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Nonnegative Tensor Factorization with Smoothness Constraints

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Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues (ICIC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5226))

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Abstract

Nonnegative Tensor Factorization (NTF) is an emerging technique in multidimensional signal analysis and it can be used to find parts-based representations of high-dimensional data. In many applications such as multichannel spectrogram processing or multiarray spectra analysis, the unknown features have locally smooth temporal or spatial structure. In this paper, we incorporate to an objective function in NTF additional smoothness constrains that considerably improve the unknown features. In our approach, we propose to use the Markov Random Field (MRF) model that is commonly-used in tomographic image reconstruction to model local smoothness properties of 2D reconstructed images. We extend this model to multidimensional case whereby smoothness can be enforced in all dimensions of a multi-dimensional array. We analyze different clique energy functions that are a subject to MRF. Some numerical results performed on a multidimensional image dataset are presented.

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Author information

Authors and Affiliations

  1. Institute of Telecommunications, Teleinformatics and Acoustics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Rafal Zdunek

  2. RIKEN Brain Science Institute, Wako-shi, Japan

    Tomasz M. Rutkowski

Authors
  1. Rafal Zdunek
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  2. Tomasz M. Rutkowski
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Editor information

Editors and Affiliations

  1. Department of Automation, University of Science and Technology of China, 230026, Hefei, Anhui, China

    De-Shuang Huang

  2. Applied Computational Intelligence Laboratory, P.O. Box

    Donald C. Wunsch II

  3. Arlington, USA

    Daniel S. Levine

  4. Graduate School of Electrical Engineering, University of Ulsan, Korea, San 29, Mugeo-Dong, 680 - 749, Nam-Ku, Ulsan, Korea

    Kang-Hyun Jo

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© 2008 Springer-Verlag Berlin Heidelberg

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Zdunek, R., Rutkowski, T.M. (2008). Nonnegative Tensor Factorization with Smoothness Constraints. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues. ICIC 2008. Lecture Notes in Computer Science, vol 5226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87442-3_38

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  • DOI: https://doi.org/10.1007/978-3-540-87442-3_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87440-9

  • Online ISBN: 978-3-540-87442-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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