4.6 Article

Alternating Direction Method of Multipliers for Convolutive Non-Negative Matrix Factorization

期刊

IEEE TRANSACTIONS ON CYBERNETICS
卷 -, 期 -, 页码 -

出版社

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2022.3204723

关键词

Alternating direction method of multipliers (ADMMs); beta-divergence; convolutive basis; non-negative matrix factorization (NMF)

资金

  1. Natural Science Foundation of China [61906213]
  2. Natural Science Foundation of Jiangsu Province for Excellent Young Scholars [BK20180080]

向作者/读者索取更多资源

This article proposes a variable splitting based convolutive NMF algorithm to address the issues of low convergence rates, difficulty in reaching optimal solutions, and sparse results. Experimental results demonstrate the superiority of the proposed algorithm in terms of efficiency, optimal solutions, and sparsity.
Non-negative matrix factorization (NMF) has become a popular method for learning interpretable patterns from data. As one of the variants of standard NMF, convolutive NMF (CNMF) incorporates an extra time dimension to each basis, known as convolutive bases, which is well suited for representing sequential patterns. Previously proposed algorithms for solving CNMF use multiplicative updates which can be derived by either heuristic or majorization-minimization (MM) methods. However, these algorithms suffer from problems, such as low convergence rates, difficulty to reach exact zeroes during iterations and prone to poor local optima. Inspired by the success of alternating direction method of multipliers (ADMMs) on solving NMF, we explore variable splitting (i.e., the core idea of ADMM) for CNMF in this article. New closed-form algorithms of CNMF are derived with the commonly used beta-divergences as optimization objectives. Experimental results have demonstrated the efficacy of the proposed algorithms on their faster convergence, better optima, and sparser results than state-of-the-art baselines.

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