异常检测用几种方法
在污染的数量已知的情况下，下面的例子介绍了执行野点和异常检测的两种不同方式：
- 基于协方差的稳健估计，假设数据是高斯分布的，那么在这样的案例中执行效果将优于One-Class SVM；
- 利用One-Class SVM，它有能力捕获数据集的形状,因此对于强非高斯数据有更加优秀的效果，例如两个截然分开的数据集；
正常值和异常值的真实状况是由点的颜色而定的，橙色填充的区域则表示这部分点被对应的方法标记为异常值。
这里我们假定，我们知道数据集中一部分的异常值。由此我们通过对decision_function设置阈值来分离出相应的部分，而不是使用'预测'方法。
1 """ 2 ========================================== 3 Outlier detection with several methods. 4 ========================================== 5 6 When the amount of contamination is known, this example illustrates two 7 different ways of performing :ref:`outlier_detection`: 8 9 - based on a robust estimator of covariance, which is assuming that the 10 data are Gaussian distributed and performs better than the One-Class SVM 11 in that case. 12 13 - using the One-Class SVM and its ability to capture the shape of the 14 data set, hence performing better when the data is strongly 15 non-Gaussian, i.e. with two well-separated clusters; 16 17 The ground truth about inliers and outliers is given by the points colors 18 while the orange-filled area indicates which points are reported as outliers 19 by each method. 20 21 Here, we assume that we know the fraction of outliers in the datasets. 22 Thus rather than using the 'predict' method of the objects, we set the 23 threshold on the decision_function to separate out the corresponding 24 fraction. 25 """ 26 print(__doc__) 27 28 import numpy as np 29 import pylab as pl 30 import matplotlib.font_manager 31 from scipy import stats 32 33 from sklearn import svm 34 from sklearn.covariance import EllipticEnvelope 35 36 # Example settings 37 n_samples = 200 38 outliers_fraction = 0.25 39 clusters_separation = [0, 1, 2] 40 41 # define two outlier detection tools to be compared 42 classifiers = { 43 "One-Class SVM": svm.OneClassSVM(nu=0.95 * outliers_fraction + 0.05, 44 kernel="rbf", gamma=0.1), 45 "robust covariance estimator": EllipticEnvelope(contamination=.1)} 46 47 # Compare given classifiers under given settings 48 xx, yy = np.meshgrid(np.linspace(-7, 7, 500), np.linspace(-7, 7, 500)) 49 n_inliers = int((1. - outliers_fraction) * n_samples) 50 n_outliers = int(outliers_fraction * n_samples) 51 ground_truth = np.ones(n_samples, dtype=int) 52 ground_truth[-n_outliers:] = 0 53 54 # Fit the problem with varying cluster separation 55 for i, offset in enumerate(clusters_separation): 56 np.random.seed(42) 57 # Data generation 58 X1 = 0.3 * np.random.randn(0.5 * n_inliers, 2) - offset 59 X2 = 0.3 * np.random.randn(0.5 * n_inliers, 2) + offset 60 X = np.r_[X1, X2] 61 # Add outliers 62 X = np.r_[X, np.random.uniform(low=-6, high=6, size=(n_outliers, 2))] 63 64 # Fit the model with the One-Class SVM 65 pl.figure(figsize=(10, 5)) 66 for i, (clf_name, clf) in enumerate(classifiers.iteritems()): 67 # fit the data and tag outliers 68 clf.fit(X) 69 y_pred = clf.decision_function(X).ravel() 70 threshold = stats.scoreatpercentile(y_pred, 71 100 * outliers_fraction) 72 y_pred = y_pred > threshold 73 n_errors = (y_pred != ground_truth).sum() 74 # plot the levels lines and the points 75 Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()]) 76 Z = Z.reshape(xx.shape) 77 subplot = pl.subplot(1, 2, i + 1) 78 subplot.set_title("Outlier detection") 79 subplot.contourf(xx, yy, Z, levels=np.linspace(Z.min(), threshold, 7), 80 cmap=pl.cm.Blues_r) 81 a = subplot.contour(xx, yy, Z, levels=[threshold], 82 linewidths=2, colors='red') 83 subplot.contourf(xx, yy, Z, levels=[threshold, Z.max()], 84 colors='orange') 85 b = subplot.scatter(X[:-n_outliers, 0], X[:-n_outliers, 1], c='white') 86 c = subplot.scatter(X[-n_outliers:, 0], X[-n_outliers:, 1], c='black') 87 subplot.axis('tight') 88 subplot.legend( 89 [a.collections[0], b, c], 90 ['learned decision function', 'true inliers', 'true outliers'], 91 prop=matplotlib.font_manager.FontProperties(size=11)) 92 subplot.set_xlabel("%d. %s (errors: %d)" % (i + 1, clf_name, n_errors)) 93 subplot.set_xlim((-7, 7)) 94 subplot.set_ylim((-7, 7)) 95 pl.subplots_adjust(0.04, 0.1, 0.96, 0.94, 0.1, 0.26) 96 97 pl.show()
Total running time of the example: 2.13 seconds
