{ "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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HWD4GAAhpPmpeegWB6+S/vN2+dMdcd+RZ73mzstRWjHTYnLfTYcVS2wkZKyJv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\npDAMbiIihWFwExEpDIObiEhh/j8Viw+nTWmr+QAAAABJRU5ErkJggg==\n", "text": "" } ], "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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BWVkZrl27htGjR+P999+v7ECSmjyEwj0nyVmu2CxBb6hcy7spbbriBiDyTs7sOVlX7nQq\ncVe1c+dOLFu2DJ999lmDO68PEzc5wxWVtrNJG2Di9ieuStyy3jkpSZKczRF5FfuFRG8ZbiH/JVvF\nXWsHrLjJQ+SsuJ1Z/e/Gdlht+w9FVNxEVDP73G+uk0Jy4C3v5LO8aSaJ/QIpkRxYcZPPccVMEiJv\nwoqbfErVVQDlnP5X9YPI01hxE9XBPtzCsWnyJqy4iWoh54wUrgVOcmLFTeQi3ASYXIUVN5ELMGmT\nKzFxExEpDBM3+RT7zA9n18p2diYJ97gkV+IYN/kEb7m9nUMk5A6suEnxmLTJ3zBxExEpDBM3EZHC\nMHETESkMEzeRTDiThNyFs0qIZODsdmZEjcHETeQEziQhT+BQCRGRwjBxExEpDBM3EZHCMHETyYDj\n2+ROvDhJ1ET2i5KxFzwdCfkbJm6iRuJMEvI0Jm4iVCZjORaqInI1Jm7ye86sCEjkCbw4SUSkMKy4\nSfGMOuB0ou1fg56VM/k+Jm7yGYUxtsRt0LturJozScgbMHETNQBnkpA34Rg3USMwaZM3YOImIlIY\npxN3fn4+Bg0ahE6dOqFz585YsWKFHHEReY2YQiDxtG3NbSJv4PQYt1arxWuvvYbu3bujpKQEPXr0\nQHp6OpKTk+WIj8jlCmMqZ6RUvajJcW3yVk4n7vj4eMTHxwMAQkJCkJycjHPnzjFxk6LYZ6PYP+zJ\nmluRkTeSdYw7NzcX+/fvR+/eveVsloiIqpBtOmBJSQnGjBmD5cuXIyQkpNprGRkZjs/T0tKQlpYm\nV7dERD4hOzsb2dnZDTpWEkIIZzusqKjA0KFD8dvf/hZPPPFE9Q4kCU3tIuKqs5GRv9EZnVssqup7\nYy/YLkryZhtqqhZnm/7eunKn00MlQghMmTIFKSkpNyVtIiXSG5i0ybs5nbi/++47rFu3Dl999RVS\nU1ORmpqKzMxMOWKjOljP5MPy3wMQpaWytSmEgOXEMZgP/AeirEy2dpXEPpOESZu8mdNj3P3794fV\napUjFmoAIQRK5zyF8nXvAdo4SMFGhGz+AuoOHZ1r12qFceoUVHyRCWijIenLEJK5FerEW2SKXBn0\nhsoPIm/FOycVxvzl5yjf+CVgOg6UHIa4OBeGByc73W7Fhx+g4ssjQNkJoPi/EBcehvGRac4HTESy\nY+JWGMuRw4DpXgDNbE+IcbCePOx8uzk/A8ahAHS2J6wPwHo0x+l23cnZC5NESsHErTCq9rcCAdsA\nFF9/5l9QJTo3TAIA6pRkQLcZgPF6R/+AqkOK0+26S0yh7Zb0pFwmbfJ9TNwKox0yAtpRA4Cg9kBo\nD0iRGdCvXeN8u2MnQTv4ViCoLRDSBVLsO9C9/ZYMEddMWK0oXTAfV5s3w9XmzWCcNxeiiddKdMbK\nOxydGZu2v19nbHobRO4gyzzuOjvgPG6XsJw4BnHlMtQdO0G64YanphJCwHryOIShBOoOyZCCgmRp\ntyZlb65A2aJ1gPFfACQgeAyCnnkAQX+a1ei25BgiScq1vd9esXNBKZKDq+ZxcyMFhVK3bS97m5Ik\nuaTdmlRs2Q4YnwGQYHuidB4qPn+rSYnbWVXXJQFYcZP341AJeYQqPhpQVbmoqjoMVVx0rcdbr16B\ncc6TKLl/NEqXLIKoqHBJXAa9bbXAC7EuaZ5IFqy4ySOCnnsW5h39IUxHAaECArYiKOObGo8VZWUo\nuftOWPN7AuVjYd6zGpaDhxDy9/Uuic2+zKtR57olXQ9V/ISfyvciTt0CdwUOgUpiDUUNx8RNHqFO\nvAWhu39ExeZ/A0JAe99iqJq3qPFY857vYD2vBcpXAZCA0mEwb4+H9dJFqKJqr9KdYdDb/nXFsq4f\nG97DwqI/4j5I+Lsk4ZOAu/BG5CeQJEnejshnMXGTx6ji4hE45Y/1H2ixANACsCc2NQDV9eedU/VO\nSXfcLWkRFiwomobdKEMKAJMAbivfgW/Ks/CbwLtdHwD5BCZu8nqa3ndACr8EUfY0YL4bCPob1L36\nQ4qxDUQbdbbhjcZufBBTCESftyLw4C8wQcAa1tHlQxalwggzzLBvMxIIoDMkXLScd2m/5Fs4sEZe\nT9LrEZqVDe3wS1B3ewkBDyYhZMOH1YYWjDogJ8X2URhTf5sxhUD4mRL8Y1UfrMjsif/N7IWlX/ZB\nWUWJC88ECFGFop26DV6CChYA3wPIEhakBnDzEWo4Jm5SBFVcPPTvvovQ7B3QvbQUkk4HYTDAMHUq\nitok4tptt6EiezsMetuMkIYk751fzUenqweRazEg12JA56sH8cmB+S4/l3eivsTHmo4IhISRUjiW\nRW7ELZp2Lu+XfAeHSkixjI8+iortZsD0FcSVHBgmjIduy04gomG36l8+/x/Mtpqgvv54nNWEv1z+\n0XUBX9dKk4TPYg+jQlRAK2ld3h/5Hlbc5PWE0YiKr7ahInt7tfXHK7ZtAkz/B6ANgKGAZSxMO7c2\nuN2I2G74WBUIKwArgI9VgYiPSJU7/Fq5Mmnnm3Oxv3wviq3XXNYHeQ4rbvJq1ouFKLlrEKyXwwAI\nqKINCMn6CqrIKEjBoRDleQAibAdr8hCkTW3weiMDBy3GP0/tQrvi4wCA4NB2mNV9UaPi+9VyDmtK\nXkexuIS7g8bgzqDfNu4EXWBp0RysM7yB1lIACqDCu1Fb0T2gp6fDIhlxrRLyaobH/oiKj4OAildt\nT2j/BO04QL/if2H6YA1K5z4HlD0MBOQgICYHd7y5C81L6l+7xb62SauTZuQXHQIAtArvDLWqspbR\nG+reCafQch73XeiMUeIK2sCCV6HDrPAVGKuf4vR5N9X3pp14+vJ92CsMiALwMYCnVS3wbbwTi2ZQ\nk3GtEvJL1uO5QMV0OOZwV9wF6/F3AQCBk/4HqsREYGsWwoN64dYB7zQoaVelVmmQFNG9SbF9XPo+\n7hHXsAK2+eR9YcSE4gUeTdzHzUeQJqyIuv74fgBjrQUwCzM0Ev+7+wp+J8mrafr0gOW/7wJl6QAE\nELQamj49HK9rf3MndLffiZhCQHMBgBu3HCuzliIKZsfjaAClwuS+AGrQQZOCtyQVCgUQA1vFfYuq\nhVNJ2yqssMLKxO9FeHGSvFrQ/AXQ9JOAgDggIA6aAYEImjvP02EBAO4JHonVCMJHAPYBmCLpMDz4\n97K1bxbmRg8z9g4cgNH6P+FWBKGrFIZZUgTejPy0Sf0LIfBK0Xx0KAhC+4IgTL80AqVCvs2pqek4\nxk2KYL1YCEhSjWuTNGU9bvvx9a27bV+fu7a7MXeZsvFq0SwUiyLcFTQas8MWO12ZGq0GzL4yFpmm\nTGihxszQ+fhT6PONauOc5QwuWS6gjaYD9Kqmrdf+L+M6rCp6FFuFEeEAJiIIkbo/4MVmq5rUnj/i\nGDf5NVV03XfUuGrnmtwk24JT9kR/o36BaegXu1/WPv9aNAPBpiwUwYJLsODu4qVoo+mEocFjGtxG\nC3UCWqgTnIpjtykTfxRGNL/+eD7K8JBpm1Ntkjw4VEKKFlMIdDpsq4xdtUhUYQxwOtGWxN1ht2k7\n/owyBMO2zcQ0GLHb9KV7Oq8iRt0a+xDgeLwPEmJUNa/gSO7FipsUyZd3dI9Rx2Of9Qy6AhAAfkQA\nmqtauT2Oh0PmYFTpBgy2XkQkBHZAhQ3N/s/tcdDNmLhJ0Xxxm7EF4asw6VIatsGKi5BwThWPf4U8\n4fY4mqki8FnMf7HdtBkmYcLTgemIV7Pi9gZM3OQSorQU5q93QJgroOmfBlV4M5f0Y9S5Zx1td+oS\ncBs+jz2Mb03bESQFIz1wGHQqvUdi0atCMCJ4nEf6ptoxcZPsrFevoOTONFgLwwAEQwqehdDt2VC1\nTvR0aE0SU1j7xUlXaaluhbG6/3Ffh6QovDhJsitb+hKsZ3oDJV8DJVshLk+Bce4zsvZh1FVeMLTP\n/JCb3mC76NnpsHuTNlF9mLhJdtaT+UDFADhuU7f0hzXvjEv6KoypTN4NWYO7sXxxDJ2Uj4mbZKcZ\n0BsIfgdAMYByIGglNH17eTosIp/BxO3jhBCw5p2G5dQJCKvVLX0GTpsB7cgUQBMHaCOh6VuB4Bf/\n4pa+62Mf/rjlVN13TcYU1r0yIJEn8ZZ3HybKy2EYPw7mXbsASQN1hzYI2fQZpPBw9/RvMABms9v6\ns19ErO0W9arzvmubiaI31N0GUWO46pZ3pyvuzMxMdOzYEe3bt8eSJUucbY5kVLb8FZi/LwfK8oDS\nPFiOdIBxvvsWaJL0erclbaBh4916Q+0J2V5lu/IuTCI5OJW4LRYLZsyYgczMTOTk5GDDhg34+eef\n5YqNnGTZdxAoHQcgAIAKME2EZf9BT4fldezDJ0m5HBohZXAqce/duxft2rVDUlIStFotxo0bh02b\nNskVGzlJndwOCPwcth0VBaDdDPWt7T0dlldhlU1K5NQNOGfPnkWrVpVrKCQkJGDPnj1OB0XyCJrz\nDMw7h8ByrBMgBUEVZUbw0ixPh+VS9vndRl3lqn41JWSOZZOSOZW4JUlq0HEZGRmOz9PS0pCWluZM\nt9RAkl6PkG1ZsBz4D2A2Q93tNkhBQZ4Oyy0KY2yJ26C/+YKkJ+6EJKpPdnY2srOzG3SsU4m7ZcuW\nyM/PdzzOz89HQsLNawBXTdzkXpJGA00PzqEGqo9ls8omb3NjUfvCCy/UeqxTY9y33347jh07htzc\nXJSXl+PDDz/E8OHDnWmSSBY1Lftq32zBm5L2r5ZzmH15LMZduB2Li2ajTJR5OiRSAKcqbo1Ggzfe\neAP33HMPLBYLpkyZguTkZLliI2qS+uZze4sSazHGFPbEWOsFPAQzVppz8CfzEbwdtcXToZGX4w04\n5DPq21yh02Gg5w+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mlnWwMguuj61Apo4rbjU+p90lTJ/3l50U3DKg6VGdOduu4Mpnm8DsNnTtVw5z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\neOMNVFdXIyYmpvMKJOycvH6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"text": "" } ], "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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OhTOOR+225BgLW0mP2w+ElZl/8fWmUiLValKBSwEDYEDPKcNJWgTGObSNptwLd1eoNuVj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\nzg9uX5aZaO6drxplXdB7klc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jHEx63B5EVVWmZA6kTcn/WKCWsNFwiLvTd/JZ60MutbJfnLYNX8b/QYbxOMGa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\n0QAaHZZrVgE0oAkAo6HCdsY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VVXXUwVJTUxk4cCApKSn4+/tbGlAU6tvEqShHVSaEsFWRHxw1HOBP/S9EGcNI8BqGRpHL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\nly8g88NXKT156ffdMsatAto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"text": "" } ], "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": {} } ] }