Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation
<|reference_start|>Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation: 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.<|reference_end|>
@article{führling2024discrete,
    title={Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm
  Approximation},
    author={Niclas F"uhrling, Kengo Ando, Giuseppe Thadeu Freitas de Abreu, David
  Gonz'alez G., Osvaldo Gonsa},
    journal={arXiv preprint arXiv:2405.02101},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.02101},
    primaryClass={eess.SP cs.LG}
}