在污染的數量已知的情況下，下面的例子介紹了執行野點和異常檢測的兩種不同方式：
- 基於協方差的穩健估計，假設數據是高斯分布的，那么在這樣的案例中執行效果將優於One-Class SVM；
- 利用One-Class SVM，它有能力捕獲數據集的形狀,因此對於強非高斯數據有更加優秀的效果，例如兩個截然分開的數據集；
正常值和異常值的真實狀況是由點的顏色而定的，橙色填充的區域則表示這部分點被對應的方法標記為異常值。
這里我們假定，我們知道數據集中一部分的異常值。由此我們通過對decision_function設置閾值來分離出相應的部分，而不是使用'預測'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