Computes the distance correlation between two matrices in Python.

dcor.py

#!/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__ = "[email protected]"
__copyright__ = "Copyright (c) 2019"
__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)