几种异常点检测算法

代码来自 sklearn的demo：http://scikit-learn.org/stable/auto_examples/ensemble/plot_isolation_forest.html#sphx-glr-auto-examples-ensemble-plot-isolation-forest-py

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
import matplotlib.font_manager

from sklearn import svm
from sklearn.covariance import EllipticEnvelope
from sklearn.ensemble import IsolationForest
from sklearn.neighbors import LocalOutlierFactor


rng = np.random.RandomState(42)

# Example settings
n_samples = 200
outliers_fraction = 0.25
clusters_separation = [0, 1, 2]

# define two outlier detection tools to be compared
classifiers = {
    "One-Class SVM": svm.OneClassSVM(nu=0.95 * outliers_fraction + 0.05,
                                     kernel="rbf", gamma=0.1),
    "Robust covariance": EllipticEnvelope(contamination=outliers_fraction),
    "Isolation Forest": IsolationForest(max_samples=n_samples,
                                        contamination=outliers_fraction,
                                        random_state=rng),
    "Local Outlier Factor": LocalOutlierFactor(
        n_neighbors=35,
        contamination=outliers_fraction)}

# Compare given classifiers under given settings
xx, yy = np.meshgrid(np.linspace(-7, 7, 100), np.linspace(-7, 7, 100))
n_inliers = int((1. - outliers_fraction) * n_samples)
n_outliers = int(outliers_fraction * n_samples)
ground_truth = np.ones(n_samples, dtype=int)
ground_truth[-n_outliers:] = -1

# Fit the problem with varying cluster separation
for i, offset in enumerate(clusters_separation):
    np.random.seed(42)
    # Data generation
    X1 = 0.3 * np.random.randn(n_inliers // 2, 2) - offset
    X2 = 0.3 * np.random.randn(n_inliers // 2, 2) + offset
    X = np.r_[X1, X2]
    # Add outliers
    X = np.r_[X, np.random.uniform(low=-6, high=6, size=(n_outliers, 2))]

    # Fit the model
    plt.figure(figsize=(9, 7))
    for i, (clf_name, clf) in enumerate(classifiers.items()):
        # fit the data and tag outliers
        if clf_name == "Local Outlier Factor":
            y_pred = clf.fit_predict(X)
            scores_pred = clf.negative_outlier_factor_
        else:
            clf.fit(X)
            scores_pred = clf.decision_function(X)
            y_pred = clf.predict(X)
            
        # 选取预定的前25%的分数的分界线作为阈值
        threshold = stats.scoreatpercentile(scores_pred,100 * outliers_fraction)
        
        # 计算误差
        n_errors = (y_pred != ground_truth).sum()
        
        
        # 绘制等高线
        if clf_name == "Local Outlier Factor":
            # decision_function is private for LOF
            Z = clf._decision_function(np.c_[xx.ravel(), yy.ravel()])
        else:
            Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
        Z = Z.reshape(xx.shape)
        subplot = plt.subplot(2, 2, i + 1)
        subplot.contourf(xx, yy, Z, levels=np.linspace(Z.min(), threshold, 7),
                         cmap=plt.cm.Blues_r)
        
        # 用红线画阈值边界
        a = subplot.contour(xx, yy, Z, levels=[threshold],
                            linewidths=2, colors='red')
        # 用橙色填充阈值区域内的背景
        subplot.contourf(xx, yy, Z, levels=[threshold, Z.max()],
                         colors='orange')
        b = subplot.scatter(X[:-n_outliers, 0], X[:-n_outliers, 1], c='white',
                            s=20, edgecolor='k')
        c = subplot.scatter(X[-n_outliers:, 0], X[-n_outliers:, 1], c='black',
                            s=20, edgecolor='k')
        subplot.axis('tight')
        subplot.legend(
            [a.collections[0], b, c],
            ['learned decision function', 'true inliers', 'true outliers'],
            prop=matplotlib.font_manager.FontProperties(size=10),
            loc='lower right')
        subplot.set_xlabel("%d. %s (errors: %d)" % (i + 1, clf_name, n_errors))
        subplot.set_xlim((-7, 7))
        subplot.set_ylim((-7, 7))
    plt.subplots_adjust(0.04, 0.1, 0.96, 0.94, 0.1, 0.26)
    plt.suptitle("Outlier detection")

plt.show()