Discrete Aware Matrix Completion via Convexized ℓ₀-Norm Approximation

2024/05/03 by Führling, Niclas, Ando, Kengo, de Abreu, Giuseppe Thadeu Freitas +2
#FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2405.02101

Abstract

We consider a novel algorithm, for the completion of partially observed low-rank matrices in a structured setting where each entry can be chosen from a finite discrete alphabet set, such as in common recommender systems. The proposed low-rank matrix completion (MC) method is an improved variation of state-of-the-art (SotA) discrete aware matrix completion method which we previously proposed, in which discreteness is enforced by an ℓ₀-norm regularizer, not by replaced with the ℓ₁-norm, but instead approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework. Simulation results demonstrate the superior performance of the new method compared to the SotA techniques as well as the earlier ℓ₁-norm-based discrete-aware matrix completion approach.

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