Second order subspace analysis and simple decompositions

Authors:
Harold W. Gutch;Takanori Maehara;Fabian J. Theis
Affiliations:
Max Planck Institute for Dynamics and Self-Organization, Department of Nonlinear Dynamics, Germany and Technical University of Munich, Germany;University of Tokyo, Japan;Technical University of Munich, Germany and Helmholtz-Institute Neuherberg, Germany
Venue:
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Year:
2010

Citing 4
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Abstract

The recovery of the mixture of an N-dimensional signal generated by N independent processes is a well studied problem (see e.g. [1,10]) and robust algorithms that solve this problem by Joint Diagonalization exist. While there is a lot of empirical evidence suggesting that these algorithms are also capable of solving the case where the source signals have block structure (apart from a final permutation recovery step), this claim could not be shown yet - even more, it previously was not known if this model separable at all. We present a precise definition of the subspace model, introducing the notion of simple components, show that the decomposition into simple components is unique and present an algorithm handling the decomposition task.