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Algorithms for sparse nonnegative Tucker decompositions.

Morten Mørup1, Lars Kai Hansen, Sidse M Arnfred

  • 1Technical University of Denmark, 2800 Kongens Lyngby, Denmark. mm@imm.dtu.dk

Neural Computation
|April 5, 2008
PubMed
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This study introduces sparse nonnegative Tucker decomposition (SN-TUCKER) algorithms for analyzing multiway data. These methods improve interpretability and model selection for nonnegative tensor data.

Area of Science:

  • Multiway data analysis
  • Tensor decomposition
  • Nonnegative matrix factorization

Background:

  • Increasing interest in analyzing large-scale multiway (tensor) data.
  • Tucker and PARAFAC models are common tensor decomposition techniques.
  • Nonnegative matrix factorization (NMF) offers interpretable, part-based representations.

Purpose of the Study:

  • Extend NMF to Tucker decomposition for nonnegative tensor data.
  • Develop sparse nonnegative Tucker decomposition (SN-TUCKER) algorithms.
  • Reduce ambiguities in tensor decomposition through imposed sparseness.

Main Methods:

  • Developed novel updates for sparse nonnegative Tucker decompositions (SN-TUCKER).
  • Algorithms impose sparseness in any combination of tensor modalities.

Related Experiment Videos

  • Utilized sparse coding for model selection and component selection.

    • Main Results:

    • Proposed SN-TUCKER algorithms outperform existing Tucker decomposition methods for nonnegative data.
    • Demonstrated superiority in handling nonnegative tensor data and interactions.
    • Showcased sparse coding's ability to aid model (PARAFAC vs. Tucker) and component selection.

    Conclusions:

    • SN-TUCKER provides a powerful tool for analyzing nonnegative multiway data.
    • Sparse coding enhances the interpretability and selection capabilities of tensor decomposition.
    • Algorithms are available for practical application in multiway data analysis.