# ml-class / ex8.py

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142``` ```#!/usr/bin/env python import numpy as np import matplotlib.pyplot as plt from scipy.io import loadmat from sklearn.covariance import EmpiricalCovariance, MinCovDet from sklearn.metrics import fbeta_score from sklearn.decomposition import PCA def p1(x, var, mue): return (1/np.sqrt(2*np.pi*var))*(np.e**(-(((x-mue)**2)/2*var))) def p(x, mue, var): total = 1 for xi, vari, muei in zip(x, var, mue): total *= p1(xi, vari, muei) return total def calc_contour(data, fn): xs = np.linspace(data[:,0].min(), data[:,0].max(), 100) ys = np.linspace(data[:,1].min(), data[:,1].max(), 100) z = np.zeros(shape=(len(xs), len(ys))) for x, xv in enumerate(xs): for y, yv in enumerate(ys): z[x, y] = fn(np.array([xv, yv])) return xs, ys, z def anplot(data, fn, use_exps=True): xs, ys, z = calc_contour(data, lambda x: fn(x)) plt.scatter(data[:,0], data[:,1], marker='x') if use_exps: exps = np.arange(-20, -1, 3) fn = np.vectorize(lambda n: 10**n) plt.contour(xs, ys, z, fn(exps)) else: plt.contour(xs, ys, z) plt.grid() plt.show() def anomaly(): data = loadmat('ex8/ex8data1.mat') train = data['X'] mue = train.mean(0) var = train.var(0) fn = lambda x: p(x, mue, var) anplot(train, fn) def anomaly_skl(): data = loadmat('ex8/ex8data1.mat') X = data['X'] #cov = MinCovDet().fit(X) cov = EmpiricalCovariance().fit(X) anplot(X, cov.score, False) def find_threshold(fn, filename='ex8/ex8data1.mat'): raw = loadmat(filename) X = raw['Xval'] y = raw['yval'].ravel() dists = np.fromiter((fn(x) for x in X), float) best_f = 0 best_t = 0 for t in np.linspace(dists.min(), dists.max(), 100): preds = (dists > t).astype(int) f = fbeta_score(y, preds, 1.) if f > best_f: best_f = f best_t = t return best_t, best_f def show_threshold(filename='ex8/ex8data1.mat'): data = loadmat(filename) X = data['X'] cov = MinCovDet().fit(X) #cov = EmpiricalCovariance().fit(X) def dist(x): return abs(cov.score(x)) t, f = find_threshold(dist, filename) print('threshold: {}\nfscore: {}'.format(t, f)) fn = cov.score xs, ys, z = calc_contour(X, fn) plt.scatter(X[:,0], X[:,1], marker='x') plt.contour(xs, ys, z) oxs, oys = [], [] for x in X: if abs(cov.score(x)) > t: oxs.append(x[0]) oys.append(x[1]) plt.scatter(oxs, oys, marker='o', color='red') plt.grid() plt.show() def show_threshold2(filename='ex8/ex8data2.mat'): data = loadmat(filename) X = data['X'] cov = MinCovDet().fit(X) #cov = EmpiricalCovariance().fit(X) def dist(x): return abs(cov.score(x)) t, f = find_threshold(dist, filename) print('threshold: {}\nfscore: {}'.format(t, f)) pca = PCA(2) reduced = pca.fit_transform(X) plt.scatter(reduced[:,0], reduced[:,1], marker='x') outliers = [] for x in X: if abs(cov.score(x)) > t: outliers.append(x) ored = pca.transform(outliers) plt.scatter(ored[:,0], ored[:,1], marker='o', color='red') plt.grid() plt.show() if __name__ == '__main__': #anomaly() show_threshold2() raw_input() ```