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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02101 |
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| _version_ | 1866909378715582464 |
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| author | Führling, Niclas Ando, Kengo de Abreu, Giuseppe Thadeu Freitas G., David González Gonsa, Osvaldo |
| author_facet | Führling, Niclas Ando, Kengo de Abreu, Giuseppe Thadeu Freitas G., David González Gonsa, Osvaldo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02101 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation Führling, Niclas Ando, Kengo de Abreu, Giuseppe Thadeu Freitas G., David González Gonsa, Osvaldo Signal Processing Machine Learning 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. |
| title | Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2405.02101 |