借鉴于http://scikit-learn.org/stable/modules/outlier_detection.html#novelty-and-outlier-detection
一、概况
两大异常
novelty detection
这些训练数据没有被异常值所污染，我们有兴趣在新的观测中发现异常。
outlier detection
训练数据中包含异常值，和我们需要合适的训练数据中心模式忽略的越轨的意见。
机器学习（无监督学习）
学习：estimator.fit(X_train)
预测：estimator.predict(X_test)，异常值为-1
二、novelty detection
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以下为建模代码：
import numpy as np
from sklearn import svm
xx, yy = np.meshgrid(np.linspace(-5, 5, 500), np.linspace(-5, 5, 500))
# Generate train data 生成训练数据
X = 0.3 * np.random.randn(100, 2)
X_train = np.r_[X + 2, X - 2]
# Generate some regular novel observations 生成一些常规的新奇观察
X = 0.3 * np.random.randn(20, 2)
X_test = np.r_[X + 2, X - 2]
# Generate some abnormal novel observations 产生一些异常新颖的观察
X_outliers = np.random.uniform(low=-4, high=4, size=(20, 2))
# fit the model 模型学习
clf = svm.OneClassSVM(nu=0.1, kernel="rbf", gamma=0.1)
clf.fit(X_train)
y_pred_train = clf.predict(X_train)
y_pred_test = clf.predict(X_test)
y_pred_outliers = clf.predict(X_outliers)
n_error_train = y_pred_train[y_pred_train == -1].size
n_error_test = y_pred_test[y_pred_test == -1].size
n_error_outliers = y_pred_outliers[y_pred_outliers == 1].size
三、Outlier Detection
covariance.EmpiricalCovariance算法
在高斯分布数据上显示具有马氏距离的协方差估计的示例。
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以下为建模代码：
import numpy as np
from sklearn.covariance import EmpiricalCovariance, MinCovDet
n_samples = 125
n_outliers = 25
n_features = 2
# generate data 生成数据
gen_cov = np.eye(n_features)
gen_cov[0, 0] = 2.
X = np.dot(np.random.randn(n_samples, n_features), gen_cov)
# add some outliers 添加一些异常值
outliers_cov = np.eye(n_features)
outliers_cov[np.arange(1, n_features), np.arange(1, n_features)] = 7.
X[-n_outliers:] = np.dot(np.random.randn(n_outliers, n_features),outliers_cov)
# fit a Minimum Covariance Determinant (MCD) robust estimator to data
# 拟合最小协方差行列式(MCD)对数据的鲁棒估计
robust_cov = MinCovDet().fit(X)
# compare estimators learnt from the full data set with true parameters
# 比较估计器从完整的数据集和真实参数的学习
emp_cov = EmpiricalCovariance().fit(X)
# Computes the squared Mahalanobis distances of given observations.
# 计算给定观测值的平方Mahalanobis距离。
Y = emp_cov.mahalanobis(X)
ensemble.IsolationForest算法
在高维数据集中执行异常值检测的一种有效方法是使用随机森林
neighbors.LocalOutlierFactor（LOF）算法
对中等高维数据集执行异常值检测的另一种有效方法是使用局部离群因子（LOF）算法。
结合以上四种异常检测方法建模比较：
sklearn.svm（支持向量机）
sklearn.covariance.EllipticEnvelope（高斯分布的协方差估计）
sklearn.ensemble.IsolationForest（随机森林）
sklearn.neighbors.LocalOutlierFactor（LOF）
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import numpy as np
from scipy import stats
from sklearn import svm
from sklearn.covariance import EllipticEnvelope
from sklearn.ensemble import IsolationForest
from sklearn.neighbors import LocalOutlierFactor
#随机数发生器
rng = np.random.RandomState(42)
# Example settings 示例设置
n_samples = 200
outliers_fraction = 0.25
clusters_separation = [0, 1, 2]
# define two outlier detection tools to be compared 定义两个异常的检测工具进行比较
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.LocalOutlierFactor(n_neighbors = 35,
contamination=outliers_fraction)
}
# Compare given classifiers under given settings 比较给定设置下的分类器
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 将不同的集群分离拟合
for i, offset in enumerate(clusters_separation):
np.random.seed(42)
# Data generation 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]
# Add outliers 添加异常值
X = np.r_[X, np.random.uniform(low=-6, high=6, size=(n_outliers, 2))]
# Fit the model 模型拟合
for i, (clf_name, clf) in enumerate(classifiers.items()):
# fit the data and tag outliers 拟合数据和标签离群值
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()
print(scores_pred)
if clf_name == "Local Outlier Factor":
# decision_function is private for LOF 决策函数是LOF的私有函数
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)
print(Z)