Python机器学习（1）——异常点检测

本文主要介绍4种异常点检测方法，One-Class SVM（一分类向量机，非高斯分布）、EllipticEnvelope（基于高斯概率密度的异常点检测）、Isolation Forest（基于集成学习方法异常点检测）、LocalOutlierFactor（基于密度的局部异常因子），并基于同一数据集，对比不同检测方法的效果。

实现代码如下所示：

'''
目标：比较One-Class SVM、EllipticEnvelope、Isolation Forest、
LocalOutlierFactor这4种异常检测算法在相同数据集下的异常检测效果。
'''

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)

#设置样本数量、异常样本比例，不同类样本分离度
n_samples = 256
outliers_fraction = 0.25
clusters_separation = [0,1,2]

#定义各种异常检测方法
classifiers = {
    "One-Class SVM":svm.OneClassSVM(nu=0.95 * outliers_fraction + 0.05,kernel='rbf',gamma=0.1),
    "Roubst 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)}
#样本集各变量赋初值
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

#在不同的样本分离度下测试异常检测效果
for i,offset in enumerate(clusters_separation):
    np.random.seed(42)
    #生成数据
    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]
    X = np.r_[X,np.random.uniform(low=-6,high=6,size=(n_outliers,2))]
    
    #模型匹配
    plt.figure(figsize=(9,7))
    for j,(clf_name,clf) in enumerate(classifiers.items()):
        #数据匹配
        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)
        threshold = stats.scoreatpercentile(scores_pred,100 * outliers_fraction)
        n_errors = (y_pred != ground_truth).sum()

        #画图
        if clf_name == "Local Outlier Factor":
            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,j+1)
        subplot.contourf(xx,yy,Z,levels=np.linspace(Z.min(),threshold,7),
                        cmap=plt.cm.Blues_r)
        a = subplot.contour(xx,yy,Z,levels=[threshold],linewidths=2,colors='red')
        subplot.contourf(xx,yy,Z,levels=[threshold,Z.max()],colors='orange')
        #正常样本
        b = subplot.scatter(X[:-n_outliers,0],X[:-n_outliers,1],c='white',s=20,edgecolor='k')
        #异常样本
        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("{}.{}({})".format(j+1,clf_name,n_errors))
        subplot.set_xlim((-7,7))
        subplot.set_ylim((-7,7))
    plt.subplots_adjust(0.04,0.1,0.96,0.94,0.1,0.20)
    plt.suptitle("Outlier detection{}".format(i+1))
    
plt.show()
        
        

对比结果如下图所示：