  In this paper, we present the algorithm that alters the subset of marginals
of multivariate standard distributed data into such modelled by an Archimedean
copula. Proposed algorithm leaves a correlation matrix almost unchanged, but
introduces a higher order correlation into a subset of marginals. Our data
transformation algorithm can be used to analyse whether particular machine
learning algorithm, especially a dimensionality reduction one, utilises higher
order correlations or not. We present an exemplary application on two features
selection algorithms, mention that features selection is one of the approaches
to dimensionality reduction. To measure higher order correlation, we use
multivariate higher order cumulants, hence to utilises higher order
correlations be to use the Joint Skewness Band Selection (JSBS) algorithm that
uses third-order multivariate cumulant. We show the robust performance of the
JSBS in contrary to the poor performance of the Maximum Ellipsoid Volume (MEV)
algorithm that does not utilise such higher order correlations. With this
result, we confirm the potential application of our data generation algorithm
to analyse a performance of various dimensionality reduction algorithms.
