Nonnegative Tensor Factorization with Smoothness Constraints

  • Rafal Zdunek
  • Tomasz M. Rutkowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5226)

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.

Keywords

Nonnegative Tensor Factorization (NTF) multiarray spectra analysis Markov Random Field (MRF) 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rafal Zdunek
    • 1
  • Tomasz M. Rutkowski
    • 2
  1. 1.Institute of Telecommunications, Teleinformatics and AcousticsWroclaw University of TechnologyWroclawPoland
  2. 2.RIKEN Brain Science InstituteWako-shiJapan

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