A robust low-rank matrix completion based on truncated nuclear norm and Lp-norm
Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate fro...
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| Autor*in: |
Liang, Hao [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: The journal of supercomputing - Springer US, 1987, 78(2022), 11 vom: 13. März, Seite 12950-12972 |
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volume:78 ; year:2022 ; number:11 ; day:13 ; month:03 ; pages:12950-12972 |
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10.1007/s11227-022-04385-8 |
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| 520 | |a Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. | ||
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10.1007/s11227-022-04385-8 doi (DE-627)OLC207907346X (DE-He213)s11227-022-04385-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Liang, Hao verfasserin aut A robust low-rank matrix completion based on truncated nuclear norm and Lp-norm 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. Sparse representation Low-rank matrix completion Lp-norm Truncated nuclear norm Alternating direction multiplier method Kang, Li (orcid)0000-0003-4094-3348 aut Huang, Jianjun aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 11 vom: 13. März, Seite 12950-12972 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:11 day:13 month:03 pages:12950-12972 https://doi.org/10.1007/s11227-022-04385-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 11 13 03 12950-12972 |
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10.1007/s11227-022-04385-8 doi (DE-627)OLC207907346X (DE-He213)s11227-022-04385-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Liang, Hao verfasserin aut A robust low-rank matrix completion based on truncated nuclear norm and Lp-norm 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. Sparse representation Low-rank matrix completion Lp-norm Truncated nuclear norm Alternating direction multiplier method Kang, Li (orcid)0000-0003-4094-3348 aut Huang, Jianjun aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 11 vom: 13. März, Seite 12950-12972 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:11 day:13 month:03 pages:12950-12972 https://doi.org/10.1007/s11227-022-04385-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 11 13 03 12950-12972 |
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10.1007/s11227-022-04385-8 doi (DE-627)OLC207907346X (DE-He213)s11227-022-04385-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Liang, Hao verfasserin aut A robust low-rank matrix completion based on truncated nuclear norm and Lp-norm 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. Sparse representation Low-rank matrix completion Lp-norm Truncated nuclear norm Alternating direction multiplier method Kang, Li (orcid)0000-0003-4094-3348 aut Huang, Jianjun aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 11 vom: 13. März, Seite 12950-12972 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:11 day:13 month:03 pages:12950-12972 https://doi.org/10.1007/s11227-022-04385-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 11 13 03 12950-12972 |
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10.1007/s11227-022-04385-8 doi (DE-627)OLC207907346X (DE-He213)s11227-022-04385-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Liang, Hao verfasserin aut A robust low-rank matrix completion based on truncated nuclear norm and Lp-norm 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. Sparse representation Low-rank matrix completion Lp-norm Truncated nuclear norm Alternating direction multiplier method Kang, Li (orcid)0000-0003-4094-3348 aut Huang, Jianjun aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 11 vom: 13. März, Seite 12950-12972 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:11 day:13 month:03 pages:12950-12972 https://doi.org/10.1007/s11227-022-04385-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 11 13 03 12950-12972 |
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10.1007/s11227-022-04385-8 doi (DE-627)OLC207907346X (DE-He213)s11227-022-04385-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Liang, Hao verfasserin aut A robust low-rank matrix completion based on truncated nuclear norm and Lp-norm 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. Sparse representation Low-rank matrix completion Lp-norm Truncated nuclear norm Alternating direction multiplier method Kang, Li (orcid)0000-0003-4094-3348 aut Huang, Jianjun aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 11 vom: 13. März, Seite 12950-12972 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:11 day:13 month:03 pages:12950-12972 https://doi.org/10.1007/s11227-022-04385-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 11 13 03 12950-12972 |
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Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
| abstract_unstemmed |
Abstract The low-rank matrix completion problem has aroused notable attention in various fields, such as engineering and applied sciences. The classical methods approximate the rank minimization problem by minimizing the nuclear norm, therefore obtaining unsatisfactory results, which may deviate from the true solution. In addition, most methods minimize the square error directly, which may be sensitive to the outliers. This paper presents a robust matrix completion model, which is suitable for a low sampling rate. First, the truncated nuclear norm is introduced, which is a more accurate and robust approximation to the rank function. Then, the Lp-norm may be employed as an error function, which provides a robust estimation. Finally, several optimization algorithms are employed to solve the model. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm can better approximate rank minimization problems and enhance robustness to outliers, especially when the sampling rate is very low. The method’s practical potential is illustrated on the MovieLens-1M dataset. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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A robust low-rank matrix completion based on truncated nuclear norm and Lp-norm |
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