python - 为什么 nump.cov() 和 np.std() 计算的相关性与 np.corrcoef() 计算的结果不同

Question

我希望有人能帮我回答为什么numpy.cov()和np.std()计算的相关结果与直接计算的结果不同>np.corrcoef().

下面的代码显示了差异

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

X = np.random.rand(50)
Y = np.random.rand(50)

plt.scatter(X,Y)
plt.xlabel('X Value')
plt.ylabel('Y Value')

# taking the relevant value from the matrix returned by np.cov
print 'Correlation: ' + str(np.cov(X,Y)[0,1]/(np.std(X)*np.std(Y)))
# Let's also use the builtin correlation function
print 'Built-in Correlation: ' + str(np.corrcoef(X, Y)[0, 1])

一个示例输出:

Correlation: -0.0972430699897

Built-in Correlation: -0.0952982085899

Answer 1

感谢Brian Borchers的建议

查文档发现差异是由于np.std()的参数ddof(delta自由度)默认为0造成的code>，而 1 用于 np.corrcoef()

修改如下，代码可以生成相同的结果:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

X = np.random.rand(50)
Y = np.random.rand(50)

plt.scatter(X,Y)
plt.xlabel('X Value')
plt.ylabel('Y Value')

# taking the relevant value from the matrix returned by np.cov
print 'Correlation: ' + str(np.cov(X,Y)[0,1]/(np.std(X,ddof=1)*np.std(Y,ddof=1)))
# Let's also use the builtin correlation function
print 'Built-in Correlation: ' + str(np.corrcoef(X, Y)[0, 1])

示例输出:

Correlation: -0.174042621953

Built-in Correlation: -0.174042621953