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Welling,
Max
A Constrained EM Algorithm for Independent Component Analysis We introduce a novel way of performing Independent Component Analysis using a constrained version of the Expectation Maximization algorithm. The constraint imposes othogonality on the mixing matrix, A, and removes D(D+1) degrees of freedom from the estimation problem, where D is the number of sources. This results in an efficient algorithm, especially in the case of a large number of sources, without restricting its general applicability. The source distributions are modeled as D one-dimensional mixtures of Gaussians. The observed data are modeled as linear mixtures of the sources with additive, isotropic noise. This generative model is fit to the data using constrained E.M. In order to adaptively model both, sub- and super-Gaussian source distributions, we introduce a "soft-switch" approach which updates one parameter per source at every iteration of E.M. We experimentally show that the method performs comparably to other widely used approaches to the Independent Component Analysis problem and performs particularly well in the case of few data.
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