异常检测—IsolationForest算法简介以及Python实现

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IsolationForest是一种适合高维数据集的异常值检测算法。

核心思想

通过随机切分数据集，异常点应该是容易被隔离的。

算法简介

随机选择一个特征，再在该特征下最大与最小值间随机选择一个值作为切分点，递归切分数据集，直到每个样本点被隔开，从而构建一颗类似CART分类树的随机树。重复构建多颗随机树。
从根节点到叶节点的路径越长，代表该点越难被隔离，即该点越不可能是异常点。计算每个样本点路径长的平均值，即得到该点得分，得分越低越可能是异常点。原论文中，提出了以下方法对异常分值进行归一化：

式中 $c(\psi)$ 值样本的个数。s值越大越可能是异常值

代码示例

# 实现IsolationForest高维数据的异常值检测算法
import numpy as np
import math
from collections import Counterclass Node:def __init__(self, val=None, right=None, left=None):self.val = val  # 存储样本索引,仅叶节点self.right = rightself.left = leftclass RandomTree:def __init__(self):self.tree = Noneself.n_feas = Nonedef get_split(self, data, inds):# 随机构建切分点f = np.random.choice(self.n_feas)  # 随机选择一个特征up = max(data[inds, f])down = min(data[inds, f])v = (up - down) * np.random.sample() + down  # 在该特征的最大与最小值间随机选择一个数return f, vdef split(self, data, inds):# 切分数据集f, v = self.get_split(data, inds)left_ind = []right_ind = []for i in inds:if data[i, f] <= v:left_ind.append(i)else:right_ind.append(i)return left_ind, right_inddef buildTree(self, data, inds):if len(inds) < 3:  # 叶节点return Node(val=inds)left_ind, right_ind = self.split(data, inds)left = self.buildTree(data, left_ind)right = self.buildTree(data, right_ind)return Node(left=left, right=right)def fit(self, data):self.n_feas = data.shape[1]inds = np.arange(data.shape[0])self.tree = self.buildTree(data, inds)returndef traverse(self):# 遍历树，统计每个样本的路径长path_len = Counter()i = -1def helper(currentNode):nonlocal ii += 1if currentNode.val is not None:for ind in currentNode.val:path_len[ind] = ireturnfor child in [currentNode.left, currentNode.right]:helper(child)i -= 1returnhelper(self.tree)return path_lenclass IsolationForest:def __init__(self, n_tree, epsilon):self.n_tree = n_treeself.epsilon = epsilon  # 异常点比例self.scores = Counter()def fit_predict(self, data):for _ in range(self.n_tree):RT = RandomTree()RT.fit(data)path_len = RT.traverse()self.scores = self.scores + path_lenn_sample = data.shape[0]phi = 2 * math.log(n_sample - 1) - 2 * (n_sample - 1) / n_samplefor key, val in self.scores.items():self.scores[key] = 2 ** -(val / self.n_tree / phi)  # 归一化q = np.quantile(list(self.scores.values()), 1 - self.epsilon)outliers = [key for key, val in self.scores.items() if val > q]return outliersif __name__ == '__main__':np.random.seed(42)X_inliers = 0.3 * np.random.randn(100, 2)X_inliers = np.r_[X_inliers + 2, X_inliers - 2]X_outliers = np.random.uniform(low=-4, high=4, size=(20, 2))data = np.r_[X_inliers, X_outliers]IF = IsolationForest(100, 0.1)out_ind = IF.fit_predict(data)outliers = data[out_ind]import matplotlib.pyplot as pltplt.scatter(data[:, 0], data[:, 1], color='b')plt.scatter(outliers[:, 0], outliers[:, 1], color='r')plt.show()