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Independent subspace analysis is unique, given irreducibility.
Lect. Notes Comput. Sc. 4666, 49-56 (2007)
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.
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Publikationstyp
Artikel: Journalartikel
Dokumenttyp
Wissenschaftlicher Artikel
ISSN (print) / ISBN
0302-9743
e-ISSN
1611-3349
Zeitschrift
Lecture Notes in Computer Science
Quellenangaben
Band: 4666,
Seiten: 49-56
Verlag
Springer
Verlagsort
Berlin [u.a.]
Nichtpatentliteratur
Publikationen
Institut(e)
Institute of Computational Biology (ICB)