Towards Nonstationary, Nonparametric Independent Process Analysis with Unknown Source Component Dimensions

The goal of this paper is to extend independent subspace analysis (ISA) to the case of (i) nonparametric, not strictly stationary source dynamics and (ii) unknown source component dimensions. We make use of functional autoregressive (fAR) processes to model the temporal evolution of the hidden sources. An extension of the ISA separation principle--which states that the ISA problem can be solved by traditional independent component analysis (ICA) and clustering of the ICA elements--is derived for the solution of the defined fAR independent process analysis task (fAR-IPA): applying fAR identification we reduce the problem to ISA. A local averaging approach, the Nadaraya-Watson kernel regression technique is adapted to obtain strongly consistent fAR estimation. We extend the Amari-index to different dimensional components and illustrate the efficiency of the fAR-IPA approach by numerical examples.