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Bulletin of the Polish Academy of Sciences Technical Sciences

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Fast and unique Tucker decompositions via multiway blind source separation

G. Zhou
  • Laboratory for Advanced Brain Signal Processing, RIKEN, Brain Science Institute, Wako-shi, Saitama 3510198, Japan / School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510641, China
/ A. Cichocki
  • RIKEN Brain Science Institute, 2-1 Hirosawa Wako City, Saitarna 351-0198, Japan / Electrotechnical Faculty, Warsaw University of Technology, 1 Politechniki Sq., 00-661 Warszawa, Poland / System Research Institute, 6 Newelska St., 01-447 Warszawa, Poland
  • :
Published Online: 2012-12-22 | DOI: https://doi.org/10.2478/v10175-012-0051-4


A multiway blind source separation (MBSS) method is developed to decompose large-scale tensor (multiway array) data. Benefitting from all kinds of well-established constrained low-rank matrix factorization methods, MBSS is quite flexible and able to extract unique and interpretable components with physical meaning. The multilinear structure of Tucker and the essential uniqueness of BSS methods allow MBSS to estimate each component matrix separately from an unfolding matrix in each mode. Consequently, alternating least squares (ALS) iterations, which are considered as the workhorse for tensor decompositions, can be avoided and various robust and efficient dimensionality reduction methods can be easily incorporated to pre-process the data, which makes MBSS extremely fast, especially for large-scale problems. Identification and uniqueness conditions are also discussed. Two practical issues dimensionality reduction and estimation of number of components are also addressed based on sparse and random fibers sampling. Extensive simulations confirmed the validity, flexibility, and high efficiency of the proposed method. We also demonstrated by simulations that the MBSS approach can successfully extract desired components while most existing algorithms may fail for ill-conditioned and large-scale problems.

Keywords : Multiway Blind Source Separation (MBSS); Multilinear Independent Component Analysis (MICA); Constrained tensor decompositions; Tucker models; Nonnegative Tucker Decomposition (NTD).

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Published Online: 2012-12-22

Published in Print: 2012-12-01

Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences. Volume 60, Issue 3, Pages 389–405, ISSN (Print) 0239-7528, DOI: https://doi.org/10.2478/v10175-012-0051-4, December 2012

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