On the Construction of Multivariate Correlation Coefficients

Abstract

A multivariate (un)correlation coefficient maps a vector-valued random variable X = (X1,... XN) to a real number between 0 and 1, which indicates how linearly (un)correlated its components Xi, i = 1,..., N, are. In this paper, we provide a unified framework for multivariate (un)correlation coefficients known in literature, and construct new multivariate (un)correlation coefficients using Rényi entropies, which allow applications in many scientific areas.