1. https://zhuanlan.zhihu.com/p/46626607

import pandas as pd
import numpy as np
from scipy.spatial.distance import mahalanobis
import matplotlib.pyplot as plt
import seaborn as sns

# 加載上傳的Excel文件
file_path = 'C:/Users/Aaron_zhang/Desktop/馬氏距離數(shù)據(jù).xlsx'
data = pd.read_excel(file_path)
print('數(shù)據(jù)集的形狀：', data.shape)

# 提取數(shù)值數(shù)據(jù)（排除標(biāo)識符列）
numerical_data = data.iloc[:, 1:].values

# 計算協(xié)方差矩陣及其逆矩陣
cov_matrix = np.cov(numerical_data, rowvar=False)  # 計算協(xié)方差矩陣
inv_cov_matrix = np.linalg.inv(cov_matrix)  # 計算協(xié)方差矩陣的逆矩陣

# 初始化馬氏距離矩陣
n = numerical_data.shape[0]
mahalanobis_distances = np.zeros((n, n))  # 初始化全零矩陣用于存儲馬氏距離

# 計算每對樣本（行）之間的馬氏距離
for i in range(n):
    for j in range(n):
        mahalanobis_distances[i, j] = mahalanobis(numerical_data[i], numerical_data[j], inv_cov_matrix)

print('馬氏距離矩陣的形狀：', mahalanobis_distances.shape)

# 保存馬氏距離矩陣到 Excel 文件
output_file_path = 'C:/Users/Aaron_zhang/Desktop/mahalanobis_distances.xlsx'
mahalanobis_df = pd.DataFrame(mahalanobis_distances)
mahalanobis_df.to_excel(output_file_path, index=False)

# 可視化馬氏距離矩陣的熱圖
plt.figure(figsize=(10, 8))
sns.heatmap(mahalanobis_distances, cmap="YlGnBu", xticklabels=False, yticklabels=False)
plt.title("Mahalanobis Distance Matrix")
plt.xlabel("Sample Index")
plt.ylabel("Sample Index")
plt.show()