Python【相关矩阵】和【协方差矩阵】

相关系数矩阵

• pandas.DataFrame(数据).corr()

import pandas as pd
df = pd.DataFrame({
    'a': [11, 22, 33, 44, 55, 66, 77, 88, 99],
    'b': [10, 24, 30, 48, 50, 72, 70, 96, 90],
    'c': [91, 79, 72, 58, 53, 47, 34, 16, 10],
    'd': [99, 10, 98, 10, 17, 10, 77, 89, 10]})
df_corr = df.corr()
# 可视化
import matplotlib.pyplot as mp, seaborn
seaborn.heatmap(df_corr, center=0, annot=True, cmap='YlGnBu')
mp.show()

协方差矩阵

• numpy.cov(数据)

import numpy as np
matric = [
    [11, 22, 33, 44, 55, 66, 77, 88, 99],
    [10, 24, 30, 48, 50, 72, 70, 96, 90],
    [91, 79, 72, 58, 53, 47, 34, 16, 10],
    [55, 20, 98, 19, 17, 10, 77, 89, 14]]
covariance_matrix = np.cov(matric)
# 可视化
print(covariance_matrix)
import matplotlib.pyplot as mp, seaborn
seaborn.heatmap(covariance_matrix, center=0, annot=True, xticklabels=list('abcd'), yticklabels=list('ABCD'))
mp.show()

补充

协方差

$$\begin{gathered} Cov(X,Y)=E[(X-E[X])(Y-E[Y])] \\ =E[XY]-2E[Y][X]+E[X][Y] \\ =E[XY]-E[X][Y] \end{gathered}$$

相关系数

$$r(X,Y)=\frac{Cov(X,Y)}{\sqrt{Var[X]Var[Y]}}$$

EXCEL也能做

CORREL函数