Independent Subspace Analysis on Innovations

Independent subspace analysis (ISA) that deals with multi-dimensional independent sources, is a generalization of independent component analysis (ICA). However, all known ISA algorithms may become ineffective when the sources possess temporal structure. The innovation process instead of the original mixtures has been proposed to solve ICA problems with temporal dependencies. Here we show that this strategy can be applied to ISA as well. We demonstrate the idea on a mixture of 3D processes and also on a mixture of facial pictures used as two-dimensional deterministic sources. ISA on innovations was able to find the original subspaces, while plain ISA was not.