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Sketch-based multiplicative updating algorithms for symmetric nonnegative tensor factorizations with applications to face image clustering

Author

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  • Maolin Che

    (Southwestern University of Finance and Economics
    Center for Intelligent Multidimensional Data Analysis, Hong Kong Science Park)

  • Yimin Wei

    (Fudan University)

  • Hong Yan

    (City University of Hong Kong)

Abstract

Nonnegative tensor factorizations (NTF) have applications in statistics, computer vision, exploratory multi-way data analysis, and blind source separation. This paper studies randomized multiplicative updating algorithms for symmetric NTF via random projections and random samplings. For random projections, we consider two methods to generate the random matrix and analyze the computational complexity, while for random samplings the uniform sampling strategy and its variants are examined. The mixing of these two strategies is then considered. Some theoretical results are presented based on the bounds of the singular values of sub-Gaussian matrices and the fact that randomly sampling rows from an orthogonal matrix results in a well-conditioned matrix. These algorithms are easy to implement, and their efficiency is verified via test tensors from both synthetic and real datasets, such as for clustering facial images.

Suggested Citation

  • Maolin Che & Yimin Wei & Hong Yan, 2024. "Sketch-based multiplicative updating algorithms for symmetric nonnegative tensor factorizations with applications to face image clustering," Journal of Global Optimization, Springer, vol. 89(4), pages 995-1032, August.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:4:d:10.1007_s10898-024-01374-4
    DOI: 10.1007/s10898-024-01374-4
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