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In this paper, we present the algorithm that alters the subset of marginalsof multivariate standard distributed data into such modelled by an Archimedeancopula. Proposed algorithm leaves a correlation matrix almost unchanged, butintroduces a higher order correlation into a subset of marginals. Our datatransformation algorithm can be used to analyse whether particular machinelearning algorithm, especially a dimensionality reduction one, utilises higherorder correlations or not. We present an exemplary application on two featuresselection algorithms, mention that features selection is one of the approachesto dimensionality reduction. To measure higher order correlation, we usemultivariate higher order cumulants, hence to utilises higher ordercorrelations be to use the Joint Skewness Band Selection (JSBS) algorithm thatuses third-order multivariate cumulant. We show the robust performance of theJSBS in contrary to the poor performance of the Maximum Ellipsoid Volume (MEV)algorithm that does not utilise such higher order correlations. With thisresult, we confirm the potential application of our data generation algorithmto analyse a performance of various dimensionality reduction algorithms.

Introducing higher order correlations to marginals' subset of multivariate data by means of Archimedean copulas