Matrix Completion via Non-Convex Relaxation and Adaptive Correlation Learning
The existing matrix completion methods focus on optimizing the relaxation of rank function such as nuclear norm, Schatten- p norm, etc. They usually need many iterations to converge. Moreover, only the low-rank property of matrices is utilized in most existing models and several methods that incorpo...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 45(2023), 2 vom: 07. Feb., Seite 1981-1991 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2023
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article |
| Zusammenfassung: | The existing matrix completion methods focus on optimizing the relaxation of rank function such as nuclear norm, Schatten- p norm, etc. They usually need many iterations to converge. Moreover, only the low-rank property of matrices is utilized in most existing models and several methods that incorporate other knowledge are quite time-consuming in practice. To address these issues, we propose a novel non-convex surrogate that can be optimized by closed-form solutions, such that it empirically converges within dozens of iterations. Besides, the optimization is parameter-free and the convergence is proved. Compared with the relaxation of rank, the surrogate is motivated by optimizing an upper-bound of rank. We theoretically validate that it is equivalent to the existing matrix completion models. Besides the low-rank assumption, we intend to exploit the column-wise correlation for matrix completion, and thus an adaptive correlation learning, which is scaling-invariant, is developed. More importantly, after incorporating the correlation learning, the model can be still solved by closed-form solutions such that it still converges fast. Experiments show the effectiveness of the non-convex surrogate and adaptive correlation learning |
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| Beschreibung: | Date Completed 06.04.2023 Date Revised 06.04.2023 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2022.3157083 |