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Open Access Green as soon as Postprint is submitted to ZB.
Uniqueness of linear factorizations into independent subspaces.
J. Multivar. Anal. 112, 48-62 (2012)
Given a random vector X, we address the question of linear separability of X. that is, the task of finding a linear operator W such that we have (S-1, ... , S-M) = (WX) with statistically independent random vectors Si. As this requirement alone is already fulfilled trivially by X being independent of the empty rest, we require that the components be not further decomposable. We show that if X has finite covariance, such a representation is unique up to trivial indeterminacies. We propose an algorithm based on this proof and demonstrate its applicability. Related algorithms, however with fixed dimensionality of the subspaces, have already been successfully employed in biomedical applications, such as separation of fMRI recorded data. Based on the presented uniqueness result, it is now clear that also subspace dimensions can be determined in a unique and therefore meaningful fashion, which shows the advantages of independent subspace analysis in contrast to methods like principal component analysis.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Statistical Independence ; Independent Component Analysis ; Independent Subspace Analysis ; Separability ; Inverse Models; BLIND SOURCE SEPARATION; COMPONENT ANALYSIS; ALGORITHM; FMRI; ICA
ISSN (print) / ISBN
0047-259X
e-ISSN
1095-7243
Journal
Journal of Multivariate Analysis
Quellenangaben
Volume: 112,
Pages: 48-62
Publisher
Elsevier
Non-patent literature
Publications
Reviewing status
Peer reviewed