2016
DOI: 10.1109/tsp.2016.2526960
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Joint Independent Subspace Analysis Using Second-Order Statistics

Abstract: International audienceThis paper deals with a novel generalization of classical blind source separation (BSS) in two directions. First, relaxing the constraint that the latent sources must be statistically independent. This generalization is well-known and sometimes termed independent subspace analysis (ISA). Second, jointly analyzing several ISA problems, where the link is due to statistical dependence among corresponding sources in different mixtures. When the data are one-dimensional, i.e., multiple classic… Show more

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Cited by 31 publications
(58 citation statements)
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“…IVA extends CCA [1] and its multiset extension (MCCA) [3], which have both been widely used for fusion [31], [36], [58], [116]- [118], to the case where not only second-order statistics but all-order statistics are taken into account [82]. Recently, a generalization of IVA that allows decomposition into terms of rank larger than one has been proposed [119]- [121]. In addition, since IVA is a generalization of ICA, it readily accommodates additional types of diversity such as coloured (i.e., not spectrally flat) or nonstationary sources [111], [122] (recall Section III-C1).…”
Section: A Link Between Data Sets As a New Form Of Diversitymentioning
confidence: 99%
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“…IVA extends CCA [1] and its multiset extension (MCCA) [3], which have both been widely used for fusion [31], [36], [58], [116]- [118], to the case where not only second-order statistics but all-order statistics are taken into account [82]. Recently, a generalization of IVA that allows decomposition into terms of rank larger than one has been proposed [119]- [121]. In addition, since IVA is a generalization of ICA, it readily accommodates additional types of diversity such as coloured (i.e., not spectrally flat) or nonstationary sources [111], [122] (recall Section III-C1).…”
Section: A Link Between Data Sets As a New Form Of Diversitymentioning
confidence: 99%
“…More specifically, they readily admit various types of diversity. A first generalization of these basic models is by relaxing the assumptions within each decomposition: allowing statistical dependence between latent sources of the same mixture in ICA (respectively, IVA) leads to independent subspace analysis (ISA) [128]- [132] (respectively, joint independent subspace analysis (JISA) [119]- [121]) as well as other BSS models [133], [134]. Relaxing the sum-of-rank-1-terms constraint in PARAFAC leads to more flexible tensor decompositions such as Tucker [6], [7], block term decomposition (BTD) [135], three-way decomposition into directional components (DEDICOM) [136], and others [137].…”
Section: A Link Between Data Sets As a New Form Of Diversitymentioning
confidence: 99%
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“…This observation is in agreement with the literature. The joint separation of correlated mixtures can be achieved using only second-order statistics [6], [51]. Uncorrelated mixtures arise, for instance, in the frequency-domain separation of convolutive mixtures.…”
Section: B Gradient Of the Contrast Functionmentioning
confidence: 99%
“…In linear second-order independence-based MDU models, identifiability is not attainable in cases were two or more subspaces share an identical block correlation structure [39], [40]. Recent initial work [41] developed for linear second-order independence-based MDM models suggests a combination of conditions from SDM and MDU. In the non-linear case, however, independence-based SDU models are unidentifiable if independence is the only assumption [1, Ch.14].…”
Section: A Unified Framework For Subspace Modeling and Developmentmentioning
confidence: 99%