Smooth nonnegative matrix and tensor factorizations for robust multi-way data analysis

Tatsuya Yokota

doi:10.1016/j.sigpro.2015.02.003

Smooth nonnegative matrix and tensor factorizations for robust multi-way data analysis

2015-08-01

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DOI：10.1016/j.sigpro.2015.02.003

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Abstract

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In this paper, we discuss new efficient algorithms for nonnegative matrix factorization (NMF) with smoothness constraints imposed on nonnegative components or factors. Such constraints allow us to alleviate certain ambiguity problems, which facilitates better physical interpretation or meaning. In our approach, various basis functions are exploited to flexibly and efficiently represent the smooth nonnegative components. For noisy input data, the proposed algorithms are more robust than the existing smooth and sparse NMF algorithms. Moreover, we extend the proposed approach to the smooth nonnegative Tucker decomposition and smooth nonnegative canonical polyadic decomposition (also called smooth nonnegative tensor factorization). Finally, we conduct extensive experiments on synthetic and real-world multi-way array data to demonstrate the advantages of the proposed algorithms. (C) 2015 Elsevier B.V. All rights reserved.

Keywords:

Nonnegative matrix factorization (NMF)

Nonnegative tensor factorization (NTF)

Smooth component analysis (SmCA)

Blind source separation (BSS)

Multi-way data analysis

Gaussian radial basis function (GRBF)

Smooth nonnegative matrix and tensor factorizations for robust multi-way data analysis

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