Scipy：距离相关性大于1
Scipy: distance correlation is higher than 1
我正在寻找 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
这里有什么问题或者我该如何衡量？
upd1: Link to issue github
根据文档，我不明白为什么这是个问题。
The correlation distance between u and v, is defined as 1 - \frac{(u - \bar{u}) \cdot (v - \bar{v})}
{{||(u - \bar{u})||}_2 {||(v - \bar{v})||}_2}
根据Cauchy-Schwarz Inequality，减号后面的表达式的绝对值最多为1。没有任何规定它不会是负数，但实际上，如果（均值归一化）向量是反相关的，就会发生这种情况。
AFAICT，如果你得到一个大于 2 或小于 0 的值，你应该感到惊讶。使用@Cleb 的评论和范围是 [0, 2] 的事实，我猜其他一些包只是将距离定义为 half 这个表达式。
@josef-pkt 对 github 的回答如下：
It's not a distance correlation which is a nonlinear measure of
dependence. e.g. my take
http://jpktd.blogspot.ca/2012/06/non-linear-dependence-measures-distance.html
However, "correlation" in scipy.spatial.distance.correlation is a bit
misleading because according to the formula in the docstring it's a
distance measure and not a correlation. perfectly correlated with
correlation coefficient equal to 1 has zero distance perfectly
negatively correlated with correlation coefficient equal to -1 has
maximal distance at 2.
相关距离是相关性的倒数，仅查看模式之间的 angle/similarity（有点像归一化）。相关距离从 0 到 2，0 是完全相关，1 是不相关，2 是完全反相关。所以一个小的相关距离值意味着在相关 space 中靠近在一起（小 angular 差异）。
Corr = 1 – 距离；
校正距离 = 1 – 校正；
所以虽然高相关性=高关系；低 CORR DISTINANCE = 高关系
我正在寻找 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
这里有什么问题或者我该如何衡量？
upd1: Link to issue github
根据文档，我不明白为什么这是个问题。
The correlation distance between u and v, is defined as 1 - \frac{(u - \bar{u}) \cdot (v - \bar{v})} {{||(u - \bar{u})||}_2 {||(v - \bar{v})||}_2}
根据Cauchy-Schwarz Inequality，减号后面的表达式的绝对值最多为1。没有任何规定它不会是负数，但实际上，如果（均值归一化）向量是反相关的，就会发生这种情况。
AFAICT，如果你得到一个大于 2 或小于 0 的值，你应该感到惊讶。使用@Cleb 的评论和范围是 [0, 2] 的事实，我猜其他一些包只是将距离定义为 half 这个表达式。
@josef-pkt 对 github 的回答如下：
It's not a distance correlation which is a nonlinear measure of dependence. e.g. my take http://jpktd.blogspot.ca/2012/06/non-linear-dependence-measures-distance.html However, "correlation" in scipy.spatial.distance.correlation is a bit misleading because according to the formula in the docstring it's a distance measure and not a correlation. perfectly correlated with correlation coefficient equal to 1 has zero distance perfectly negatively correlated with correlation coefficient equal to -1 has maximal distance at 2.
相关距离是相关性的倒数，仅查看模式之间的 angle/similarity（有点像归一化）。相关距离从 0 到 2，0 是完全相关，1 是不相关，2 是完全反相关。所以一个小的相关距离值意味着在相关 space 中靠近在一起（小 angular 差异）。 Corr = 1 – 距离； 校正距离 = 1 – 校正； 所以虽然高相关性=高关系；低 CORR DISTINANCE = 高关系