Hierarchical Extraction of Independent Subspaces of Unknown Dimensions

Authors:
Peter Gruber;Harold W. Gutch;Fabian J. Theis
Affiliations:
Computational Intelligence Group, Institute for Biophysics, University of Regensburg, Regensburg, Germany 93040;Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany;Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany and CMB, Institute for Bioinformatics and Systems Biology, Helmholtz Zentrum München, Germany
Venue:
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Year:
2009

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Abstract

Independent Subspace Analysis (ISA) is an extension of Independent Component Analysis (ICA) that aims to linearly transform a random vector such as to render groups of its components mutually independent. A recently proposed fixed-point algorithm is able to locally perform ISA if the sizes of the subspaces are known, however global convergence is a serious problem as the proposed cost function has additional local minima. We introduce an extension to this algorithm, based on the idea that the algorithm converges to a solution, in which subspaces that are members of the global minimum occur with a higher frequency. We show that this overcomes the algorithm's limitations. Moreover, this idea allows a blind approach, where no a priori knowledge of subspace sizes is required.