A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion

2023/10/08 by Wang, Zhi-Yong, So, Hing Cheung
#Audio and Speech Processing (eess.AS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Image and Video Processing (eess.IV) #Information Retrieval (cs.IR) #Machine Learning (cs.LG) #Optimization and Control (math.OC) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2310.04954

Abstract

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.

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