{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T06:43:50Z","timestamp":1775544230991,"version":"3.50.1"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T00:00:00Z","timestamp":1587081600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T00:00:00Z","timestamp":1587081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2020,10]]},"DOI":"10.1007\/s13042-020-01121-7","type":"journal-article","created":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T17:03:14Z","timestamp":1587142994000},"page":"2327-2339","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Accelerated inexact matrix completion algorithm via closed-form q-thresholding $$(q = 1\/2, 2\/3)$$ operator"],"prefix":"10.1007","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2167-830X","authenticated-orcid":false,"given":"Zhi","family":"Wang","sequence":"first","affiliation":[]},{"given":"Chao","family":"Gao","sequence":"additional","affiliation":[]},{"given":"Xiaohu","family":"Luo","sequence":"additional","affiliation":[]},{"given":"Ming","family":"Tang","sequence":"additional","affiliation":[]},{"given":"Jianjun","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Wu","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,17]]},"reference":[{"key":"1121_CR1","doi-asserted-by":"crossref","unstructured":"Rennie J, Srebro N (2005) Fast maximum margin matrix factorization for collaborative prediction. In: Proceedings of the 22nd international conference on machine learning (ICML-05), pp 713\u2013719","DOI":"10.1145\/1102351.1102441"},{"key":"1121_CR2","doi-asserted-by":"crossref","unstructured":"Koren Y (2008) Factorization meets the neighborhood: A multifaceted collaborative filtering model. In: Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 426\u2013434","DOI":"10.1145\/1401890.1401944"},{"key":"1121_CR3","first-page":"128","volume":"310","author":"X Li","year":"2017","unstructured":"Li X, Wang Z, Gao C, Shi L (2017) Reasoning human emotional responses from large-scale social and public media. Appl Math Comput 310:128\u2013193","journal-title":"Appl Math Comput"},{"issue":"12","key":"1121_CR4","doi-asserted-by":"publisher","first-page":"2499","DOI":"10.1109\/TNNLS.2015.2490080","volume":"27","author":"X Peng","year":"2016","unstructured":"Peng X, Zhang Y, Tang H (2016) A unified framework for representation-based subspace clustering of out-of-sample and large-scale data. IEEE Trans Neural Netw Learn Syst 27(12):2499\u20132512","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"1121_CR5","doi-asserted-by":"publisher","first-page":"940","DOI":"10.1016\/j.neucom.2017.09.039","volume":"275","author":"L Yang","year":"2018","unstructured":"Yang L, Nie F, Gao Q (2018) Nuclear-norm based semi-supervised multiple labels learning. Neurocomputing 275:940\u2013947","journal-title":"Neurocomputing"},{"key":"1121_CR6","unstructured":"Yang L, Gao Q, Li J, Han J, Shao L (2018) Zero shot learning via low-rank embedded semantic autoencoder. In: Proceedings of the international joint conference on artificial intelligence, pp 2490\u20132496"},{"issue":"1","key":"1121_CR7","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1109\/TPAMI.2014.2343234","volume":"37","author":"R Cabral","year":"2015","unstructured":"Cabral R, De la Torre F, Costeira JP, Bernardino A (2015) Matrix completion for weakly-supervised multi-label image classification. IEEE Trans Pattern Anal Mach Intell 37(1):121\u2013135","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"1121_CR8","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/j.neucom.2018.10.075","volume":"330","author":"L Yang","year":"2019","unstructured":"Yang L, Shan C, Gao Q, Gao X, Han J, Cui R (2019) Hyperspectral image denoising via minimizing the partial sum of singular values and superpixel segmentation. Neurocomputing 330:465\u2013482","journal-title":"Neurocomputing"},{"issue":"3","key":"1121_CR9","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1137\/070697835","volume":"52","author":"B Recht","year":"2010","unstructured":"Recht B, Fazel M, Parrilo PA (2010) Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev 52(3):471\u2013501","journal-title":"SIAM Rev"},{"issue":"6","key":"1121_CR10","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"EJ Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s EJ, Recht B (2009) Exact matrix completion via convex optimization. Found Compt Math 9(6):717\u2013772","journal-title":"Found Compt Math"},{"key":"1121_CR11","unstructured":"Fazel M (2002) Matrix rank minimization with applications. Ph.D. thesis, Stanford University"},{"issue":"4","key":"1121_CR12","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"J-F Cai","year":"2010","unstructured":"Cai J-F, Cand\u00e8s EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956\u20131982","journal-title":"SIAM J Optim"},{"issue":"3","key":"1121_CR13","first-page":"615","volume":"6","author":"K-C Toh","year":"2010","unstructured":"Toh K-C, Yun S (2010) An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems. Pac J Optim 6(3):615\u2013640","journal-title":"Pac J Optim"},{"issue":"1\u20132","key":"1121_CR14","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s10107-009-0306-5","volume":"128","author":"S Ma","year":"2011","unstructured":"Ma S, Goldfarb D, Chen L (2011) Fixed point and Bregman iterative methods for matrix rank minimization. Math Program 128(1\u20132):321\u2013353","journal-title":"Math Program"},{"key":"1121_CR15","first-page":"2287","volume":"11","author":"R Mazumder","year":"2010","unstructured":"Mazumder R, Hastie T, Tibshirani R (2010) Spectral regularization algorithms for learning large incomplete matrices. J Mach Learn Res 11:2287\u20132322","journal-title":"J Mach Learn Res"},{"key":"1121_CR16","unstructured":"Yao Q, Kwok JT (2015) Accelerated inexact soft-impute for fast largescale matrix completion. In: Proceedings of the international joint conference on artificial intelligence, pp 4002\u20134008"},{"key":"1121_CR17","doi-asserted-by":"publisher","first-page":"1348","DOI":"10.1198\/016214501753382273","volume":"96","author":"J Fan","year":"2001","unstructured":"Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its Oracle properties. J Am Stat Assoc 96:1348\u20131361","journal-title":"J Am Stat Assoc"},{"key":"1121_CR18","first-page":"1081","volume":"11","author":"T Zhang","year":"2010","unstructured":"Zhang T (2010) Analysis of multi-stage convex relaxation for sparse regularization. J Mach Learn Res 11:1081\u20131107","journal-title":"J Mach Learn Res"},{"issue":"5\u20136","key":"1121_CR19","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","volume":"14","author":"EJ Cand\u00e8s","year":"2008","unstructured":"Cand\u00e8s EJ, Wakin MB, Boyd SP (2008) Enhancing sparsity by reweighted $$l_{1}$$ minimization. J Fourier Anal Appl 14(5\u20136):877\u2013905","journal-title":"J Fourier Anal Appl"},{"issue":"19","key":"1121_CR20","doi-asserted-by":"publisher","first-page":"2117","DOI":"10.1109\/TPAMI.2012.271","volume":"35","author":"Y Hu","year":"2013","unstructured":"Hu Y, Zhang D, Ye J, Li X, He X (2013) Fast and accurate matrix completion via truncated nuclear norm regularization. IEEE Trans Pattern Anal Mach Intell 35(19):2117\u20132130","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"2","key":"1121_CR21","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1214\/09-AOS729","volume":"38","author":"C-H Zhang","year":"2010","unstructured":"Zhang C-H (2010) Nearly unbiased variable selection under minimax concave penalty. Ann Stat 38(2):894\u2013942","journal-title":"Ann Stat"},{"issue":"11","key":"1121_CR22","doi-asserted-by":"publisher","first-page":"5714","DOI":"10.1109\/TSP.2012.2212015","volume":"60","author":"G Marjanovic","year":"2012","unstructured":"Marjanovic G, Solo V (2012) On $$l_{q}$$ optimization and matrix completion. IEEE Trans Signal Process 60(11):5714\u20135724","journal-title":"IEEE Trans Signal Process"},{"key":"1121_CR23","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.ins.2014.03.128","volume":"279","author":"O Abu Arqub","year":"2014","unstructured":"Abu Arqub O, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396\u2013415","journal-title":"Inf Sci"},{"issue":"8","key":"1121_CR24","doi-asserted-by":"publisher","first-page":"3283","DOI":"10.1007\/s00500-015-1707-4","volume":"20","author":"O Abu Arqub","year":"2016","unstructured":"Abu Arqub O, AL-Smadi M, Momani S, Hayat M (2016) Numerical solutions of fuzzy differential equtions using reproducing kernel Hilbert space method. Soft Comput 20(8):3283\u20133302","journal-title":"Soft Comput"},{"issue":"23","key":"1121_CR25","doi-asserted-by":"publisher","first-page":"7191","DOI":"10.1007\/s00500-016-2262-3","volume":"21","author":"O Abu Arqub","year":"2017","unstructured":"Abu Arqub O, AL-Smadi M, Momani S, Hayat M (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21(23):7191\u20137206","journal-title":"Soft Comput"},{"issue":"7","key":"1121_CR26","doi-asserted-by":"publisher","first-page":"1591","DOI":"10.1007\/s00521-015-2110-x","volume":"28","author":"O Abu Arqub","year":"2017","unstructured":"Abu Arqub O (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm\u2013Volterra integrodifferential equations. Neural Comput Appl 28(7):1591\u20131610","journal-title":"Neural Comput Appl"},{"issue":"7","key":"1121_CR27","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1109\/TNNLS.2012.2197412","volume":"23","author":"Z Xu","year":"2012","unstructured":"Xu Z, Chang X, Xu F, Zhang H (2012) $$L_{1\/2}$$ regularization: a thresholding representation theory and a fast solver. IEEE Trans Neural Netw Learn Syst 23(7):1013\u20131027","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"1","key":"1121_CR28","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.jvcir.2012.10.006","volume":"24","author":"W Cao","year":"2013","unstructured":"Cao W, Sun J, Xu Z (2013) Fast image deconvolution using closed-form thresholding formulas of $$l_{q}(q = 1\/2, 2\/3)$$ regularization. J Vis Commun Image R 24(1):31\u201341","journal-title":"J Vis Commun Image R"},{"key":"1121_CR29","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/s10589-017-9898-5","volume":"67","author":"D Peng","year":"2017","unstructured":"Peng D, Xiu N, Yu J (2017) $$S_{1\/2}$$ regularization methods and fixed point algorithms for affine rank minimization problems. Comput Optim Appl 67:543\u2013569","journal-title":"Comput Optim Appl"},{"key":"1121_CR30","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1016\/j.neucom.2018.10.065","volume":"330","author":"Z Wang","year":"2019","unstructured":"Wang Z, Wang W, Wang J, Chen S (2019) Fast and efficient algorithm for matrix completion via closed-form 2\/3-thresholding operator. Neurocomputing 330:212\u2013222","journal-title":"Neurocomputing"},{"issue":"6","key":"1121_CR31","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.1007\/s13042-018-0814-9","volume":"10","author":"W Qian","year":"2019","unstructured":"Qian W, Cao F (2019) Adaptive algorithms for low-rank and sparse matrix recovery with truncated nuclear norm. Int J Mach Learn Cyb 10(6):1341\u20131355","journal-title":"Int J Mach Learn Cyb"},{"issue":"1","key":"1121_CR32","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10107-012-0629-5","volume":"140","author":"Y Nesterov","year":"2013","unstructured":"Nesterov Y (2013) Gradient methods for minimizing composite functions. Math Program 140(1):125\u2013161","journal-title":"Math Program"},{"key":"1121_CR33","unstructured":"Li H, Lin Z (2015) Accelerated proximal gradient methods for noncovex programming. In: Proceedings of the advances in neural information processing systems, pp 379\u2013387"},{"issue":"9","key":"1121_CR34","doi-asserted-by":"publisher","first-page":"1665","DOI":"10.1109\/TKDE.2018.2867533","volume":"31","author":"Q Yao","year":"2019","unstructured":"Yao Q, Kwok J (2019) Accelerated and inexact soft-impute for large-scale matrix and tensor completion. IEEE Trans Knowl Data En 31(9):1665\u20131679","journal-title":"IEEE Trans Knowl Data En"},{"issue":"11","key":"1121_CR35","doi-asserted-by":"publisher","first-page":"2628","DOI":"10.1109\/TPAMI.2018.2858249","volume":"41","author":"Q Yao","year":"2019","unstructured":"Yao Q, Kwok J, Wang T, Liu T (2019) Large-scale low-rank matrix learning with nonconvex regularizers. IEEE Trans Pattern Anal Mach Intell 41(11):2628\u20132643","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"1121_CR36","doi-asserted-by":"crossref","unstructured":"Gu B, Wang D, Huo Z, Huang H (2018) Inexact proximal gradient methods for non-convex and non-smooth optimization. In: AAAI conference on artificial intelligence","DOI":"10.1609\/aaai.v32i1.11802"},{"key":"1121_CR37","doi-asserted-by":"crossref","unstructured":"Yao Q, Kwok J, Gao F, Chen W, Liu T (2017) Efficient inexact proximal gradient algorithm for nonconvex problems. In: Proceedings of the international joint conference on artificial intelligence, pp 3308\u20133314","DOI":"10.24963\/ijcai.2017\/462"},{"issue":"2","key":"1121_CR38","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1109\/TPAMI.2017.2677440","volume":"40","author":"T Oh","year":"2018","unstructured":"Oh T, Matsushita Y, Tai Y, Kweon I (2018) Fast randomized singular value thresholding for low-rank optimization. IEEE Trans Pattern Anal Mach Intell 40(2):376\u2013391","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"2","key":"1121_CR39","doi-asserted-by":"publisher","first-page":"1805","DOI":"10.1137\/090771806","volume":"53","author":"N Halko","year":"2011","unstructured":"Halko N, Martinsson P-G, Tropp J (2011) Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev 53(2):1805\u20131811","journal-title":"SIAM Rev"},{"key":"1121_CR40","unstructured":"Hsieh C.-J, Olsen P (2014) Nuclear norm minimization via active subspace selection. In: Proceedings of the 31st international conference on machine learning (ICML-14), pp 575\u2013583"},{"key":"1121_CR41","doi-asserted-by":"crossref","unstructured":"Larsen R (1998) Lanczos bidiagonalization with partial reorthogonalization. Department of Computer Science, Aarhus University, DAIMI PB-357","DOI":"10.7146\/dpb.v27i537.7070"},{"key":"1121_CR42","unstructured":"Gong P, Zhang C, Lu Z, Huang J, Ye J (2013) A general iterative shrinkage and tresholding algorithm for non-convex regularized optimization problems. In: Proceedings of the 30th international conference on machine learning (ICML-13), pp 37\u201345"},{"issue":"4","key":"1121_CR43","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s12532-012-0044-1","volume":"44","author":"Z Wen","year":"2012","unstructured":"Wen Z, Yin W, Zhang Y (2012) Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Math Program Comput 44(4):333\u2013361","journal-title":"Math Program Comput"},{"issue":"1","key":"1121_CR44","doi-asserted-by":"publisher","first-page":"A488","DOI":"10.1137\/130934271","volume":"37","author":"Z Wang","year":"2015","unstructured":"Wang Z, Lai M, Lu Z, Fan W, Davulcu H, Ye J (2015) Orthogonal rank-one matrix pursuit for low rank matrix completion. SIAM J Sci Comput 37(1):A488\u2013A514","journal-title":"SIAM J Sci Comput"},{"key":"1121_CR45","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/j.acha.2015.08.003","volume":"40","author":"J Tanner","year":"2016","unstructured":"Tanner J, Wei K (2016) Low rank matrix completion by alternating steepest descent methods. Appl Comput Harmon A 40:417\u2013420","journal-title":"Appl Comput Harmon A"},{"key":"1121_CR46","doi-asserted-by":"crossref","unstructured":"Xu C, Lin Z, Zha H (2017) A unified convex surrogate for the schatten-$$p$$ norm. In: AAAI conference on artificial intelligence","DOI":"10.1609\/aaai.v31i1.10646"},{"issue":"2","key":"1121_CR47","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1109\/TIP.2015.2511584","volume":"25","author":"C Lu","year":"2016","unstructured":"Lu C, Tang J, Yan S, Lin Z (2016) Noncovex nonsmooth low rank minimization via iteratively reweighted nuclear norm. IEEE Trans Image Process 25(2):829\u2013839","journal-title":"IEEE Trans Image Process"},{"key":"1121_CR48","unstructured":"Jain P, Meka R, Dhillon I (2010) Guaranteed rank minimization via singular value projection. In: Proceedings of the advances in neural information processing systems, pp 937\u2013945"},{"key":"1121_CR49","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1137\/110840364","volume":"5","author":"M Lai","year":"2013","unstructured":"Lai M, Xu Y, Yin W (2013) Improved iteratively rewighted least squares for unconstrained smoothed $$l_{p}$$ minimization. SIAM J Numer Anal 5:927\u2013957","journal-title":"SIAM J Numer Anal"},{"key":"1121_CR50","first-page":"3367","volume":"16","author":"T Hastie","year":"2015","unstructured":"Hastie T, Mazumder R, Lee J, Zadeh R (2015) Matrix completion and low-rank SVD via fast alternating least squares. J Mach Learn Res 16:3367\u20133402","journal-title":"J Mach Learn Res"},{"issue":"13","key":"1121_CR51","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1049\/el:20080522","volume":"44","author":"Q Thu","year":"2008","unstructured":"Thu Q, Ghanbari M (2008) Scope of validity of PSNR in image\/video quality assesment. Electron Lett 44(13):800\u2013801","journal-title":"Electron Lett"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-020-01121-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-020-01121-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-020-01121-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T16:43:50Z","timestamp":1666370630000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-020-01121-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,17]]},"references-count":51,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["1121"],"URL":"https:\/\/doi.org\/10.1007\/s13042-020-01121-7","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,17]]},"assertion":[{"value":"12 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}