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

Maolin Che (), Yimin Wei () and Hong Yan ()
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Maolin Che: Southwestern University of Finance and Economics
Yimin Wei: Fudan University
Hong Yan: City University of Hong Kong

Journal of Global Optimization, 2024, vol. 89, issue 4, No 7, 995-1032

Abstract: 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.

Keywords: Symmetric nonnegative tensor factorization; Multiplicative updating algorithms; Sketching; Random projection; Random sampling; 15A18; 15A69; 65F55; 68W20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01374-4

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