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distance covariance and correlation
# -*- coding: utf-8 -*-
"""
Created on Fri Jun 15 14:00:29 2012
Author: Josef Perktold
License: MIT, BSD-3 (for statsmodels)
http://en.wikipedia.org/wiki/Distance_correlation
Yaroslav and Satrajit on sklearn mailing list
Univariate only, distance measure is just absolute distance
Note: Same as R package energy DCOR, except DCOR reports sqrt of all returns of dcov_all
"""
import numpy as np
def dist(x, y):
#1d only
return np.abs(x[:, None] - y)
def d_n(x):
d = dist(x, x)
dn = d - d.mean(0) - d.mean(1)[:,None] + d.mean()
return dn
def dcov_all(x, y):
dnx = d_n(x)
dny = d_n(y)
denom = np.product(dnx.shape)
dc = (dnx * dny).sum() / denom
dvx = (dnx**2).sum() / denom
dvy = (dny**2).sum() / denom
dr = dc / (np.sqrt(dvx) * np.sqrt(dvy))
return dc, dr, dvx, dvy
import matplotlib.pyplot as plt
fig = plt.figure()
for case in range(1,5):
np.random.seed(9854673)
x = np.linspace(-1,1, 501)
if case == 1:
y = - x**2 + 0.2 * np.random.rand(len(x))
elif case == 2:
y = np.cos(x*2*np.pi) + 0.1 * np.random.rand(len(x))
elif case == 3:
x = np.sin(x*2*np.pi) + 0.0 * np.random.rand(len(x)) #circle
elif case == 4:
x = np.sin(x*1.5*np.pi) + 0.1 * np.random.rand(len(x)) #bretzel
dc, dr, dvx, dvy = dcov_all(x, y)
print dc, dr, dvx, dvy
ax = fig.add_subplot(2,2, case)
#ax.set_xlim(-1, 1)
ax.plot(x, y, '.')
yl = ax.get_ylim()
ax.text(-0.95, yl[0] + 0.9 * np.diff(yl), 'dr=%4.2f' % dr)
plt.show()

What python version are you running? And what exactly would the inputs be? I have 2 lists of floats (x,y) x =[5.1,5.3,5.2 ...] and y = [7.0,6.8,7.2 ...] should I use those as the input?

I'm using 2.7 and getting an error on the distance method. x[:, None] gives me the error TypeError: list indices must be integers, not tuple

Thanks

@nickhsmith: Format your inputs as arrays like so:
x = np.array([5.1, 5.3, 5.2, ...])
y = np.array([7.0, 6.8, 7.2, ...])

macoj commented Dec 12, 2016

Hi, where you have in line 41

dr = dc / (np.sqrt(dvx) * np.sqrt(dvy))

I believe it should be

dr = np.sqrt(dc) / np.sqrt(np.sqrt(dvx) * np.sqrt(dvy))

This code is hard to understand

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