Gutch, Harold W. and Theis, Fabian J. (2007) Independent Subspace Analysis Is Unique, Given Irreducibility. In: Davies, Mike E. and James, Christopher J., (eds.) Independent Component Analysis and Signal Separation. 7th International Conference, ICA 2007, London, UK, September 9-12, 2007. Proceedings. Lecture notes in computer science, 4666. Springer, Berlin, pp. 49-56. ISBN 978-3-540-74493-1 (Printausgabe), 978-3-540-74494-8 (e-book).
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Independent Subspace Analysis (ISA) is a generalization of ICA. It tries to find a basis in which a given random vector can be decomposed into groups of mutually independent random vectors. Since the first introduction of ISA, various algorithms to solve this problem have been introduced, however a general proof of the uniqueness of ISA decompositions remained an open question. In this contribution we address this question and sketch a proof for the separability of ISA. The key condition for separability is to require the subspaces to be not further decomposable (irreducible). Based on a decomposition into irreducible components, we formulate a general model for ISA without restrictions on the group sizes. The validity of the uniqueness result is illustrated on a toy example. Moreover, an extension of ISA to subspace extraction is introduced and its indeterminacies are discussed.
|Item Type:||Book Section|
|Institutions:||Biology, Preclinical Medicine > Institut für Biophysik und physikalische Biochemie > Prof. Dr. Elmar Lang|
|Subjects:||500 Science > 570 Life sciences|
|Created at the University of Regensburg:||Unknown|
|Deposited On:||28 Sep 2010 06:22|
|Last Modified:||28 Sep 2010 06:22|