Nonparametric measure of multivariate dependence between several random variables proposed in Gaißer, Ruppert & Schmid (2010). Unlike Pearson's or rank correlation (Kendall's tau, Spearman's rho), it picks up dependence of any form.
data - n x d matrix containing n realizations of d random variables, association between which is to be measures.
Output: phi - 1x1 measure of association (phi = 0 corresponds to mutual independence of variables in columns of data, phi = 1 - increasing deterministic (not necessarily linear) relationship.
Gaißer, S., Ruppert, M., & Schmid, F. (2010). A multivariate version of Hoeffding’s Phi-Square. Journal of Multivariate Analysis, 101(10), 2571-2586.
Ivan Medovikov (2020). Multivariate Hoeffding's Phi-Squared (https://www.mathworks.com/matlabcentral/fileexchange/46773-multivariate-hoeffding-s-phi-squared), MATLAB Central File Exchange. Retrieved .