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Computes the distance correlation between two matrices in Python.
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#!/usr/bin/env python | |
# -*- coding: utf-8 -*- | |
"""Computes the distance correlation between two matrices. | |
https://en.wikipedia.org/wiki/Distance_correlation | |
""" | |
import numpy as np | |
from scipy.spatial.distance import pdist, squareform | |
__author__ = "Kailash Budhathoki" | |
__email__ = "kbudhath@mpi-inf.mpg.de" | |
__copyright__ = "Copyright (c) 2016" | |
__license__ = "MIT" | |
def dcov(X, Y): | |
"""Computes the distance covariance between matrices X and Y. | |
""" | |
n = X.shape[0] | |
XY = np.multiply(X, Y) | |
cov = np.sqrt(XY.sum()) / n | |
return cov | |
def dvar(X): | |
"""Computes the distance variance of a matrix X. | |
""" | |
return np.sqrt(np.sum(X ** 2 / X.shape[0] ** 2)) | |
def cent_dist(X): | |
"""Computes the pairwise euclidean distance between rows of X and centers | |
each cell of the distance matrix with row mean, column mean, and grand mean. | |
""" | |
M = squareform(pdist(X)) # distance matrix | |
rmean = M.mean(axis=1) | |
cmean = M.mean(axis=0) | |
gmean = rmean.mean() | |
R = np.tile(rmean, (M.shape[0], 1)).transpose() | |
C = np.tile(cmean, (M.shape[1], 1)) | |
G = np.tile(gmean, M.shape) | |
CM = M - R - C + G | |
return CM | |
def dcor(X, Y): | |
"""Computes the distance correlation between two matrices X and Y. | |
X and Y must have the same number of rows. | |
>>> X = np.matrix('1;2;3;4;5') | |
>>> Y = np.matrix('1;2;9;4;4') | |
>>> dcor(X, Y) | |
0.76267624241686649 | |
""" | |
assert X.shape[0] == Y.shape[0] | |
A = cent_dist(X) | |
B = cent_dist(Y) | |
dcov_AB = dcov(A, B) | |
dvar_A = dvar(A) | |
dvar_B = dvar(B) | |
dcor = 0.0 | |
if dvar_A > 0.0 and dvar_B > 0.0: | |
dcor = dcov_AB / np.sqrt(dvar_A * dvar_B) | |
return dcor | |
if __name__ == "__main__": | |
X = np.matrix('1;2;3;4;5') | |
Y = np.matrix('1;2;9;4;4') | |
print dcor(X, Y) |
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Tried this code, got the following error:
File "", line 79
print dcor(X, Y)
^
SyntaxError: invalid syntax
Any ideas on a solution?