Scipy：距离相关性高于1 [英] Scipy: distance correlation is higher than 1

问题描述

我正在尝试在各列之间找到距离相关，请看下面的代码。大多数情况下，它返回的结果高于1，这是不可能的，因为距离相关性介于0和1之间。您可以阅读有关scipy的距离相关性此处。

I'm trying to find distance correlation between columns, look at the code below. Most of time it returns higher than 1 result, which is not possible, because distance correlation is between 0 and 1. You can read about scipy's distance correlation here.

import numpy as np
from scipy.spatial import distance

x = np.random.uniform(-1, 1, 10000)
print distance.correlation(x, x**2)

1.00210811815

1.00210811815

这里出了什么问题或如何测量？

What is wrong here or how can I measure it?

upd1： 在github上发布链接

推荐答案

根据文档，我看不出这是为什么。

I don't see why this is a problem according to the documentation.

来自文档：

u和v之间的相关距离定义为 1-racfrac {（u-\bar {u}）\cdot（v-\bar {v}）}
{{||（u-\bar {u}）|| } _2 {||（v-\bar {v}）||} _2}

通过< a href = https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality rel = noreferrer> Cauchy-Schwarz不等式，减号后的表达式带有绝对值为1 。但是，并没有规定它不会是负数的-实际上，如果（平均归一化的）向量是反相关的，就会发生这种情况。

By the Cauchy-Schwarz Inequality, the expression following the minus sign has an absolute value that is at most 1. There is nothing stipulating that it won't be negative, though - in fact, this will happen if the (mean normalized) vectors are anticorrelated.

AFAICT，您应该如果您得到的值大于2或小于0感到很惊讶。使用@Cleb的注释以及范围为[0，2]的事实，我猜想其他一些包将距离简单地定义为一半这个表达式。

AFAICT, you should be surprised if you'd get a value larger than 2 or smaller than 0. Using the comment by @Cleb and the fact that the range is [0, 2], I'm guessing that some other packages simply define the distance as half this expression.

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