sklearn 之 单类支持向量机（One-Class SVM）

这里先列出 sklearn 官方给出的使用高斯核（RBF kernel) one class svm 实现二维数据的异常检测：

#!/usr/bin/python
# -*- coding:utf-8 -*-

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.font_manager
from sklearn import svm

xx, yy = np.meshgrid(np.linspace(-5, 5, 500), np.linspace(-5, 5, 500))

# Generate train data
X = 0.3 * np.random.randn(100, 2)
X_train = np.r_[X + 2, X - 2]

# Generate some regular novel observations
X = 0.3 * np.random.randn(20, 2)
X_test = np.r_[X + 2, X - 2]

# Generate some abnormal novel observations
X_outliers = np.random.uniform(low=-4, high=4, size=(20, 2))

# fit the model
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

# plot the line, the points, and the nearest vectors to the plane
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

plt.title("Novelty Detection")
plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.PuBu)  #绘制异常样本的区域
a = plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors='darkred')  #绘制正常样本和异常样本的边界
plt.contourf(xx, yy, Z, levels=[0, Z.max()], colors='palevioletred')   #绘制正常样本的区域
s = 40
b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c='white', s=s, edgecolors='k')
b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c='blueviolet', s=s,
                 edgecolors='k')
c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c='gold', s=s,
                edgecolors='k')
plt.axis('tight')
plt.xlim((-5, 5))
plt.ylim((-5, 5))
plt.legend([a.collections[0], b1, b2, c],
           ["learned frontier", "training observations",
            "new regular observations", "new abnormal observations"],
           loc="upper left",
           prop=matplotlib.font_manager.FontProperties(size=11))
plt.xlabel(
    "error train: %d/200 ; errors novel regular: %d/40 ; "
    "errors novel abnormal: %d/40"
    % (n_error_train, n_error_test, n_error_outliers))
plt.show()

效果如下图：

下面简单介绍一下 sklearn.svm.OneClassSVM 函数的用法：

1. decision_function(self, X) 点到分割超平面的有符号距离
2. fit(self, X[, y, sample_weight]) 训练出样本 X 的软边界
3. fit_predict(self, X[, y]) 训练出样本 X 的软边界后返回标签（是否异常）
4. get_params(self[, deep]) 获取估计器训练参数
5. predict(self, X) 返回样本 X 的标签

对于可视化图像绘制的函数

1. matplotlib.pyplot.contour 和 matplotlib.pyplot.contourf 可以绘制出等高线和填充等高线，两个函数的参数和调用方式一样。其中 levels 代表了分割线的 list，以 plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.PuBu) 这句话为例：表示的是绘制以 xx 和 yy 构成的二维平面，以 Z 作为每个点的高程绘制等高线，从 Z.min() 到 0 分成 7 份，当 Z 等于这 7 个值时绘制等高线。plt.cm.PuBu 代表一种颜色映射，具体的样式见 Colormap reference。
2. matplotlib.pyplot.scatter 绘制散点图

下面是改编的代码用于异常检测：

#!/usr/bin/python
# -*- coding:utf-8 -*-

import pickle
import numpy as np
import pandas as pd
from math import ceil
import matplotlib.pyplot as plt
import matplotlib.font_manager
from sklearn import svm
from sklearn.preprocessing import MinMaxScaler
from sklearn.preprocessing import StandardScaler

def get_dataset_to_pandas(file_name, dropList=[]):
	dataset = pd.read_csv(file_name)
	for drop_str in dropList:
		dataset = dataset.drop(drop_str,axis=1)
	return dataset

def pre_scaler(dataset, type_str = "std"):
	if type_str == "minmax":
		scaler = MinMaxScaler()
	elif type_str == "std":
		scaler = StandardScaler()
	else : 
		return None
	scaler.fit(dataset)
	return scaler,scaler.transform(dataset)

def train_test_split(dataset, test_ratio = 0.3, seed = 42):
	if seed:
		np.random.seed(seed)
	shuffle_index = np.random.permutation(len(dataset))
	test_size = ceil(len(dataset) * test_ratio)
	test_index = shuffle_index[:test_size]
	train_index = shuffle_index[test_size:]
	dataset_train = dataset[train_index]
	dataset_test = dataset[test_index]
	return dataset_train, dataset_test

def variable_save(variable, file_name):	
	data_output = open(file_name, 'wb')
	pickle.dump(variable,data_output)
	data_output.close()

def variable_load(file_name):	
	data_input = open(file_name, 'rb')
	variable = pickle.load(data_input)
	data_input.close()
	return variable

if __name__ == '__main__':
	dataset = get_dataset_to_pandas("walk1.csv", ["Loss","TimeStamp","LT_Foot_TimeStamp","RT_Foot_TimeStamp",'Chest_TimeStamp'])
	scaler, dataset = pre_scaler(dataset,"minmax")
	X_train, X_test = train_test_split(dataset)
	
	# fit the model
	clf = svm.OneClassSVM(nu=0.05, kernel="rbf", gamma="auto")
	clf.fit(X_train)

	y_pred_train = clf.predict(X_train)
	y_pred_test = clf.predict(X_test)

	n_error_train = y_pred_train[y_pred_train == -1].size
	n_error_test = y_pred_test[y_pred_test == -1].size

	print(n_error_train,",",n_error_test)
	
	# distances = clf.decision_function(dataset)
	
	# save clf and scaler
	# variable_save((clf,scaler),'./one_class_svm')
	# (clf,scaler) = variable_load('./one_class_svm')
	
	# print(clf,'\n',scaler)

在训练完成之后可以通过 clf.decision_function 检测与边界的距离来判断是否异常和 clf.predict 直接判断是否是异常点。