Distance Correlation in Python

distcorr.py

from scipy.spatial.distance import pdist, squareform
import numpy as np

from numbapro import jit, float32

def distcorr(X, Y):
    """ Compute the distance correlation function
    
    >>> a = [1,2,3,4,5]
    >>> b = np.array([1,2,9,4,4])
    >>> distcorr(a, b)
    0.762676242417
    """
    X = np.atleast_1d(X)
    Y = np.atleast_1d(Y)
    if np.prod(X.shape) == len(X):
        X = X[:, None]
    if np.prod(Y.shape) == len(Y):
        Y = Y[:, None]
    X = np.atleast_2d(X)
    Y = np.atleast_2d(Y)
    n = X.shape[0]
    if Y.shape[0] != X.shape[0]:
        raise ValueError('Number of samples must match')
    a = squareform(pdist(X))
    b = squareform(pdist(Y))
    A = a - a.mean(axis=0)[None, :] - a.mean(axis=1)[:, None] + a.mean()
    B = b - b.mean(axis=0)[None, :] - b.mean(axis=1)[:, None] + b.mean()
    
    dcov2_xy = (A * B).sum()/float(n * n)
    dcov2_xx = (A * A).sum()/float(n * n)
    dcov2_yy = (B * B).sum()/float(n * n)
    dcor = np.sqrt(dcov2_xy)/np.sqrt(np.sqrt(dcov2_xx) * np.sqrt(dcov2_yy))
    return dcor

@seanlaw, yes, that seems to be the case.

(Eq. (2.8) - (2.10) in Székely, Rizzo, and Bakirov, 2007)

@seanlaw and @tfiers :

yes, this is the same distance correlation.

Small reproducible example:

from sklearn.datasets import load_iris
import pandas as pd
import dcor
# https://dcor.readthedocs.io/en/latest/energycomparison.html

iris = load_iris()
iris_df = pd.DataFrame(data= np.c_[iris['data'], iris['target']],
                     columns= iris['feature_names'] + ['target'])

print ("dcor distance correlation = {:.3f}".format(dcor.distance_correlation(iris_df['sepal length (cm)'], 
                                                                        iris_df['petal length (cm)'])))
print ("distcorr distance correlation = {:.3f}".format(distcorr(iris_df['sepal length (cm)'], iris_df['petal length (cm)'])))

returns:

dcor distance correlation = 0.859
distcorr distance correlation = 0.859

Can anyone help me how to plot this like a matrix in pandas?

Is it possible to have a distance correlation matrix similar to a correlation matrix?

Thanks a lot.