A geometric algorithm for overcomplete linear ICA

Geometric algorithms for linear square independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative case of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (Neural Process. Lett. 2 (1995), Signal Processing 46 (1995) 267) in order to separate linear mixtures. We generalize these algorithms to overcomplete cases with more sources than sensors. With geometric ICA we get an efficient method for the matrix-recovery step in the framework of a two-step approach to the source separation problem. The second step-source-recovery-uses a maximum-likelihood approach. There we prove that the shortest-path algorithm as proposed by Bofill and Zibulevsky (in: P. Pajunen, J. Karhunen (Eds.), Independent Component Analysis and Blind Signal Separation (Proceedings of ICA'2000), 2000, pp. 87-92) indeed solves the maximum-likelihood conditions. (C) 2003 Elsevier B.V. All rights reserved.