Copula Based Independent Component Analysis
Kobi Abayomi, Upmanu Lall, Victor de la Peña · SSRN Electronic Journal · 2008
We propose a parametric version of Independent Component Analysis (ICA) via Copulas families of multivariate distributions that join univariate margins to multivariate distributions. Our procedure exploits the role for copula models in information theory and in measures of association, specically: the use of copulae densities as parametric mutual information, and as measures of association on the rank statistics. The copula approach oers a unied view of component analysis procedures, in particular, by parameterizing multivariate dependence. ICA then, via the copula, is a generalization of Principal Component Analysis (PCA) - where the copula model may be non-Gaussian. Generally, the goal is to orthogonalize a measure of multivariate dispersion, yielding an orthogonal basis for a multivariate data set. The exibility of the copula approach allows for parameterizations of non-gaussian, non-monotone dependence. Additionally, we note a possible use for the copula approach in generalized component extraction procedures (such as Canonical Correlation Analysis) and ultimately the broader class of Generalized Linear Models.