Regensburg 2007 – scientific programme

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BP: Fachverband Biologische Physik

BP 26: Poster Session II

BP 26.45: Poster

Thursday, March 29, 2007, 17:00–19:30, Poster B

Identifying multidimensional subspaces in multivariate data — •Harold Gutch and Fabian Theis — Max-Planck-Institut für Dynamik und Selbstorganisation, Bunsenstraße 10, 37037 Göttingen, Germany

ICA is the task of recovering n signals S given only n linear mixings X of them (so X=AS) under the additional assumption of stochastical independence of the sources.

However, since we are operating blindly, i.e. we only know X not S, we cannot verify that X actually follows the ICA assumptions. We denote the task of recovering the sources S in the general case, where some dependencies exist between source components as independent subspace analysis (ISA). We call subsets of source components that are jointly stochastically independent of the rest and cannot be factorized nontrivially irreducible. Similarly to ICA, we again face the obvious indeterminacies of permutations of any number of irreducible random vectors of the same size, and scaling (which here translates to any linear invertible mixing within a single subspace).

In experiments, extensions of ICA algorithms have been shown to handle this model well, which is a good indicator that ISA gives unique solutions. Under the additional slight assumption of square-integrability of S (and hence X), we provide a full uniqueness proof in the case where S consists of two irreducible components. An algorithmic implementation handles the extraction of a single irreducible subspace from arbitrary X well, and we illustrate how to use this subspace extraction algorithm for dimension reduction.