMGUtRt+Btv4ekrfhv74XaPwfJLzL\nQH2Ffuej+Qt9w7IzyQy7HbwTx/zPYTx2078JR0Psf9LUsnMTVJUP3viYTCrDptt/piiQY7CjmoDE\nbIoLJCbQ9r8gsYOqMo9TdzQa/JzxKbjLIbIvUncE0sUnIHVHoYl/Qe5Dz6QUAELQeEFR9zYR8Rr6\nDAzVUAyLgI3zPm/kbfM7ZqGIBIEmYEWZ51osvmhits+yXc1/stTjEN0fCYxGRl6Em9gDVp/LWrOS\nAGFovg4nMnlgBe9nJm03kVhDtMhvEIqGmLTtRHb58o7sevBOFY354Zsf87NDLmHVkhbEEYKhIOfe\n8F12PmDHaorev7ilTDd4DuPqIeHtkXD35jmRGIyeBYl70NSj4IxF6o5FQp+rqiy9oRqmpBeBzUVk\nkoiEMc7k2V2OmQ2c6L2fDjymxu0+GzjGi1qaBGwOvFAFmSzDgdynFMd4Y8JXc4sLNjmxA5HmqyD8\neRPpEdkfGX37OqcUAPY84vM0jm4oeKIPhoOM23gMO31pu4rHy6Qz/GDqL1j8/hKS7SkSrUlaV7Zx\nwfTfsfSjIWTWdcaUeOoWCNfmdyASQeqOxGm+EqfpgkGhFKAKisHzGZwJPAjMB25V1TdE5H9FpKPa\n1jXAaM+5fDbwY+/cN4BbMY7qB4Bv92dEkmXdQsI7gPhVQQ1AqPgGKJFdcUZdjzPuCZzmPyKhzftf\nyBoQjoT405xfs9f0XYnEwkTrI+xz/Be47OlfdpbVroQXHzCF9LomS+eyOe6/9rEqSd3/iAQ8+3++\nSccBiSEN3++3eVVzuO23mLIWyw/Dbf87qqWbHw0GquJjUNX7gPu6bPt53vsk4Nu0QFUvAi6qhhyW\nYUZkHwhM8LKaO+zGUQjvCKHe9WxWdzWknvLG32vIZkQ3rzeSn/zze1UZq2XpGnK5romBkE1nWbFo\nZVXm6G9Uc5B6EtL/gegBphtabhmEd0QazkSC/VflWFu+C6l/02nGbH0PTT4Ao27s15DTvjBknM8W\nS1dEgjDqJrT9akjOBoIQm47Un9irqA03cY/nh+j4b5FFm36NEzu4mmIPObbba0vULVYMsYYoO32p\ndwp4IFFNm+ZMmTeAOBACAkjz//W6C2DZc2deK1QKACQh+1/zABKd2q/z95ZhVRLDsu4hTj1O41k4\nYx/FGfsgTsM3Ma6uytDcYk8ppIB275WC1eeafcOYjbbYgGnHfaEzzBUgEgszYcsN2eOwwd/pTuO3\nQ+Z1jFIAkymfRFvOQdW/dWnVSL+Ebw9njaPpwetOtSsGiwW82PZS+x40uRPDmLP/ejo7TtuGe656\nmFQizbTj9uTg0/bzrf816EjOxj/J0TUKI1x5ZJXmVkDybtRdgYR3hfDuvqtUTb+CUURdiYIzcK06\nK2UI/FUtlgGgo41iETnQ4VUuwg8RYdpxX2DacV+otSiVI6XqoLnd7CuNpuagLaeBukAKjV8PoR2h\neSaSN55mF3iZ+CXEqju04rkHCmtKslgAIlPxf04KevssQxWJHU1hJFLHjkYIblXRWKpZU5ZFE3QG\nPGjc1PFK3Fl4bOIBfM1IAHXHIs7A1WmrFKsYLBZAQltA3fGYG4h4rxjUHWf2WYYu0S9D7GAgAkRN\nLoM0Ic1XIVLhLTDzBv6FHBNo4vYu20oVaIgigY1L7BscWFOSxeLhjPgRGt0PTdwNgMS+gtQo8clS\nPUQEaboIrf8GpF8ApxkiU3tXVbXb8NIuvV6i+6PtMyk2USpE96187gHEKgaLJQ8JT7bKYB1Fgpt6\nfb/7QHArs+Lo2iRHYkhdYaqWhLZAG06DtqswJiXHvBp/hATW75sc/YxVDBZLFXHjd0Hb78FdDM54\naDwHJ/aVWotlqRIiDoy8wrTuVBcTcRSE8FSIFv+dnYYz0egBkHwECJj6XcEJAy12xVjF0A2pRIp0\nMkNjc0OtRbFUiGrGJL7FbzKOwshUpPHsfn1Sc+N3wpqf01m/yf0EVp+Hi4NTpcqdltoj4e1h7NOQ\nesg03wnvgoS2KX18cDNo2GwAJew7VjH40L66nd/PuIpn73oRgPUnjeOcv57ONnuWV57YUnu05WxT\nAqHjJp28G03/G8Y8gDgj1h6Xecd0ywpsDKEd+lbnvu0yfBu3t/0OrGIYNGjuE1MOI7iZ6Z/QC8Sp\nh9jhVZZs8GAVgw/nHfRr3p77Ltm0CTVb+NYnnPvli7hq3qVssOngtg1aMM3UU09QWHc/B24bGp+F\nNJxiyiS0fAdSz3kORTXKYdR13YYRmqLAblGNG1UF91P/k3Kf9PEbWaqBumvM3zz9sslf0CzacCZO\nw4yKxzG/rywa2h2S90LiX4BC7HCvJEsV24XWABuu2oX3X/+IBfPeJ5MujD/OpLPc8cf7SpxlGVRk\n3uxs21hIEjIvA5hokdSzZpu2m1j07Lvo6p/4DqmaxW29DF26E7pkK9xlB6KpOZ37RcT4FPwIlGjo\nbhlQtOVsSM8FUl5zpyS0X4EmH+7+vNwiNHEHmnwMN34funRPdPX56OoLYPnexqeUWwC5d6HtT+jK\nE1Etri01lLArhi4sfn+pb2eqXCbHx/+1T35DguDGnmOwK2HoqKIZv4XiTl5ZSD2NaqKo25au+V8v\ngckzFeUWoKtmwOh/rrUvN3y/0McAQBQazunzV7L0Dc2tgPQcispTaAJtvwaJ7ld8jira+huI32BW\nlSqYGlpdyR/TK5CXfhYie1bxGwwsdsXQhU22m0gmVZytGI6G2HqPz9ZAIkvFBLeF4CRMFc08JIjU\nHWfelyxzoUVd4dRdA4nbKfYfpNC2Kzs/OXWHwYhfmkZACAQ2hKZfW8fzYEBXlVhFAm6JZkPpJyHx\nT8wKI46/UvCbKw6Z//RGykGDVQxdWG/iWPb+6m5E6tZW6HQcIVof5Svf+lINJbOUi4ggo/4Gkb0w\nyiEIgc2R5uuQgGfuiUyja0ISAMFNEaexcFvukxI1dRSy7xRsceoONY2A1n8LZ+zjVikMFgIT8f17\nE4Swf/0njd/slb6olNigLpBXDtaU5MMP/nYGk7abyF1/up9Ea4IpB+zAKb86npFjh2bTluGIOM1I\n859NA3hNFzXckcZzTJSS24pZCYRBQkjTr4sHC2zk01sawIGgjVQbCoiE0MafwprzWbvyC4E0IA2n\n+5/kxv239zhZEKIH9u7cQYJo1359lZwsMgq4BfgM8AFwlKqu6nLMDsCfgRGY3PCLVPUWb9/fgb2B\n1d7hJ6nqvJ7mnTJlis6dO7fXclssAG7yQWj5MeZGoRDaEWm+wjcqyV3zK88vkf8EGUNG34qErIlx\nqKDpF9G2q02OSXh3pP4UJOD/dK/xWWjrhSVWDR1hzWGQsOkzDhBYDxn5ByS0db/I31dE5CVVndLj\ncX1UDL8BVqrqxSLyY6BZVX/U5ZgtAFXVd0RkA+AlYEtVbfEUwz2qelsl81rFYKkUzS2G5P2mvHZk\nKkgAXX4khTf6IAS3QEbfUZTPoOqi7ddC/BpwV0Noa6TxPNN32rJOYjq/nWjyXDSOMUU5pqWs1IHU\nI7Evo8HJiLvQnBTYuG+5MP1MuYqhr6akQ4Eveu+vA54AChSDqr6d9/4TEVkKjAVa+ji3xVIWbnw2\nrDkPU+0yB21XejbnrlUys6YXcHY+hArLMYs4SMOp0HBqj/OpKmTmoqk5iDMSYgcN6hLLFn9EwjDq\nekg9agorpp8BXEg/BZqD6P4QmowjDjiDv8xFJfTV+byeqnZk9SwG1uvuYBHZBQgD7+ZtvkhEXhWR\ny6SbrBARmSEic0Vk7rJlJaIILJYuqNviKYUURhHkgCTk3sG/MU8Ackt6P5/m0JZvoau+Ce1/Qlt/\niy6bWpDz0Ouxsx/jrj4Xd9k03BXHoakn+zxmrVFNo5m30dzyWovii0gQie4PuUXGpKQJb/WQguTD\naLwiY8eQoUfFICKPiMjrPq+C9kNqbFIl7VIiMh64HjhZ12Z/nAt8DtgZGEWX1UaX8Weq6hRVnTJ2\n7Niev5nFAqbhuu/C2MU3SkXb0OSjqK+zuQySs002tcYx/x2SJla+5bu9HxOjFHTFYSaXIrfQrEhW\nfRe3/Z+9HrPWuPFb0KWfR1cejS77Iu7Kb6Jua0VjaOYt3BXH4y7eEnfJZNw1l6Dq1y+h92juE8gu\nwPxm8klA4oaqzjVY6FExqOq+qrqNz+suYIl3w++48S/1G0NERgD3Auep6py8sT9VQwr4G7BLNb6U\nxbKW7uy9YXyVQ3I22vqrXs2m8Tvw7y+cgcxrvRoTQNuv8Eo9569yEtD226rfCAcCTT0Da37lZZ23\nA2lIP4e2fK/8MXKfoCuPgcyLmBasbRC/wWQ4V1dYSt4qtWuS5LpBX01Js4GOLuknAnd1PUBEwsAd\nwD+6OpnzlIoAhwGv91Eei6WQyF74t1eMwcg/gDT77EtCfJYJda2Ubh2PfXBKpl+g+IkVQCH3ce/H\nrRHa/leKFWga0i+gOd/nS58x/gFFSjEFqSfR7MJqiGkITISuuS0ARIZ8WGop+qoYLgb2E5F3gH29\nz4jIFBG52jvmKGAv4CQRmee9OkI5bhSR14DXgDHAhX2Ux2IpQJwmaLoY09YxgjErRaHueJzo1NI3\ncnFMSeVK54tNB/HpL0wEQttWPF4nTonijZqFoejYzi323y4hcMv0N2Rep6jEBZjw0dy7xdt7iYiD\nNF2KafvqJb5KHQQ2ROpPqdo8g4k+RSWp6gpgH5/tc4FTvfc3AL6GOFWd1pf5LZZycGIHoeEpkHzQ\nLP2jU02NfIDgNpB+gmL3WACcXviyogdB8lFIPY5xdodBHJMf0W1bSH+MmchBGmagq96g8Ck7bPpM\nOH6rnv5HNWlMZ6mHwGlG6k4oq/udahoCEyD3AUWrIE2ggY3LW1uFtvJKT3Stf5SGwKTyvkSZSGRX\nGHs/Gp8FuUXmc/SgIV9FtRR9ymOoFTaPwVItNPMmuuJYuiau0Xg2Tv2JpU4rY9xXIfU8OCMhekBx\nmY2ezs++j67+KWReojN2PrgdxK+ks55TZCrSdAni1PVazt6imkRXHAXZDzHXToAINP4Ap/7rpc/L\nvI6uPNlLCPPLLA5C/Qycxp59DZpbhC4/yHP0dxCByJ44zX+u7AtVGc0tNgX4Uk+CRCF2DNJwmgmB\nrSEDkuBWK6xisFQTzbyOtl5qTBPOOKThDCR2cO3kcdegy/YBXcPalUwQAp+B0bebZCpndM1WCoCJ\nhmq9hGI/QQQZ9xziFHc9VM2iS/cEXdn94NKEs96LZcmhmTdN5dvMf4wJL/ZVpPEH4K5AM29D9n1I\nPWxKnwQnQHBLJLoXEtquvC/aC9Rdgy7f3zNFdqyIohDZHaf5L/02bzkMVIKbxTLkkdA2yKi/11qM\nTjRxh+dUzX9oy4L7CZL5DxLZrVairSX1EL7RVxIyN+mIT2G6jl4IPaFlVjEFJLQVMvpmVBURMcpn\n9Y+M2RClwMyUewtSD6Ptf0UjU5GRvzc9nKuMxmeB206hmSwJqWfR7IK1ZsxBjK2uarEMNjJv4XvT\nVRdyH5Y8TdVFM6+h6Zf6P4TVacY/ysoFGeGzHa/mUBneg9COlcuTfQttuwpddQYkH8L4d3wc0wAk\nIP04JPup8VbmPxSXaMf0dMi81T9zVhm7YrBYBgmqWbT1EkgWRX0bRCC4hf+5mfnoqtM885MDCDRd\nikSn9ousUnc8mnyMQgUmJvy3lJkmvPPaYnO+BEHCyIifli2HaaZzIcRnYRSBXza734kJNHFb/5gM\ng5t7rT+7Kmc1TaSGAHbFYLFUGc0tQ9Nzyy7zoKlncVeeii7dA+I34v+kG4bgZ32fpk2xt6+Du9g4\nYrUNtBVtOau68fx5SHgKNH4fiIA0mPBNZwNk1LUli8iJ0wAjfg5EWXvriZreBcHtjIN29N1IqIJS\n5ukXIH4b5gm9TKXQQT/5V6XuaJ+mQCETKRXsQ8jyAGJXDBZLlVDNmJ7RyQe8UswpNHoQ0nQRUqJ7\nmNt+A7T+Bl/TQycO1B2NNJzjf9P1GtMXk0MT/0Iaz/KXN7cCkvei7koksjuEdq6oMqhTfxIaO9L0\n0ZYmCG3f4/kS3QdN3OVlK4vJwRj5B5xeVqnV5Gy6v3aliCF1R/Rqzp6QwPow6gbzW8i+g4kqm4Y0\n/XJQV17NxyoGi6VKaOvlntMztbZUQvJ+NDAe8Qm/dHPLofVC/DOa85BGnBE/K73fbSnR4zoD7gp/\nWVPPoi3f8s5LRtGxKAAAEmJJREFUofG/Q/jzMPLKivItxGmEyN5lHauqXhnrd+l0rLufwKqT0TEP\nIIFua3BWl/CuEO2/yDMJbYOMmY26bcY8VuMw1UqxpiSLpVok/knx02vSMw/5sOrb9KgUAELbdL8/\nvIv/OFKH+DSkV82gLWd5zmBPgWkcUnMgeXfP8vSWzH+88h1dVjeaQeO39GpIiR6CMU11JUjp21sQ\nmn7Vq4TDShGnYcgpBbCKwWKpCqpaOsxS24o35RZD9o0yRo4hjed0e4QEPwOxI4ydP+88glt6va27\nkHkVf9NTwisC2E/kFuIflZSG3Hu9GzO8C9RNxyiHAJ2lT5p+b5zdfsiImuaADAWsKcliqQIigga3\nhqxPHUi/Gkm5JZ4fokRYqTRCaAek8eyy2kTKiF9AZHevgX0SoocidUeU8G108zyYfQvVBOJb76mP\nBLc0DW6KiPUuRBVz3WXEz9DYV42vRepMpnlgHBoYj678GoWruCg0/rBf8hfWJaxisFiqhIw430QH\ndTYECnjhlz7+geCmpUM3QzvjjC5hfio1twhE9zdNZXoitB0Q8t+na9DVP0dG/rbk6Zp6zoSIZheA\njIT6U5D6U3u82UpoczSyO6SeZe3NOghOAxI7sme5ux37cxD6XOG28PYw+ga09XeQmQ+BDZCG7yDR\novJuli7YkhgWSxXR7HumpHRmvukLXX8qEvQv6Oa2/Qna/5rXbN4BaUDG3GMiW/pLRnXRZdOM49eX\nMDLuBd8aTJqe5ym//KfwGNSdgDPih2XMnUbbZ0L8Fm9lsw/ScDYSGNer72KpDFsSw2KpARLcBGn6\ndXkH130DZBQkbjHRQ+HdkYbvVlUpqNuGJmZB+kUIfgaJHQu5T0C7a7kuoK2Aj2Jo+yPFDvYExK9H\nG8/s0QQlEkYazoSGM4vHVjXKSmID1iNb3ZVo/HbIfYiEJ6OR/SF+s+nM5rZDZG9jzutHRT0YsYrB\nYhlgVBPo6vO9kgwCThMy4oKqmzg0txxdcTi4qzG1eoJo+41Qf0L3yV1OY+mS49kF/tvFgdxSCE6s\nWEay840zvu2PnqwuGp6MNP0eCYypaLyK5s68ga48wVSqJYUm7wa9AGMG7Ag3vhtNPQVj7x9WDmur\nGCyWPqKaM/kKiduBIFI3HSL7lUxm0pZzIPU0nSUT3KVoy/dh1PVIeHtzs3SXQGCib5XSsuVq+5OX\nx9ARgZQ1r/isbs4KQuP5pf0Fwc0h7dNkR12owBxkSln8CuI3mcJ7XSO60nPRVSfD6Nn9lhSmLT8o\nnFf9yoDnQNvR+M1Iw7f6RY7BiFUMFksfUFW05UxIP9vpK9DMCxA9EGkq7hutuaWQeoriOjoptO3P\nqIRMkx8Jg2bR+lOMeak3N8fUI/iGpWoL5r9+uIscYWieiRPZveSQ0vBddOWLFPsYvlZRJJMmbof4\nrWZ+38isrMl5yL5WuvZSH9Dc8gpaoqaMKY7hoxj6FLMlIqNE5GERecf713etJSK5vLaes/O2TxKR\n50VkgYjcIkMxE8QyvEk/D+nn8hzImCfPxD2oXyXN3Kfmpl+EQmbu2uJr2gYkof1aU4a7N3R7o86a\n/c4YUw01djgy9vFulQKYSB9pnmnqNiFAyJTDkJjpQ6CuMWFpD2Uq4n/Dt4JsAY65Xv2BBCnu2leK\noIkiG0b0NZj3x8Cjqro58Kj32Y+Equ7gvQ7J234JcJmqbgasAtbNBqqWIYOqoonZuCuOxV1+OG7b\nNd3e5DT9TAkThGtWEV0pGaYa8JRB134FCRO51BvqTsD0KS6BppHm63DWm4vTdAkSKK+VqUR2hdgx\nmKSyDOhiaP8LunQ/dOke6LKp6JKdcFeejJt+Ed/IR3dNzxNppm99srtBnJEQ2h6TFFewh+LbYgip\n+1q/yDFY6atiOBS4znt/HXBYuSeKWRtPA27rzfkWS3+ga85DV//MtNTMvgFtl6MrjkNL5RzISDob\nxBcQNE/SXQ93GqD+ZApv2A5rM3d9cHvoeFYCqTsBovtSsgeCBEoote5RN+4V/st/4k8Bq0BXeO8z\nkH4GVn4dXb4vmv2ocJDIF+nekh2D2FeQwAYVy1cuMvJ34KwPUo+5/jEIfd6TLWRegYnIqKuR4IR+\nk2Mw0lcfw3qq2rHWWwyUqoIVFZG5GIPnxap6JzAaaFHVDiPoQmDDPspjsfQazb4PibspfGpPmnIN\nyYchdmDRORI7GG27vHgwAaJf8p1HGr6PBiaalYC7ypR1aPgerDoR3KXFA4V7DDv3n0cCyMjf4a7Z\nAOLXUlzO24HQVpUPnJ3vKZVyDs5BbiG66hQY81Cnr0QazkRTj5iWm6To7CEhI8AZDXVfR+qOqly2\nCpDAeBj7iFFguU8gtA3i1aVSNw4kQZqHTEXUatKjYhCRRwC/IN7z8j+oqopIqZ/KRFVdJCKbAI+J\nyGvA6koEFZEZwAyACROGl/a2DBDpufguojWOpp9G/BRDYD1o/j8TVdRJEGm+smREkYggdUdCXWG2\nr9t4Pqw+B3OjVEzmdM+1knpCGs9A00+b/sckME/DAaTpN4iUyIDuDmekF+JZLgruMqNQPEUkgXEw\n5l40fqMp3hecgNSdhIT8GxH1FyIBiOxVvN2pwy+PY7jQo2JQ1X1L7RORJSIyXlU/FZHxQNfHnY4x\nFnn/viciTwA7Av8CRopI0Fs1bAQs6kaOmcBMMJnPPcltsVSMM8bE4xf9ukLG5FACiewN4+ZA+mXz\nJB3asWT/hW6nj+2HBq5D2/4CuY8gPBmpP63PZgyRGIy+FZIPmJj8wHpI7CikwpyDzvGCm6LBTSD7\nFuU3x3GK/AriNJdMdrPUlr6akmYDJwIXe/8W9ST0IpXiqpoSkTHAHsBvvBXG48B04OZS51ssA0Zk\nT5CoZ3fP1w4Bk5vQDSJhiOzadxlCWyPNf0Qk0vex8hAJQ+wQJHZIzweXM17zVeiqGWYVIsG8kNMS\nRQE12y9hp5b+oa/O54uB/UTkHWBf7zMiMkVErvaO2RKYKyKvAI9jfAxvevt+BJwtIgswPodr+iiP\nxdJrRELIqOshMAGIGaekjESar0AC/ev+0txi3JXfQJfsgC7ZAXfFCcUO20GEBNbDGXMXMuZ2pPkq\nZNwcZMydEP4Cnf4CcySmoulPfGsvVRtVF039G3f1L3FbL0ezH/b7nOsitoiexdIFVYXcu6YLW/Cz\nvTILVTZfBl22r+d47jDNOEYpjX2sVzdU1bRJpNM1EN61X6N7OnDb/w5tl4EKxnHbBJHdje8gvH2/\nz6+a85INn/NWfUEgACMuwqmrzkppqGOL6FksvUREILjZwE2YeszcwAvs9a6pPpp8ACrsTayZ19CV\n38AEASpoDq07CWdE35zY3c6ZfAxaL6MghFXbQRMDohQASD2cpxSgswTImp+i0Wl9Ki8y3LDdKiyW\nWpP7eG2P6ALiaO79ioZSzRnbv672bsxxIAXxf6CpZ6oiru+87X+lOJM5Dal/o73Mw6hYhsQ9/nkZ\nEoT0CwMiw7qCVQwWS60JfrZEmYw6JLhlZWNlXjYrjSISve6rXBZF+RceEux1gl7FdOewt9V2KsIq\nBoul1oT38Bze+TkFQQiM9TKXK0CTlMx07kWWc9mEd8M/czvgfbf+R2LT8S8B4pgkQkvZWMVgsdQY\nEQcZ9U9Tf0iaTL/n2BHI6FupuK5kaKeSfZUldlBV5PVDGs4AaaDQbRmDxnMr/w69lSGyG9R9DYgA\nUS+qrB5p/vOAybCuYKOSLJZ1DDc+G9b8lE7nq9RBcFtk1LW9y3QuE80tRttmGgdwYDxS/01zsx5g\nNPuxKXMhDRCZNiBhskMFG5VksQxTnLpD0PDWaPw20BYkMs3cIKVEkb4qIYH1kaaf9+scZckR3BiC\nx9RajCGNVQwWyzqIBDdFRvyorGM19ynafh1kXoXg55D6k4ZdNVFLIVYxWCzDGM0uQFcc5YXLZiAz\nD03eDs3XDVz+gWXQYZ3PFsswRtdc5PU97ijJnTXVZNf8ooZSWWqNVQwWy3AmPRffxgrZN0s3J7Ks\n81jFYLEMZ6RUxE6YWlqaVTP+LUEtA4JVDBbLcKbueExby3wiJo+iBp3LNPUM7rID0CXboEsn47Ze\nhlbUFMhSDaxisFiGMdLwLS+7OmIS64hAZDdkxLkDLoumX0FXfcu0UkWN76P9b+iaCwdcluGOjUqy\nWIYxIiFk5O/R3KeQfRcCE2oWqqptVwBd6zwlIfEvtPEHtjrqAGIVg8ViQQLjITC+tkLk3vXfLkHI\nfQrO5gMrzzDGmpIsFsvgIPg5fAsAag4GoNGQZS19UgwiMkpEHhaRd7x/m32OmSoi8/JeSRE5zNv3\ndxF5P2/fDn2Rx2KxDF2k4UxMAbx8YlD3NcSpr4VIw5a+rhh+DDyqqpsDj3qfC1DVx1V1B1XdAZgG\nxIGH8g75Ycd+VZ3XR3ksFssQRUJbIqP+AaEdgBA4Y6Hxe0jjD2ot2rCjrz6GQ4Eveu+vA54AuivQ\nMh24X7U/C8NbLJahioR3QEbfWmsxhj19XTGsp6qfeu8XA+v1cPwxwE1dtl0kIq+KyGUi3bVgslgs\nFstA0OOKQUQeAdb32XVe/gdVVREpmaooIuOBbYEH8zafi1EoYWAmZrXxvyXOnwHMAJgwwVZ+tFgs\nlv6iR8WgqiV7C4rIEhEZr6qfejf+Eo1fATgKuEPzCrDkrTZSIvI3oKQxUVVnYpQHU6ZMsbnyFovF\n0k/01ZQ0GzjRe38icFc3xx5LFzOSp0wQk3t/GPB6H+WxWCwWSx/pq2K4GNhPRN4B9vU+IyJTROTq\njoNE5DPAxsCTXc6/UUReA14DxgA2991isVhqTJ+iklR1BbCPz/a5wKl5nz8ANvQ5blpf5rdYLBZL\n9bGZzxaLxWIpQIZizXMRWQZ8WKPpxwDLazR3X7Gy14ahKvtQlRus7KWYqKpjezpoSCqGWiIic1V1\nSq3l6A1W9towVGUfqnKDlb2vWFOSxWKxWAqwisFisVgsBVjFUDkzay1AH7Cy14ahKvtQlRus7H3C\n+hgsFovFUoBdMVgsFoulAKsYekBEvioib4iIKyIlIwVE5AAReUtEFohIUV+KWlBOIyXvuFxes6TZ\nAy1nF1m6vY4iEhGRW7z9z3tZ9TWnDLlPEpFledf5VL9xaoGIXCsiS0XEtySNGP7ofbdXRWTyQMvo\nRxlyf1FEVudd858PtIylEJGNReRxEXnTu7+c5XNM7a67qtpXNy9gS+CzmF4TU0ocEwDeBTbBVIp9\nBdhqEMj+G+DH3vsfA5eUOK6t1rKWex2BM4C/eO+PAW4ZInKfBPyp1rKWkH8vYDLweon9BwL3Y/pu\n7go8X2uZy5T7i8A9tZazhGzjgcne+0bgbZ/fTM2uu10x9ICqzlfVt3o4bBdggaq+p6pp4GZME6Na\ncyimgRLev4fVUJZyKOc65n+n24B9vCKMtWSw/v3LQlWfAlZ2c8ihwD/UMAcY2VEAs5aUIfegRVU/\nVdWXvfetwHyKywbV7LpbxVAdNgQ+zvu8EJ/aUDWg3EZKURGZKyJzOvpx14hyrmPnMaqaBVYDowdE\nutKU+/c/0jMJ3CYiGw+MaFVhsP6+y2E3EXlFRO4Xka1rLYwfnjl0R+D5Lrtqdt372tpznaC7ZkSq\n2l0p8ZpTpUZKE1V1kYhsAjwmIq+p6rvVlnWYczdwk6qmROQ0zKrHFpHsX17G/LbbRORA4E5g8xrL\nVICINAD/Ar6nqmtqLU8HVjHQfTOiMlmEKSvewUbetn6nO9nLbaSkqou8f98TkScwTy+1UAzlXMeO\nYxaKSBBoAlYMjHgl6VFuNZWIO7ga4/8ZKtTs990X8m+0qnqfiFwpImNUdVDUUBKREEYp3Kiqt/sc\nUrPrbk1J1eFFYHMRmSQiYYxTtKbRPR49NlISkeaOXtsiMgbYA3hzwCQspJzrmP+dpgOPqeepqyE9\nyt3FNnwIxqY8VJgNfN2LktkVWJ1nohy0iMj6Hf4nEdkFc7+r9UME0Nmc7Bpgvqr+vsRhtbvutfbO\nD/YXcDjGtpcClgAPets3AO7LO+5ATGTBuxgT1GCQfTTwKPAO8Agwyts+Bbjae787plHSK96/p9RY\n5qLriOkDfoj3PgrMAhYALwCb1Po6lyn3r4E3vOv8OPC5WsucJ/tNwKdAxvutnwKcDpzu7RfgCu+7\nvUaJ6LxBKPeZedd8DrB7rWXOk31PQIFXgXne68DBct1t5rPFYrFYCrCmJIvFYrEUYBWDxWKxWAqw\nisFisVgsBVjFYLFYLJYCrGKwWCwWSwFWMVgsFoulAKsYLBaLxVKAVQwWi8ViKeD/AUixxdkVDDOE\nAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X, y = make_moons(n_samples = 200, noise=0.1, random_state=0)\n", "\n", "\n", "figure = plt.figure()\n", "plt.scatter(X[:,0], X[:,1], c = y)\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Example 2. (Dog Dataset)__" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "image/png": 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j4edsuyL6Uoh8SH3RsTjoy5BII7/V1J+muFeGUFgUiQyyffzqighKs/5eVJY0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\nquP4/F6UR+OWt67iwFP3cWSrOdgN6Dk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NMOVIj+t3NGmZ7nJFIJRSuob0IPOFO04e3JMb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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "from sklearn.datasets import make_classification\n", "import scipy.io as sio\n", "\n", "mat_contents = sio.loadmat('KernelClassification.mat')\n", "\n", "X = mat_contents['data']#[:,0:1]\n", "#y = mat_contents['data'][:,2]\n", "\n", "x1 = X[:,0:2]\n", "y1 = X[:,2]\n", "\n", "plt.scatter(x1[:,0], x1[:,1], c= y1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__2a. Are those datasets linearly separable ?__ How would you proceed to learn the countour of the dog, or to separate the two cresecent shapes?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For more complex datasets such as the datasets given above, one could indeed use a lot of additional features, $x_1$, $x_2$, $x_1x_2$, $x_1^2$, $x_2^2$, ... Until the data can be put in a suffciently high dimensional space so that it can be separated. But this approach requires a possible infinite number of features when the boundaries are complex. Moreover those features are often not known..\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of having to explicitely increase the dimension of the data and then learn a linear classifier. We would prefer to have a model that only depends on our original number of prototypes. That is if we originally have __N points__ that are split into __two classes__ such as above, but we need every monomial as a feature to separate the two clusters ($K = \\infty$), we would like a model whose __complexity remains $O(N)$__ and not $O(K)$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is precisely what Kernels are designed for. Kernels keep track of the similarity between pairs of points from the training set instead of storing long feature vectors. An example of kernel is the Gaussian Kernel, also sometimes called RBF. \n", "\n", "\\begin{align}\n", "\\kappa(\\boldsymbol x, \\boldsymbol x') = \\exp(-\\|\\boldsymbol x - \\boldsymbol x'\\|^2/(2\\sigma^2))\n", "\\end{align}\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__2b.__ Learn a RSS model for the boundary in Examples 1 and 2 above using the kernel trick with the RBF kernel. Make the value of $\\sigma$ vary and study the effect of $\\sigma$ on the boundary you learn. Then study generalization by either increasing the size of the dataset and using train_test_split (crescent moons) or generating a few new points from the $[0,14]\\times [1,20]$ space and studying whether they are correctly classified as dog vs non dog." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.kernel_ridge import KernelRidge\n", "import numpy as np\n", "\n", "# put the code here\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3. Support Vector Machines.\n", "\n", "So far we have seen how to learn a classifier by minimizing the sum of squared residuals. When learning the separating plane from the training data, many choices are in fact possible for the separating plane. A good idea is to try to minimize generalization error. Maximal Margin classifiers relies on the notion of 'margin'. The margin can be defined as the 'smallest distance between the decision boundary and any of the samples' (CM Bishop) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Drawing\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__3a.__ Using the Support vector classifier from Scikit-learn, learn the boundary for the dog shaped dataset above." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.svm import SVC\n", "\n", "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__3b.__ Now that we have a serious classifier, combining the adaptive power of kernels with the robustness of maximum margin, we can start looking at more interesting datasets. Using the lines below load the 'Labeled Faces in the Wild (LFW) people dataset' from Scikit-learn. \n", "\n", "- Display some of the faces together witht their labels. \n", "- Split the data into training and test" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "\n", "from sklearn.datasets import fetch_lfw_people\n", "from sklearn.metrics import classification_report\n", "from sklearn.metrics import confusion_matrix\n", "from sklearn.decomposition import PCA\n", "from sklearn.svm import SVC\n", "\n", "lfw_people = fetch_lfw_people(min_faces_per_person=70, resize=0.4)\n", "\n", "X = lfw_people.data\n", "y = lfw_people.target\n", "\n", "# split the dataset into a training and a test parts\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Learning a classifier on the raw images is a little heavy. To avoid dealing with all pixels, before applying our SVC classifier to the dataset we will compress the images by using the SVD as we did at the very beginning of the class to denoise (See LAB 1). This step is done for you below. Here we consider the whole set of images as the columns of a very large matrix and we retain the dimension 150 subspace that best approximates all the faces. That is we approximate each image as \n", "\\begin{align}\n", "I = a_1 I_1 + a_2 I_2 + \\ldots + a_{150} I_{150}\n", "\\end{align}\n", "From some $150$ basis images learned for you below. The compressed images are then returned in X_train_compressed and X_test_compressed. The targets do not change. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n_components = 150\n", "\n", "pca = PCA(n_components=n_components, svd_solver='randomized',\n", " whiten=True).fit(X_train)\n", "print(\"done in %0.3fs\" % (time() - t0))\n", "\n", "eigenfaces = pca.components_.reshape((n_components, h, w))\n", "\n", "print(\"Projecting the input data on the eigenfaces orthonormal basis\")\n", "t0 = time()\n", "X_train_compressed = pca.transform(X_train)\n", "X_test_compressed = pca.transform(X_test)\n", "print(\"done in %0.3fs\" % (time() - t0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Using the compressed images together with the SVC classifier from Scikit-learn, learn a Maximal Margin classifier for the face dataset" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }