Hiding higher order cross-correlations of multivariate data using Archimedean copulas

In this paper we present the algorithm that changes the subset of marginals of multivariate normal distributed data into such modelled by an Archimedean copula. Proposed algorithm leaves a correlation matrix almost unchanged, but introduces a higher order crosscorrelation measured by high order multivariate cumulant tensors. Given the algorithm, we analyse the ability of cumulants based features selection methods to detect a subset of changed data. We show numerically that the performance of the method based on a second cumulant (a covariance matrix) is weak comparing to method that uses the 3 order multivariate cumulant tensor. Our data generation algorithm can be used for hiding information in randomly distributed data or for the features discrimination algorithms comparison.