A stochastic proximal alternating minimization algorithm for nonnegative matrix decomposition

Lijun Xu; Chenghua Ji; Yijia Zhou

doi:10.1117/12.2691997

23 August 2023 A stochastic proximal alternating minimization algorithm for nonnegative matrix decomposition

Lijun Xu, Chenghua Ji, Yijia Zhou

Proceedings Volume 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023); 127843J (2023) https://doi.org/10.1117/12.2691997
Event: 2023 2nd International Conference on Applied Statistics, Computational Mathematics and Software Engineering (ASCMSE 2023), 2023, Kaifeng, China

Abstract

The stochastic Proximal Alternating Linearized Minimization (PALM) algorithm is an effective method for solving non-smooth non-convex problems. In this paper, we extend this method to solve non-negative matrix factorization with finite and structured constraints. We propose a new approach for calculating stochastic gradients and provide the theoretical analysis on the presented stochastic proximal alternating algorithm. The new algorithm is proved to have linear convergence rates with variance-reduction stochastic gradient estimators such as SAG, SAGA and SVRG. In addition, we conduct numerical experiments to compare the performance of three stochastic gradient estimators, and finally obtain that the algorithms with SVRG gradient estimators is shown to be more effective for solving nonnegative matrix decomposition problems.

Citation Download Citation

Lijun Xu, Chenghua Ji, and Yijia Zhou "A stochastic proximal alternating minimization algorithm for nonnegative matrix decomposition", Proc. SPIE 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023), 127843J (23 August 2023); https://doi.org/10.1117/12.2691997

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