A non-convex algorithm framework based on DC programming and DCA for matrix completion

Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Geng, Juan [verfasserIn] Wang, Laisheng [verfasserIn] Wang, Yanfei [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	Non-convex algorithm DC Algorithms Non-convex penalty Matrix completion Image recovery

Übergeordnetes Werk:	Enthalten in: Numerical algorithms - Bussum : Baltzer, 1991, 68(2014), 4 vom: 29. Mai, Seite 903-921
Übergeordnetes Werk:	volume:68 ; year:2014 ; number:4 ; day:29 ; month:05 ; pages:903-921

Links:	Volltext

DOI / URN:	10.1007/s11075-014-9876-2

Katalog-ID:	SPR016425308

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520			\|a Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable.
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650		4	\|a Matrix completion \|7 (dpeaa)DE-He213
650		4	\|a Image recovery \|7 (dpeaa)DE-He213
700	1		\|a Wang, Laisheng \|e verfasserin \|4 aut
700	1		\|a Wang, Yanfei \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Numerical algorithms \|d Bussum : Baltzer, 1991 \|g 68(2014), 4 vom: 29. Mai, Seite 903-921 \|w (DE-627)318468581 \|w (DE-600)2002650-X \|x 1572-9265 \|7 nnns
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author_variant	j g jg l w lw y w yw
matchkey_str	article:15729265:2014----::nnovxloihfaeokaeodpormignda
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bklnumber	31.76
publishDate	2014
allfields	10.1007/s11075-014-9876-2 doi (DE-627)SPR016425308 (SPR)s11075-014-9876-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Geng, Juan verfasserin aut A non-convex algorithm framework based on DC programming and DCA for matrix completion 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable. Non-convex algorithm (dpeaa)DE-He213 DC Algorithms (dpeaa)DE-He213 Non-convex penalty (dpeaa)DE-He213 Matrix completion (dpeaa)DE-He213 Image recovery (dpeaa)DE-He213 Wang, Laisheng verfasserin aut Wang, Yanfei verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 68(2014), 4 vom: 29. Mai, Seite 903-921 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:68 year:2014 number:4 day:29 month:05 pages:903-921 https://dx.doi.org/10.1007/s11075-014-9876-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 68 2014 4 29 05 903-921
spelling	10.1007/s11075-014-9876-2 doi (DE-627)SPR016425308 (SPR)s11075-014-9876-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Geng, Juan verfasserin aut A non-convex algorithm framework based on DC programming and DCA for matrix completion 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable. Non-convex algorithm (dpeaa)DE-He213 DC Algorithms (dpeaa)DE-He213 Non-convex penalty (dpeaa)DE-He213 Matrix completion (dpeaa)DE-He213 Image recovery (dpeaa)DE-He213 Wang, Laisheng verfasserin aut Wang, Yanfei verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 68(2014), 4 vom: 29. Mai, Seite 903-921 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:68 year:2014 number:4 day:29 month:05 pages:903-921 https://dx.doi.org/10.1007/s11075-014-9876-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 68 2014 4 29 05 903-921
allfields_unstemmed	10.1007/s11075-014-9876-2 doi (DE-627)SPR016425308 (SPR)s11075-014-9876-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Geng, Juan verfasserin aut A non-convex algorithm framework based on DC programming and DCA for matrix completion 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable. Non-convex algorithm (dpeaa)DE-He213 DC Algorithms (dpeaa)DE-He213 Non-convex penalty (dpeaa)DE-He213 Matrix completion (dpeaa)DE-He213 Image recovery (dpeaa)DE-He213 Wang, Laisheng verfasserin aut Wang, Yanfei verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 68(2014), 4 vom: 29. Mai, Seite 903-921 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:68 year:2014 number:4 day:29 month:05 pages:903-921 https://dx.doi.org/10.1007/s11075-014-9876-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 68 2014 4 29 05 903-921
allfieldsGer	10.1007/s11075-014-9876-2 doi (DE-627)SPR016425308 (SPR)s11075-014-9876-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Geng, Juan verfasserin aut A non-convex algorithm framework based on DC programming and DCA for matrix completion 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable. Non-convex algorithm (dpeaa)DE-He213 DC Algorithms (dpeaa)DE-He213 Non-convex penalty (dpeaa)DE-He213 Matrix completion (dpeaa)DE-He213 Image recovery (dpeaa)DE-He213 Wang, Laisheng verfasserin aut Wang, Yanfei verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 68(2014), 4 vom: 29. Mai, Seite 903-921 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:68 year:2014 number:4 day:29 month:05 pages:903-921 https://dx.doi.org/10.1007/s11075-014-9876-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 68 2014 4 29 05 903-921
allfieldsSound	10.1007/s11075-014-9876-2 doi (DE-627)SPR016425308 (SPR)s11075-014-9876-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Geng, Juan verfasserin aut A non-convex algorithm framework based on DC programming and DCA for matrix completion 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable. Non-convex algorithm (dpeaa)DE-He213 DC Algorithms (dpeaa)DE-He213 Non-convex penalty (dpeaa)DE-He213 Matrix completion (dpeaa)DE-He213 Image recovery (dpeaa)DE-He213 Wang, Laisheng verfasserin aut Wang, Yanfei verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 68(2014), 4 vom: 29. Mai, Seite 903-921 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:68 year:2014 number:4 day:29 month:05 pages:903-921 https://dx.doi.org/10.1007/s11075-014-9876-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 68 2014 4 29 05 903-921
language	English
source	Enthalten in Numerical algorithms 68(2014), 4 vom: 29. Mai, Seite 903-921 volume:68 year:2014 number:4 day:29 month:05 pages:903-921
sourceStr	Enthalten in Numerical algorithms 68(2014), 4 vom: 29. Mai, Seite 903-921 volume:68 year:2014 number:4 day:29 month:05 pages:903-921
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Non-convex algorithm DC Algorithms Non-convex penalty Matrix completion Image recovery
dewey-raw	510
isfreeaccess_bool	false
container_title	Numerical algorithms
authorswithroles_txt_mv	Geng, Juan @@aut@@ Wang, Laisheng @@aut@@ Wang, Yanfei @@aut@@
publishDateDaySort_date	2014-05-29T00:00:00Z
hierarchy_top_id	318468581
dewey-sort	3510
id	SPR016425308
language_de	englisch
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author	Geng, Juan
spellingShingle	Geng, Juan ddc 510 bkl 31.76 misc Non-convex algorithm misc DC Algorithms misc Non-convex penalty misc Matrix completion misc Image recovery A non-convex algorithm framework based on DC programming and DCA for matrix completion
authorStr	Geng, Juan
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topic_title	510 ASE 31.76 bkl A non-convex algorithm framework based on DC programming and DCA for matrix completion Non-convex algorithm (dpeaa)DE-He213 DC Algorithms (dpeaa)DE-He213 Non-convex penalty (dpeaa)DE-He213 Matrix completion (dpeaa)DE-He213 Image recovery (dpeaa)DE-He213
topic	ddc 510 bkl 31.76 misc Non-convex algorithm misc DC Algorithms misc Non-convex penalty misc Matrix completion misc Image recovery
topic_unstemmed	ddc 510 bkl 31.76 misc Non-convex algorithm misc DC Algorithms misc Non-convex penalty misc Matrix completion misc Image recovery
topic_browse	ddc 510 bkl 31.76 misc Non-convex algorithm misc DC Algorithms misc Non-convex penalty misc Matrix completion misc Image recovery
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title	A non-convex algorithm framework based on DC programming and DCA for matrix completion
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title_full	A non-convex algorithm framework based on DC programming and DCA for matrix completion
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author_browse	Geng, Juan Wang, Laisheng Wang, Yanfei
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title_sort	non-convex algorithm framework based on dc programming and dca for matrix completion
title_auth	A non-convex algorithm framework based on DC programming and DCA for matrix completion
abstract	Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable.
abstractGer	Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable.
abstract_unstemmed	Abstract Matrix completion aims to recover an unknown low-rank or approximately low-rank matrix from a sampling set of its entries. It is shown that this problem can be solved via its tightest convex relaxation obtained by minimizing the nuclear norm instead of the rank function. Recent studies have also shown that some non-convex penalties like Mp minimization and weighted nuclear norm minimization algorithms are able to recover low-rank matrix in a more efficient way. In this paper, we propose a unified framework based on Difference of Convex functions (DC) programming and DC Algorithms (DCA), by which Mp minimization and weighted nuclear norm minimization algorithms can be obtained as special cases of the general framework. In addition, we give another non-convex penalty—exponential type penalty. We make some comparison between numerical tests of our algorithms and the state-of-the-art method APGL and NIHT on randomly generated matrices and real matrix completion problems, the results suggest that our methods are more effective and promising. Moreover, for the application on low-rank image recovery, these non-convex algorithms we proposed also perform well and the results are more satisfactory and reasonable.
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container_issue	4
title_short	A non-convex algorithm framework based on DC programming and DCA for matrix completion
url	https://dx.doi.org/10.1007/s11075-014-9876-2
remote_bool	true
author2	Wang, Laisheng Wang, Yanfei
author2Str	Wang, Laisheng Wang, Yanfei
ppnlink	318468581
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hochschulschrift_bool	false
doi_str	10.1007/s11075-014-9876-2
up_date	2024-07-03T22:59:56.230Z
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A non-convex algorithm framework based on DC programming and DCA for matrix completion

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