Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation

• URL: http://arxiv.org/abs/2405.02101v2
• Date: Wed, 06 Nov 2024 14:50:24 GMT
• Title: Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation
• Authors: Niclas Führling, Kengo Ando, Giuseppe Thadeu Freitas de Abreu, David González G., Osvaldo Gonsa,
• Abstract summary: We consider a novel algorithm for the completion of partially observed low-rank matrices in a structured setting. The proposed low-rank matrix completion (MC) method is an improved variation of state-of-the-art (SotA) discrete aware matrix completion method.
• Score: 7.447205347712796
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\ell_0$-norm regularizer, not by replaced with the $\ell_1$-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 $\ell_1$-norm-based discrete-aware matrix completion approach.

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