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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""Computes the distance correlation between two matrices. For more detail,
please refer to https://en.wikipedia.org/wiki/Distance_correlation
"""
import numpy as np
from scipy.spatial.distance import pdist, squareform
def dcov(X, Y):
"""Computes the distance covariance between matrices X and Y.
Args:
X (np.ndarray): multidimensional array of numbers
Y (np.ndaaray): multidimensional array of numbers
Returns:
(float): the distance covariance between 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.
Args:
X (np.ndarray): multidimensional array of numbers
Returns:
(float): the distance variance of X
"""
return np.sqrt(np.sum(X ** 2 / X.shape[0] ** 2))
def cent_dist(X):
"""Computes pairwise euclidean distance between rows of X and centers each
cell of the distance matrix with row mean, column mean, and grand mean.
Args:
X (np.ndarray): multidimensional array of numbers
Returns:
(np.ndarray): doubly centered distance matrix of X
"""
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
Args:
X (np.ndarray): multidimensional array of numbers
Y (np.ndarray): multidimensional array of numbers
Returns:
(float, float, float, float): (dCorr(X, Y), dCov(X, Y), dVar(X),
dVar(Y))
"""
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, dcov_AB, dvar_A, dvar_B
if __name__ == "__main__":
X = np.matrix('1;2;3;4;5')
Y = np.matrix('1;2;9;4;4')
print(dcor(X, Y))
# print(dcor(np.matrix('1 7 3; 8 2 9; 1 2 7'), np.matrix('9 6; 2 3; 1 8')))
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