On revealing replicating structures in multiway data: a novel tensor decomposition approach

Authors:
Anh Huy Phan;Andrzej Cichocki;Petr Tichavský;Danilo P. Mandic;Kiyotoshi Matsuoka
Affiliations:
Brain Science Institute - RIKEN, Japan;Brain Science Institute - RIKEN, Japan;Institute of Information Theory and Automation, Czech Republic;Imperial College, London, United Kingdom;Kyushu University of Technology, Japan
Venue:
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Year:
2012

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Abstract

A novel tensor decomposition is proposed to make it possible to identify replicating structures in complex data, such as textures and patterns in music spectrograms. In order to establish a computational framework for this paradigm, we adopt a multiway (tensor) approach. To this end, a novel tensor product is introduced, and the subsequent analysis of its properties shows a perfect match to the task of identification of recurrent structures present in the data. Out of a whole class of possible algorithms, we illuminate those derived so as to cater for orthogonal and nonnegative patterns. Simulations on texture images and a complex music sequence confirm the benefits of the proposed model and of the associated learning algorithms.