A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Independent component analysis for tensor-valued data
Tekijät: Virta J, Li B, Nordhausen K, Oja H
Kustantaja: ELSEVIER INC
Julkaisuvuosi: 2017
Journal: Journal of Multivariate Analysis
Tietokannassa oleva lehden nimi: JOURNAL OF MULTIVARIATE ANALYSIS
Lehden akronyymi: J MULTIVARIATE ANAL
Vuosikerta: 162
Aloitussivu: 172
Lopetussivu: 192
Sivujen määrä: 21
ISSN: 0047-259X
DOI: https://doi.org/10.1016/j.jmva.2017.09.008
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/27390341
Tiivistelmä
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. (C) 2017 Elsevier Inc. All rights reserved.
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. (C) 2017 Elsevier Inc. All rights reserved.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
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