Scatter Matrices with Independent Block Property and ISA

In Independent Component Analysis (ICA) it is often assumed that the p components of the observation vector are linear combinations of p underlying independent components. Two scatter matrices having the so called independence property can then be used to recover the independent components. The assumption of (exactly) p independent components is however often criticized, and several alternative and more realistic models have been suggested. One of these models is the independent subspace model where it is assumed that the p-variate observed vectors are based on k independent subvectors of lengths p1, pk, p1+pk = p. In Independent Subspace Analysis (ISA) the aim is to recover these subvectors.