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@dhammack
Created December 5, 2013 06:29
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Nearest neighbor classifier, and a kernel density classifier.
{
"metadata": {
"name": "Nearest Neighbors"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": "# 2.5.2 - Nearest Neighbors #\n\nNearest neighbor methods are a very simple and yet highly effective algorithm for classification and regression. This notebook has some toy examples.\n\nLet's first build a KNN classifier."
},
{
"cell_type": "code",
"collapsed": false,
"input": "%pylab inline\nfrom scipy.stats import mode\n\nclass KNNClassifier(object):\n \n def __init__(self):\n pass\n \n def fit(self, X,y):\n #just save the data for later\n self.X = X\n self.y = y\n self.class_lookup = {tuple(X[i,:]):y[i] for i in range(y.shape[0])}\n \n def predict_proba(self, X, k=3):\n #predicts the mean instead of the mode of the k nearest neighbors\n yhat = zeros(X.shape[0])\n for i,xi in enumerate(X):\n #sorry for not vectorizing.\n slist = sorted(self.X, key=lambda x: norm(x-xi))[0:k]\n preds = [self.class_lookup[tuple(datapoint)] for datapoint in slist]\n yhat[i] = mean(preds,axis=0)\n return yhat\n \n def predict(self, X, k=3):\n #each of the k nearest neighbors vote.\n #since this is toy data, I don't mind an O(K * N * log(N)) implementation\n yhat = zeros(X.shape[0])\n for i,xi in enumerate(X):\n #sorry for not vectorizing.\n slist = sorted(self.X, key=lambda x: norm(x-xi))[0:k]\n preds = [self.class_lookup[tuple(datapoint)] for datapoint in slist]\n yhat[i] = mode(preds, axis=None)[0]\n return yhat\n \n#some nice plotting code\ndef plot_contour_scatter(model, title_text, k=3,proba=False):\n #sample from a lattice (for the nice visualization)\n x1, x2 = meshgrid(arange(-5,5,0.1), arange(-5,5,0.1))\n Xnew = vstack((x1.ravel(), x2.ravel())).T\n if not proba:\n Z = model.predict(Xnew, k=k).reshape((-1,1))\n else:\n Z = model.predict_proba(Xnew, k=k).reshape((-1,1))\n \n #plot - contour plot and scatter superimposed\n contourf(arange(-5,5,0.1), arange(-5,5,0.1), Z[:,0].reshape(x1.shape),cmap ='cool',levels=arange(-0.1,1.1,0.05))\n colorsToUse= ['r' if y[i] == 1 else 'b' for i in range(y.shape[0])]\n scatter(X[:,0],X[:,1], c=colorsToUse)\n title(title_text)\n show()",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Populating the interactive namespace from numpy and matplotlib\n"
}
],
"prompt_number": 215
},
{
"cell_type": "markdown",
"metadata": {},
"source": "We can use sklearn to generate some sample data, and matplotlib to plot it."
},
{
"cell_type": "code",
"collapsed": false,
"input": "from sklearn.datasets import make_classification\n#generate the data\nX,y = make_classification(n_features=2, n_informative=2,\n n_redundant=0, n_repeated=0, n_classes=2,\n n_samples=25)\n#train our model\nmodel = KNNClassifier()\nmodel.fit(X,y)\n\n#plot\nplot_contour_scatter(model, 'K=1 nearest neighbor classifier', k=1, proba=False)\nplot_contour_scatter(model, 'K=3 nearest neighbor classifier', k=3, proba=False)\nplot_contour_scatter(model, 'K=11 nearest neighbor classifier', k=11, proba=False)",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": "<matplotlib.figure.Figure at 0x125381d0>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": "<matplotlib.figure.Figure at 0x1251d668>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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HWD4GAAhpPmpeegWB6+S/vN2+dMdcd+RZ73mzstRWjHTYnLfTYcVS2wkZKyJv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\npDAMbiIihWFwExEpDIObiEhh/j8Viw+nTWmr+QAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x1327f0b8>"
}
],
"prompt_number": 216
},
{
"cell_type": "markdown",
"metadata": {},
"source": "That's neat. We can also have the model give us 'probabilities' - take the mean instead of the mode."
},
{
"cell_type": "code",
"collapsed": false,
"input": "#plot\nplot_contour_scatter(model, 'K=1 nearest neighbor classifier', k=1, proba=True)\nplot_contour_scatter(model, 'K=3 nearest neighbor classifier', k=3, proba=True)\nplot_contour_scatter(model, 'K=11 nearest neighbor classifier', k=11, proba=True)",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": "<matplotlib.figure.Figure at 0x11f2c3c8>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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2f73BtrLNWHNlArJFMQDABCAaWuyJP49mqgjPBkey4J6TRHVoSJVt0NtuzvGW\nC5NqqFEB2y43EgALbBM3VVyJgurBnxBSNJ2xch52fRcdDXrbNMGcFNctBdsYfQMG4ooqGtMRgH8A\nGAEd7gsaiTCV++42JWVi4ibFiimsTNiN3XfSPlXQk4JVOvwj5geYdVPwXsBd6Bn6DJZFrPdsUKQI\nHCohxfGljYIjVVHIaLbS02GQwjBxk6I4M2PEvvCUQW97r1Enf3xE7sDETbITBgMQHAxJJe9InM5Y\nWW03dZpfYUzlBsPc3YaUimPcJBvr2TO41rc3ihKjUNQ8HKZ1a2Vt36izJV777exNZdADF2JtFygv\nxMoWHpHbMHGTbEomTID12BDAUgqU/4DSp+fDvH+frH3YZ4XkpDi3x6S3zTAhagwmbpKFsFph/e8u\nwPIMbLOSOwJiBCw/7HZJf/aq2dnKG6jcfIHVNykFEzfJQlKpIDVrDsC+rG8FoP4RUvMWngyrRnrD\nzTNSCmNsy8F6uvq+bLmIfxrX4V/Gv+Oq9YrnAiGvxouTJBvdW6tgmDwaUKUDyIGmdxtoBt6N8k0f\nA+Xl0KTdDVWMZ8vamELbRsE1TSM06CsvgHpijZN8cy5GF/ZET1EGswQsu6bHv2L+g3i19/3yI8/i\nWiUkK8vJ47Ds/R5SdAxUt/WEYdBAWC83B0QYJM33CNm6A+oOHZ3uxz67pDFLtNaVtKse46lb4h+/\nPBpdyjbhOVgAAE9Dg/PBE7E4Yo37gyFZcK0SUgR1m3ZQt2kHACh97s+wFvQFKt4BAAhpOUqfmouQ\nT713e7uqFzzdnbwLLWfQ83rSBoCeMGONJc+9QZAicIybXMaadw6o6F35hOgF67kCzwXUQJ4a7+4V\neA+WQYdrAC4DeB069Aq8130BkGIwcZPLaO7sD+j+D8BFAGVA0DJoBvb3dFgNYtA7P1+8saaHPosW\nwaMRAzVaQINk3URMCZntvgBIMThUQi4TMOkhWH4+ivJ3EgAIaAaORPBfF8rStt7g3ZskNIVW0mJJ\nxPtY2Gw1JEhQS2pPh0ReihcnyeWE2QxYLJACA51uy5kFphpycbIqvcG2ZKw3rN1NysSLk6RYkkYD\naJz/UWvKTBI7X6zQyX8xcZPPq1qh15S8j1/cg8PndyAkIBL9b5mEQA2XDSTvxsRNPq2+4ZHvczfi\nwz1TMMlqws+qQCz+5XXMu/dHJm/yapxVQj6tvuGRj/bNxGcWI14RFnxuMeIWQx6+P73BPcERNRET\nNymGK8YbP63QAAANMklEQVSpS8zFaH/9cwlAB2GGoZxXxcm7MXGT12vMhsCN1T3+bvxJFYjzAHYC\nWC+p0Sn+Lvk6aASTMOG8pQAWYan/YPJrTNzk1XTGmzcEvnhiL45lrULBwa1NnmpqN/mO9chrfg86\nqHWYGNwck+/YiKSI7k7H3VibjOvRvaAZBp9vgzvOt8DhigNuj4GUgxcnSVGOZL6JAx8uhrViEIRY\nBLW2DH0fW4nWvUY3qT2dNgzTBnp27ZRT5uN49upUfIsydAHwd2sZpl4ajO/iCqCSWFvRzfhTQYph\nLjPgpw3PwFL+LYT4AEAOLBWB2PXmw7h04gdPh9dkORUH0E/Sosv1x78HUGItwiWrwrewJ5dh4iav\nZ99mzGS4DEkVCiDp+it6ACmwWu5EwX+31vpe+0dNfjr3BVZ/Ow4f7HkEBdeOuiD6+rVUt8ZPMMN+\nSfQnABWQ0EwV6ZF4yPsxcZNXM+oqV+q70L0FtCF6AG8CsALYDuBHqNSl0OrCa3x/YUzl1mQ37lG5\n69R6rPtmDEbnfYheJ/6GhZm343zxCVeeTo26B/TEUN0UdJV0GCqF4W4EY1mz96CVtG6PhZSBa5WQ\nYuiMQOjeIzj10FCUXzkJIAKSuhN0UVcwZNEuaIND63z/jTfjvPBpB6wsOQb7HJI5UOFY8pN4IHUp\nAPevVXKgfB/OWvKQou2GJE1b93RKLsW1SsjvGXWAMa0jEvccR2DWLpi/2QG9thnaDHiw3qRdE7O1\nHFXf1QxWmC0m+QJupG4Bt6MbbvdY/6QcTNykOIUxgG54P8T07YfIC4C2idfwerd7GFMOL8IKixHn\nAbyq1uGJpN9XO8bIO9/JCzFxkyLZx76NOtuFx9oWkKrLfZ3mQ6MKxMxTaxGg0ePRbovQNrqX4/Wq\nFzY9tQ8lUU2cGuOeM2cONm/ejICAALRt2xZr1qxBeHj1i0Qc4yZXa+ga3fZjknIb34feULmkLFFD\nuWqM26lZJYMHD8bhw4dx4MABdOjQAYsXL3amOaImqTrzpK59Iu0zTA53cu+WZERycypxp6enQ6Wy\nNdG7d2+cOXNGlqCImqKuqX92Bn1l8q7tmBvFFFaulULkDWQb4169ejXGjx8vV3NELlUYY6vU69pR\nxz480pTxcyJXqjdxp6en49dff73p+UWLFmHYsGEAgIULFyIgIAATJkyosY2MjAzH52lpaUhLS2ta\ntER1aOx+lAa97T1G3c2J2Z6weUGS3CU7OxvZ2dkNOtbpG3DWrl2Ld955B1lZWQgKCrq5A16cJDew\nJ9qGDmdUvdhYNWmzyiY5eeUNOJmZmXj55Zexc+fOGpM2kZxEWRnKXlkKy/5DUHfqgKCn50HS66Ez\n2irnuhLtjQm9rqq8vraIPM2pirt9+/YoLy9HZKRtMZy+ffti5cqV1TtgxU0yEEKgZPgwWPZpgbIH\ngMBPoU4pQMi2LOhN6lqHSPSG6mt5V32+NvaqW2es/hyTOTWWqypurlVCimA5eRzF/QcCpbkAtAAs\ngD4Z0f/ciJbxtznmZ99YLTd0vLsmVdupOn5O1FBeOVRC5DYWCyBpAKivP6GChAA0P2NBUpktaddW\ncTdV1bne9qVl7TNRWH2TJzFxkyKExLeDuXVrlJ14BKJiPKDdhOCIAKRouyHsQuVQhisTKm+BJ2/B\n9bjJ68UUArfkqzHo2c1o9ZsghCW9iIR+Zfjtgm1QawLcHo+98ubdl+QprLjJ4+zjx7WpHAIJR/+H\n3nBXWERei4mbPMq+UUHVGRxVeeNY8o2VtjfGSL6NiZvc5saqWsk3unC8mzyJiZtcrupUuhvnRitd\n1fFuXzgfUgYmbpJFfetgK7WyJvJGTNzklIbcmNLUG2CUgOPd5AlM3NQovjROLReOd5O7MXFTg9RW\nWSu1mr5a+it2nngX5eYS9Gg1Gm2inN9dnePd5C5M3OSg1HFq+/oktU0pvNGV0gK8uKUrhpcXIU6Y\n8dovy/HwgH+ja4t7XBsokUyYuAk6Y+27wNh5Y2VtX8WvsQtJbf/lf/G78qt4Q5gBAD0tpZj3n9no\n2uKwiyIlkhcTtx+6McnVtOypt2tq0gYAU8VVJF5P2gDQGkCZuUTeAIlciInbj9Q03OGPmwZ0bzUa\nr5xci96WUsQCmKnWoXvr3zndrn2GiT9+Tcm9uB63D6krYeiMzq1N7W2cqbgBYNep9fj8wDMot5Th\n9sQJGHPbMqhV8tUxdW1CTP6DGylQneq7eOhrVaCzidvVuHclAdxIgaq4cfaENycwIpIfE7fCcJxa\nGQx6NGgTY6KmYOL2Yqysla0wxvbB7c5IbkzcXoqVte/ITar8nN8/kgMTtxdgZd10Db1bksiXMHF7\nmL2yriop1yOhKIb9F5uSvk72MW9W3CQHJm4Xq6si5FzfxvH2KYB1sY91c7yb5MDE7UKJp2v/D2pP\nQuQ/uPwryYWJWyY3bsnFmy+oNqy+yVlM3E6yr1Nd9T8fq2mqD6tvcgYTdyOxsiY5sfqmpmDibiBW\n1uQqrL6psZi4G8BeVbMiIldi9U0NxcRdh6r7LLKyJndg9U0NwcRdC1bZ5EmsvqkuTifuV155BXPm\nzMHFixcRGRkpR0xux/Fr71f1Lx9/SWKsvqk2TiXu/Px8bNu2DYmJiXLF43asrL2bku+WlAurb7qR\nU4l79uzZWLp0KUaMGCFXPC5lr6yr8ueEQMrB6puqanLi3rRpExISEtC1a1c543EZe1WtpIWJiG7E\n6puAehJ3eno6fv3115ueX7hwIRYvXoytW7c6nqtrX8mMjAzH52lpaUhLS2t8pE3EmSHka1h9+6bs\n7GxkZ2c36NgmbRZ86NAh3HXXXdDpdACAM2fOoGXLlti7dy9iY2Ord+DBzYJZZSsfx7hrpzfYFjJj\n4vZeXrVZcOfOnXH+/HnH41tuuQU//vijR2eVcPyaiPyFLPO4JUmSo5kms1fVN64jQuTLDHrgdCLH\nu/2RLIn75MmTcjTTaPYqm5sRkL/ieLd/Uuydk/aEzaEQIs428TeKSNw1jV+zyvZ9vDDZOKy+/YfX\nJ277VXOOX/sXf7zFXS6svn2fVyfulBz+4PkjvaGy2ub3vmlYffs2r07cnH9N5BxW377JqxM3ETmP\n1bfvYeIm8hOsvn0HEzeRH2H17RuYuIn8EKtvZWPiJvJTrL6Vi4mbyM+x+lYeJm4iYvWtMEzcRORQ\nGGP7134TFHknlacDILqRzmir+Jg4iGrGipu8hv02dy4g5llGXfXKm7wPEzd5BSZt78Hxbu/XpD0n\nG9WBE3tOEhH5q7pyJ8e4iYgUhombiEhhmLiJiBSGiZuISGGYuImIFIaJuxbZ2dmeDsEj/PG8/fGc\nAf88b185ZybuWvjKN7ix/PG8/fGcAf88b185ZyZuIiKFYeImIlIYl985mZaWhp07d7qyCyIinzNw\n4MBah3ZcnriJiEheHCohIlIYJm4iIoVh4m6AV155BSqVCpcvX/Z0KC43Z84cJCcno1u3bhg1ahSK\nioo8HZJLZWZmomPHjmjfvj2WLFni6XBcLj8/H4MGDUKnTp3QuXNnrFixwtMhuY3FYkFqaiqGDRvm\n6VCcxsRdj/z8fGzbtg2JiYm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"text": "<matplotlib.figure.Figure at 0x1327d7b8>"
},
{
"metadata": {},
"output_type": "display_data",
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F97p165CRkYHS0lLU1NT4vN+cOXPc/y8vL0d5ebmU1QaNwpvIQWthQKHdkV5Du6amxm+O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\neOMNVFdXIyYmpvMKJOycvH6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"text": "<matplotlib.figure.Figure at 0x13257390>"
}
],
"prompt_number": 217
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Very interesting dynamics with the K=11 probabilistic classifier. \n\nAnother trick we can do is to get rid of the k parameter. We'll just have a kernel density estimator for each class and take the class with the highest estimated probability. In other words, we'll weight the predictions based on an exponential decay in distance.\n\n"
},
{
"cell_type": "code",
"collapsed": false,
"input": "from scipy.stats import kde\n\nclass KernelDensityClassifier(object):\n \n def __init__(self):\n pass\n \n def fit(self, X, y,k=0.5):\n #build kernel density estimators\n self.zero_kde = kde.gaussian_kde(X[where(y==0)].T, bw_method=k)\n self.one_kde = kde.gaussian_kde(X[where(y==1)].T, bw_method=k)\n \n def predict_proba(self, X, k=None):\n #prediction based on kernel density\n yhat = zeros(X.shape[0])\n p_0 = self.zero_kde.evaluate(X.T).T\n p_1 = self.one_kde.evaluate(X.T).T\n #predict \n return greater_equal(p_0,p_1)*(p_0) + less_equal(p_0,p_1)*(1-p_1)\n \n def predict(self, X, k=3):\n return around(self.predict_proba(X), decimals=0)\n ",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 221
},
{
"cell_type": "code",
"collapsed": false,
"input": "for test in range(3):\n X,y = make_classification(n_features=2, n_informative=2,\n n_redundant=0, n_repeated=0, n_classes=2,\n n_samples=50)\n \n #train our model\n model = KernelDensityClassifier()\n model.fit(X,y)\n \n #plot\n plot_contour_scatter(model, 'Kernel Density Classifier', proba=True)",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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bNTsorD5F15BeNA+Ms7nGho7bsyfv4k/Fb3P2LACbgamBSXySeNBp27BXzRPM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\nzg9uX5aZaO6drxplXdB7klc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"text": "<matplotlib.figure.Figure at 0x1223b0b8>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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jHEx63B5EVVWmZA6kTcn/WKCWsNFwiLvTd/JZ60MutbJfnLYNX8b/QYbxOMGa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\n0QAaHZZrVgE0oAkAo6HCdsY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"text": "<matplotlib.figure.Figure at 0x11f405f8>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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GY//AOyNgjGYDenMJ/81+jx/PrcJPG8QDkfPp6nuF3cc+3s4y9FFRxZ51TQyH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\n",
"text": "<matplotlib.figure.Figure at 0x1252ba20>"
}
],
"prompt_number": 223
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The Kernel Density Classifier has similarities with RBF networks and SVM's with RBF kernels. It can be thought of as a RBF network with the centroids fixed on the training points, and the weights fixed based on class label. "
}
],
"metadata": {}
}
]
}
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