Nonlinear Coordinate Unfolding Via Principal Curve Projections with Application to Nonlinear BSS

Authors:
Deniz Erdogmus;Umut Ozertem
Affiliations:
Department of CSEE, Oregon Health and Science University, Portland, USA;Department of CSEE, Oregon Health and Science University, Portland, USA
Venue:
Neural Information Processing
Year:
2008

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Abstract

Nonlinear independent components analysis (NICA) is known to be an ill-posed problem when only the independence of the sources are sought. Additional constraints on the distribution of the sources or the structure of the mixing nonlinearity are imposed to achieve a solution that is unique in a suitable sense. In this paper, we present a technique that tackles nonlinear blind source separation (NBSS) as a nonlinear invertible coordinate unfolding problem utilizing a recently developed definition of maximum-likelihood principal curves. The proposition would be applicable most conveniently to independent unimodal source distributions with mixtures that have diminishing second order derivatives along the source axes. Application to multimodal sources would be possible with some modifications that are not discussed in this paper. The ill-posed nature of NBSS is also discussed from a differential geometric perspective in this context.