Independent component analysis for tensor-valued data

In preprocessing tensor-valued data, e.g., images and videos, a common procedure is to vectorize the observations and subject the resulting vectors to one of the many methods used for independent component analysis (ICA). However, the tensor structure of the original data is lost in the vectorizatio...

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Bibliographic Details
Published inJournal of multivariate analysis Vol. 162; pp. 172 - 192
Main Authors Virta, Joni, Li, Bing, Nordhausen, Klaus, Oja, Hannu
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2017
Subjects
FOBI
Kronecker structure
Matrix-valued data
Multilinear algebra
Matrix-valued data
FOBI
Multilinear algebra
62G20
62H10
62H12
Kronecker structure
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Summary:In preprocessing tensor-valued data, e.g., images and videos, a common procedure is to vectorize the observations and subject the resulting vectors to one of the many methods used for independent component analysis (ICA). However, the tensor structure of the original data is lost in the vectorization and, as a more suitable alternative, we propose the matrix- and tensor fourth order blind identification (MFOBI and TFOBI). In these tensorial extensions of the classic fourth order blind identification (FOBI) we assume a Kronecker structure for the mixing and perform FOBI simultaneously on each direction of the observed tensors. We discuss the theory and assumptions behind MFOBI and TFOBI and provide two different algorithms and related estimates of the unmixing matrices along with their asymptotic properties. Finally, simulations are used to compare the method’s performance with that of classical FOBI for vectorized data and we end with a real data clustering example.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2017.09.008