RESEARCH ARTICLE

Nonnegative non-redundant tensor decomposition

  • Olexiy KYRGYZOV , 1 ,
  • Deniz ERDOGMUS 2
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  • 1. Laboratoire d’Outils pour l’Analyse de Donńeees, LIST, CEA, Gif-sur-Yvette, F-91911, France
  • 2. Cognitive Systems Lab, Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA

Received date: 01 Apr 2012

Accepted date: 10 Oct 2012

Published date: 01 Feb 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Nonnegative tensor decomposition allows us to analyze data in their ‘native’ form and to present results in the form of the sum of rank-1 tensors that does not nullify any parts of the factors. In this paper, we propose the geometrical structure of a basis vector frame for sum-of-rank-1 type decomposition of real-valued nonnegative tensors. The decomposition we propose reinterprets the orthogonality property of the singularvectors of matrices as a geometric constraint on the rank-1 matrix bases which leads to a geometrically constrained singularvector frame. Relaxing the orthogonality requirement, we developed a set of structured-bases that can be utilized to decompose any tensor into a similar constrained sum-of-rank-1 decomposition. The proposed approach is essentially a reparametrization and gives us an upper bound of the rank for tensors. At first, we describe the general case of tensor decomposition and then extend it to its nonnegative form. At the end of this paper, we show numerical results which conform to the proposed tensor model and utilize it for nonnegative data decomposition.

Cite this article

Olexiy KYRGYZOV , Deniz ERDOGMUS . Nonnegative non-redundant tensor decomposition[J]. Frontiers of Mathematics in China, 0 , 8(1) : 41 -61 . DOI: 10.1007/s11464-012-0261-y

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