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arXiv · 2405.02101

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

Niclas Führling·Kengo Ando·Giuseppe Thadeu Freitas de Abreu·David González G.·Osvaldo Gonsa
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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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Niclas Führling, Kengo Ando, Giuseppe Thadeu Freitas de Abreu, David González G., Osvaldo Gonsa. 2024-05-03. Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation. https://arxiv.org/abs/2405.02101

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