Abstract
Recently geometric independent component analysis (ICA) has been generalized to overcomplete cases (overcomplete geoICA) with more sources than sensors. Here, we put this algorithm in the two-step framework. We generalize the geometric theory of quadratic case to the overcomplete case showing that fixpoints of geometric ICA fulfill a so called geometric convergence condition, which the mixed ...
Abstract
Recently geometric independent component analysis (ICA) has been generalized to overcomplete cases (overcomplete geoICA) with more sources than sensors. Here, we put this algorithm in the two-step framework. We generalize the geometric theory of quadratic case to the overcomplete case showing that fixpoints of geometric ICA fulfill a so called geometric convergence condition, which the mixed images of the unit vectors satisfy, too. This leads to a conjecture claiming that in the supergaussian unimodal symmetric case there is only one stable fixpoint, thus demonstrating uniqueness of overcomplete geoICA after convergence.
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