A geometric algorithm for overcomplete linear ICA

Geometric algorithms for linear quadratic independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA has been proposed first by Puntonet and Prieto [1] [2] 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 matrixrecovery step in the framework of a two-step approach to the source separation problem. The second step — sourcerecovery — uses a maximum-likelihood approach. There we prove that the shortest-path algorithm as proposed by Bofill and Zibulevsky in [3] indeed solves the maximumlikelihood conditions.