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

Tatsuya Yokota, Rafal Zdunek, Andrzej Cichocki, Yukihiko Yamashita

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)234-249
Number of pages16
JournalSignal Processing
Publication statusPublished - Aug 2015
Externally publishedYes


  • Blind source separation (BSS)
  • Gaussian radial basis function (GRBF)
  • Multi-way data analysis
  • Nonnegative matrix factorization (NMF)
  • Nonnegative tensor factorization (NTF)
  • Smooth component analysis (SmCA)


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