 Uniqueness of linear factorizations into independent subspacesHarold W. Gutch and Fabian J. Theis Journal of Multivariate Analysis, 2012, vol. 112, issue C, 48-62 Abstract: 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 (S1,…,SM)=(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. Keywords: Statistical independence; Independent component analysis; Independent subspace analysis; Separability; Inverse models (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:112:y:2012:i:c:p:48-62 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2012.05.019 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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