Scatter Matrices and Independent Component Analysis

Abstract

In the independent component analysis (ICA) it is assumed that the components of the multivariate independent and identically distributed observations are linear transformations of latent independent components. The problem then is to find the (linear) transformation which transforms the observations back to independent components. In the paper the ICA is discussed and it is shown that, under some mild assumptions, two scatter matrices may be used together to find the independent components. The scatter matrices must then have the so called independence property. The theory is illustrated by examples.