在jupyter notebook实现马氏距离异常值剔除的代码

以下是在 Jupyter Notebook 中实现马氏距离异常值剔除的代码：

import numpy as np
from scipy.stats import chi2

def mahalanobis_distance(x, data):
    """
    计算马氏距离
    """
    covariance_matrix = np.cov(data.T)
    inv_covariance_matrix = np.linalg.inv(covariance_matrix)
    mean = np.mean(data, axis=0)
    x_diff = (x - mean).reshape(1, -1)
    return np.sqrt(np.dot(np.dot(x_diff, inv_covariance_matrix), x_diff.T))

def mahalanobis_outlier_detection(data, significance_level):
    """
    马氏距离异常值剔除
    """
    distances = []
    for i in range(len(data)):
        distances.append(mahalanobis_distance(data[i], data))
    distances = np.array(distances)
    p = 1 - significance_level
    threshold = chi2.ppf(p, len(data[0]))
    outliers = np.where(distances > np.sqrt(threshold))[0]
    return outliers

# 示例
data = np.random.normal(size=(100, 5))
outliers = mahalanobis_outlier_detection(data, 0.95)
print(outliers)