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