{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T15:29:31Z","timestamp":1778513371112,"version":"3.51.4"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T00:00:00Z","timestamp":1766793600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T00:00:00Z","timestamp":1766793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Sichuan Provincial Science and Technology","award":["2023NSFSC1425"],"award-info":[{"award-number":["2023NSFSC1425"]}]},{"name":"Sichuan Provincial Science and Technology","award":["2023NSFSC0071"],"award-info":[{"award-number":["2023NSFSC0071"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101090"],"award-info":[{"award-number":["12101090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s10489-025-07040-w","type":"journal-article","created":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T08:03:44Z","timestamp":1766822624000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Bipartite graph regularized robust low-rank matrix factorization for fast semi-supervised image clustering"],"prefix":"10.1007","volume":"56","author":[{"given":"Nan","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjun","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zezhong","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanhua","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaibo","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Badong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,27]]},"reference":[{"key":"7040_CR1","doi-asserted-by":"crossref","unstructured":"Bo D, Wang P, Shi C et\u00a0al (2020) Structural deep clustering network. In: Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pp 1318\u20131328","DOI":"10.1145\/3366423.3380214"},{"issue":"4","key":"7040_CR2","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1137\/050644641","volume":"17","author":"J Bolte","year":"2007","unstructured":"Bolte J, Daniilidis A, Lewis A (2007) The \u0142ojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J Optim 17(4):1205\u20131223","journal-title":"SIAM J Optim"},{"issue":"6","key":"7040_CR3","doi-asserted-by":"publisher","first-page":"902","DOI":"10.1109\/TKDE.2010.165","volume":"23","author":"D Cai","year":"2010","unstructured":"Cai D, He X, Han J (2010a) Locally consistent concept factorization for document clustering. IEEE Trans Knowl Data Eng 23(6):902\u2013913","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"8","key":"7040_CR4","first-page":"1548","volume":"33","author":"D Cai","year":"2010","unstructured":"Cai D, He X, Han J et al (2010b) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33(8):1548\u20131560","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"7040_CR5","unstructured":"Cichocki A, Zdunek R, Amari Si (2006) New algorithms for non-negative matrix factorization in applications to blind source separation. In: 2006 IEEE international conference on acoustics speech and signal processing proceedings. IEEE, pp V\u2013V"},{"issue":"2","key":"7040_CR6","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/MASSP.1984.1162229","volume":"1","author":"R Gray","year":"1984","unstructured":"Gray R (1984) Vector quantization. IEEE Assp Magazine 1(2):4\u201329","journal-title":"IEEE Assp Magazine"},{"issue":"14","key":"7040_CR7","doi-asserted-by":"publisher","first-page":"2447","DOI":"10.1016\/S0167-8655(03)00089-8","volume":"24","author":"D Guillamet","year":"2003","unstructured":"Guillamet D, Vitria J, Schiele B (2003) Introducing a weighted non-negative matrix factorization for image classification. Pattern Recogn Lett 24(14):2447\u20132454","journal-title":"Pattern Recogn Lett"},{"key":"7040_CR8","doi-asserted-by":"crossref","unstructured":"Guo Y, Ding G, Zhou J et\u00a0al (2015) Robust and discriminative concept factorization for image representation. In: Proceedings of the 5th ACM on international conference on multimedia retrieval, pp 115\u2013122","DOI":"10.1145\/2671188.2749317"},{"issue":"3","key":"7040_CR9","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1137\/0911028","volume":"11","author":"PC Hansen","year":"1990","unstructured":"Hansen PC (1990) Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. SIAM J Sci Stat Comput 11(3):503\u2013518","journal-title":"SIAM J Sci Stat Comput"},{"issue":"2","key":"7040_CR10","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1109\/TNNLS.2019.2908504","volume":"31","author":"F He","year":"2019","unstructured":"He F, Nie F, Wang R et al (2019) Fast semisupervised learning with bipartite graph for large-scale data. IEEE Trans Neural Netw Learn Syst 31(2):626\u2013638","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"9","key":"7040_CR11","doi-asserted-by":"publisher","first-page":"3245","DOI":"10.1109\/TKDE.2020.2968523","volume":"33","author":"F He","year":"2020","unstructured":"He F, Nie F, Wang R et al (2020) Fast semi-supervised learning with optimal bipartite graph. IEEE Trans Knowl Data Eng 33(9):3245\u20133257","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"6","key":"7040_CR12","doi-asserted-by":"publisher","first-page":"1485","DOI":"10.1109\/TIP.2010.2103949","volume":"20","author":"R He","year":"2011","unstructured":"He R, Hu BG, Zheng WS et al (2011) Robust principal component analysis based on maximum correntropy criterion. IEEE Trans Image Process 20(6):1485\u20131494","journal-title":"IEEE Trans Image Process"},{"issue":"6","key":"7040_CR13","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1037\/h0071325","volume":"24","author":"H Hotelling","year":"1933","unstructured":"Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24(6):417","journal-title":"J Educ Psychol"},{"key":"7040_CR14","doi-asserted-by":"publisher","unstructured":"Iqbal I, Younus M, Walayat K et al (2021) Automated multi-class classification of skin lesions through deep convolutional neural network with dermoscopic images. Comput Med Imaging Graph 88:101843. https:\/\/doi.org\/10.1016\/j.compmedimag.2020.101843","DOI":"10.1016\/j.compmedimag.2020.101843"},{"key":"7040_CR15","doi-asserted-by":"publisher","unstructured":"Iqbal I, Ullah I, Peng T et al (2025) An end-to-end deep convolutional neural network-based data-driven fusion framework for identification of human induced pluripotent stem cell-derived endothelial cells in photomicrographs. Eng Appl Artif Intell 139:109573. https:\/\/doi.org\/10.1016\/j.engappai.2024.109573","DOI":"10.1016\/j.engappai.2024.109573"},{"key":"7040_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.110702","volume":"146","author":"M Jia","year":"2023","unstructured":"Jia M, Liu S, Bai Y (2023) Auto weighted robust dual graph nonnegative matrix factorization for multiview clustering. Appl Soft Comput 146:110702","journal-title":"Appl Soft Comput"},{"key":"7040_CR17","doi-asserted-by":"crossref","unstructured":"Jiang Z, Zheng H, Tan C et\u00a0al (2017) Variational deep embedding: an unsupervised and generative approach to clustering. In: Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining, pp 1205\u20131214","DOI":"10.24963\/ijcai.2017\/273"},{"key":"7040_CR18","unstructured":"Lee D, Seung HS (2000) Algorithms for non-negative matrix factorization. Adv Neural Inf Process Syst 13"},{"issue":"6755","key":"7040_CR19","doi-asserted-by":"publisher","first-page":"788","DOI":"10.1038\/44565","volume":"401","author":"DD Lee","year":"1999","unstructured":"Lee DD, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401(6755):788\u2013791","journal-title":"Nature"},{"key":"7040_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2851-4","volume-title":"Independent component analysis","author":"TW Lee","year":"1998","unstructured":"Lee TW, Lee TW (1998) Independent component analysis. Springer"},{"issue":"7","key":"7040_CR21","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1109\/TPAMI.2011.217","volume":"34","author":"H Liu","year":"2011","unstructured":"Liu H, Wu Z, Li X et al (2011) Constrained nonnegative matrix factorization for image representation. IEEE Trans Pattern Anal Mach Intell 34(7):1299\u20131311","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"7","key":"7040_CR22","first-page":"1214","volume":"44","author":"H Liu","year":"2013","unstructured":"Liu H, Yang G, Wu Z et al (2013) Constrained concept factorization for image representation. IEEE Trans Cybern 44(7):1214\u20131224","journal-title":"IEEE Trans Cybern"},{"key":"7040_CR23","unstructured":"Liu W, He J, Chang SF (2010) Large graph construction for scalable semi-supervised learning. In: Proceedings of the 27th international conference on machine learning (ICML-10). Citeseer, pp 679\u2013686"},{"key":"7040_CR24","doi-asserted-by":"crossref","unstructured":"Lov\u00e1sz L, Plummer MD (2009) Matching theory, vol 367. American Mathematical Soc","DOI":"10.1090\/chel\/367"},{"key":"7040_CR25","unstructured":"Mairal J, Bach F, Ponce J et\u00a0al (2010) Online learning for matrix factorization and sparse coding. J Mach Learn Res 11(1)"},{"key":"7040_CR26","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.engappai.2017.11.008","volume":"69","author":"Y Meng","year":"2018","unstructured":"Meng Y, Shang R, Jiao L et al (2018) Dual-graph regularized non-negative matrix factorization with sparse and orthogonal constraints. Eng Appl Artif Intell 69:24\u201335","journal-title":"Eng Appl Artif Intell"},{"key":"7040_CR27","first-page":"478","volume":"80","author":"F Min","year":"2018","unstructured":"Min F, Cao Z, Zhu X et al (2018) Deep clustering: a survey. Pattern Recogn 80:478\u2013496","journal-title":"Pattern Recogn"},{"key":"7040_CR28","doi-asserted-by":"crossref","unstructured":"Nie F, Wang X, Jordan M et\u00a0al (2016) The constrained laplacian rank algorithm for graph-based clustering. In: Proceedings of the AAAI conference on artificial intelligence","DOI":"10.1609\/aaai.v30i1.10302"},{"key":"7040_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111712","volume":"161","author":"AG Oskouei","year":"2024","unstructured":"Oskouei AG, Samadi N, Tanha J (2024) Feature-weight and cluster-weight learning in fuzzy c-means method for semi-supervised clustering. Appl Soft Comput 161:111712","journal-title":"Appl Soft Comput"},{"key":"7040_CR30","unstructured":"Papoulis A, Unnikrishna\u00a0Pillai S (2002) Probability, random variables and stochastic processes"},{"key":"7040_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2020.107683","volume":"111","author":"S Peng","year":"2021","unstructured":"Peng S, Ser W, Chen B et al (2021) Robust semi-supervised nonnegative matrix factorization for image clustering. Pattern Recogn 111:107683","journal-title":"Pattern Recogn"},{"key":"7040_CR32","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.neunet.2022.07.021","volume":"154","author":"S Peng","year":"2022","unstructured":"Peng S, Yang Z, Nie F et al (2022) Correntropy based semi-supervised concept factorization with adaptive neighbors for clustering. Neural Netw 154:203\u2013217","journal-title":"Neural Netw"},{"key":"7040_CR33","doi-asserted-by":"crossref","unstructured":"Peng Z, Wu T, Xu Y et\u00a0al (2016) Coordinate friendly structures, algorithms and applications. arXiv:1601.00863","DOI":"10.4310\/AMSA.2016.v1.n1.a2"},{"key":"7040_CR34","doi-asserted-by":"crossref","unstructured":"Principe JC (2010) Information theoretic learning: Renyi\u2019s entropy and kernel perspectives. Springer Science & Business Media","DOI":"10.1007\/978-1-4419-1570-2"},{"key":"7040_CR35","unstructured":"Rockafellar RT (2015) Convex analysis:(pms-28). In: Convex analysis. Princeton University Press"},{"key":"7040_CR36","doi-asserted-by":"crossref","unstructured":"Sain SR (1996) The nature of statistical learning theory","DOI":"10.1080\/00401706.1996.10484565"},{"key":"7040_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2022.109932","volume":"133","author":"R Shang","year":"2023","unstructured":"Shang R, Zhang W, Li Z et al (2023) Attribute community detection based on latent representation learning and graph regularized non-negative matrix factorization. Appl Soft Comput 133:109932","journal-title":"Appl Soft Comput"},{"key":"7040_CR38","unstructured":"Shi HJM, Tu S, Xu Y et\u00a0al (2016) A primer on coordinate descent algorithms. arXiv:1610.00040"},{"issue":"6","key":"7040_CR39","doi-asserted-by":"publisher","first-page":"2352","DOI":"10.1137\/S0036142901393814","volume":"40","author":"D Sun","year":"2002","unstructured":"Sun D, Sun J (2002) Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems. SIAM J Numer Anal 40(6):2352\u20132367","journal-title":"SIAM J Numer Anal"},{"issue":"7","key":"7040_CR40","doi-asserted-by":"publisher","first-page":"1864","DOI":"10.1109\/TKDE.2016.2535367","volume":"28","author":"M Wang","year":"2016","unstructured":"Wang M, Fu W, Hao S et al (2016) Scalable semi-supervised learning by efficient anchor graph regularization. IEEE Trans Knowl Data Eng 28(7):1864\u20131877","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"12","key":"7040_CR41","doi-asserted-by":"publisher","first-page":"6348","DOI":"10.1109\/TNNLS.2018.2830761","volume":"29","author":"W Wu","year":"2018","unstructured":"Wu W, Jia Y, Kwong S et al (2018) Pairwise constraint propagation-induced symmetric nonnegative matrix factorization. IEEE Trans Neural Netw Learn Syst 29(12):6348\u20136361","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"7040_CR42","unstructured":"Xie J, Girshick R, Farhadi A (2016) Unsupervised deep embedding for clustering analysis. In: International conference on machine learning. PMLR, pp 478\u2013487"},{"key":"7040_CR43","doi-asserted-by":"crossref","unstructured":"Xu W, Gong Y (2004) Document clustering by concept factorization. In: Proceedings of the 27th annual international ACM SIGIR conference on Research and development in information retrieval, pp 202\u2013209","DOI":"10.1145\/1008992.1009029"},{"key":"7040_CR44","doi-asserted-by":"crossref","unstructured":"Xu W, Liu X, Gong Y (2003) Document clustering based on non-negative matrix factorization. In: Proceedings of the 26th annual international ACM SIGIR conference on research and development in informaion retrieval, pp 267\u2013273","DOI":"10.1145\/860435.860485"},{"key":"7040_CR45","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111590","volume":"158","author":"Y Xu","year":"2024","unstructured":"Xu Y, Niu G (2024) Research on multi-view clustering algorithm based on sequential three-way decision. Appl Soft Comput 158:111590","journal-title":"Appl Soft Comput"},{"issue":"3","key":"7040_CR46","doi-asserted-by":"publisher","first-page":"1758","DOI":"10.1137\/120887795","volume":"6","author":"Y Xu","year":"2013","unstructured":"Xu Y, Yin W (2013) A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion. SIAM J Imag Sci 6(3):1758\u20131789","journal-title":"SIAM J Imag Sci"},{"issue":"2","key":"7040_CR47","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1007\/s10915-017-0376-0","volume":"72","author":"Y Xu","year":"2017","unstructured":"Xu Y, Yin W (2017) A globally convergent algorithm for nonconvex optimization based on block coordinate update. J Sci Comput 72(2):700\u2013734","journal-title":"J Sci Comput"},{"key":"7040_CR48","unstructured":"Yang F, Parikh D, Batra D (2017) Towards k-means-friendly spaces: simultaneous deep learning and clustering. In: International conference on machine learning. PMLR, pp 3861\u20133870"},{"key":"7040_CR49","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2022.109274","volume":"137","author":"J Yin","year":"2023","unstructured":"Yin J, Peng S, Yang Z et al (2023) Hypergraph based semi-supervised symmetric nonnegative matrix factorization for image clustering. Pattern Recogn 137:109274","journal-title":"Pattern Recogn"},{"key":"7040_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111576","volume":"158","author":"K Yu","year":"2024","unstructured":"Yu K, Zhu Y, Yin X et al (2024) Structure-aware preserving projections with applications to medical image clustering. Appl Soft Comput 158:111576","journal-title":"Appl Soft Comput"},{"key":"7040_CR51","doi-asserted-by":"crossref","unstructured":"Yuan Z, Oja E (2005) Projective nonnegative matrix factorization for image compression and feature extraction. In: Image analysis: 14th Scandinavian Conference, SCIA 2005, Joensuu, Finland, June 19-22, 2005. Proceedings 14. Springer, pp 333\u2013342","DOI":"10.1007\/11499145_35"},{"issue":"7","key":"7040_CR52","doi-asserted-by":"publisher","first-page":"1717","DOI":"10.1109\/TPAMI.2012.274","volume":"35","author":"Z Zhang","year":"2012","unstructured":"Zhang Z, Zhao K (2012) Low-rank matrix approximation with manifold regularization. IEEE Trans Pattern Anal Mach Intell 35(7):1717\u20131729","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"7040_CR53","doi-asserted-by":"crossref","unstructured":"Zhou N, Choi KS, Chen B et\u00a0al (2022) Correntropy-based low-rank matrix factorization with constraint graph learning for image clustering. IEEE Trans Neural Netw Learn Syst","DOI":"10.1109\/TNNLS.2022.3166931"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-025-07040-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-025-07040-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-025-07040-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T10:17:42Z","timestamp":1774865862000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-025-07040-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,27]]},"references-count":53,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["7040"],"URL":"https:\/\/doi.org\/10.1007\/s10489-025-07040-w","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,27]]},"assertion":[{"value":"30 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"22"}}