{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T21:01:33Z","timestamp":1780347693021,"version":"3.54.1"},"reference-count":44,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Pattern Recognition"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.patcog.2026.114086","type":"journal-article","created":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T15:24:07Z","timestamp":1780154647000},"page":"114086","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"PB","title":["Hierarchical Dynamic Self-Supervised Learning for Robust Deep Non-negative Matrix Factorization in clustering tasks"],"prefix":"10.1016","volume":"180","author":[{"given":"Fang","family":"Yuan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dengxiu","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangyong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuqiang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2756-0054","authenticated-orcid":false,"given":"Min","family":"Gan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.patcog.2026.114086_b1","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1109\/TNN.2006.873291","article-title":"Exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification","volume":"17","author":"Zafeiriou","year":"2006","journal-title":"IEEE Trans. Neural Netw."},{"key":"10.1016\/j.patcog.2026.114086_b2","series-title":"Proceedings of the 2018 World Wide Web Conference","first-page":"1105","article-title":"Short-text topic modeling via non-negative matrix factorization enriched with local word-context correlations","author":"Shi","year":"2018"},{"issue":"5","key":"10.1016\/j.patcog.2026.114086_b3","doi-asserted-by":"crossref","DOI":"10.1145\/3767726","article-title":"Nonnegative matrix factorization in dimensionality reduction: A survey","volume":"58","author":"Saberi-Movahed","year":"2025","journal-title":"ACM Comput. Surv."},{"issue":"1","key":"10.1016\/j.patcog.2026.114086_b4","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/TPAMI.2008.277","article-title":"Convex and semi-nonnegative matrix factorizations","volume":"32","author":"Ding","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10.1016\/j.patcog.2026.114086_b5","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.112597","article-title":"An autoencoder-like deep NMF representation learning algorithm for clustering","volume":"305","author":"Wang","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"10.1016\/j.patcog.2026.114086_b6","series-title":"Chinese Conference on Biometric Recognition","first-page":"583","article-title":"Deep convex NMF for image clustering","author":"Qian","year":"2016"},{"key":"10.1016\/j.patcog.2026.114086_b7","series-title":"Proceedings of the 27th ACM International Conference on Information and Knowledge Management","first-page":"1393","article-title":"Deep autoencoder-like nonnegative matrix factorization for community detection","author":"Ye","year":"2018"},{"key":"10.1016\/j.patcog.2026.114086_b8","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2022.109210","article-title":"Deep alternating non-negative matrix factorisation","volume":"251","author":"Sun","year":"2022","journal-title":"Knowl.-Based Syst."},{"issue":"10","key":"10.1016\/j.patcog.2026.114086_b9","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1109\/TAI.2025.3559053","article-title":"Recommender systems based on nonnegative matrix factorization: A survey","volume":"6","author":"Ahmadian","year":"2025","journal-title":"IEEE Trans. Artif. Intell."},{"issue":"8","key":"10.1016\/j.patcog.2026.114086_b10","doi-asserted-by":"crossref","first-page":"4591","DOI":"10.1109\/TII.2019.2893714","article-title":"Deep matrix factorization with implicit feedback embedding for recommendation system","volume":"15","author":"Yi","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"10.1016\/j.patcog.2026.114086_b11","doi-asserted-by":"crossref","DOI":"10.1016\/j.patcog.2025.112027","article-title":"Deep matrix factorization with adaptive weights for multi-view clustering","volume":"170","author":"Khalafaoui","year":"2026","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.patcog.2026.114086_b12","doi-asserted-by":"crossref","DOI":"10.1016\/j.patcog.2025.112454","article-title":"Multi-view biclustering via non-negative matrix tri-factorisation","volume":"172","author":"Orme","year":"2026","journal-title":"Pattern Recognit."},{"issue":"10","key":"10.1016\/j.patcog.2026.114086_b13","doi-asserted-by":"crossref","first-page":"6245","DOI":"10.1109\/TGRS.2018.2834567","article-title":"Hyperspectral unmixing using sparsity-constrained deep nonnegative matrix factorization with total variation","volume":"56","author":"Feng","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"issue":"3","key":"10.1016\/j.patcog.2026.114086_b14","first-page":"3","article-title":"Learning deep features and topological structure of cells for clustering of scRNA-sequencing data","author":"Haiyue","year":"2022","journal-title":"Brief. Bioinform."},{"key":"10.1016\/j.patcog.2026.114086_b15","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.compbiolchem.2017.03.014","article-title":"Discovering DNA methylation patterns for long non-coding RNAs associated with cancer subtypes","author":"Ma","year":"2017","journal-title":"Comput. Biol. Chem."},{"issue":"4","key":"10.1016\/j.patcog.2026.114086_b16","first-page":"531","article-title":"The extraction of drug-disease correlations based on module distance in incomplete human interactome","volume":"10","author":"Yu","year":"2016","journal-title":"BMC Syst. Biol."},{"issue":"Suppl 1","key":"10.1016\/j.patcog.2026.114086_b17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1752-0509-6-S1-S6","article-title":"Discovering protein complexes in protein interaction networks via exploring the weak ties effect","volume":"6","author":"Ma","year":"2012","journal-title":"Bmc Syst. Biol."},{"key":"10.1016\/j.patcog.2026.114086_b18","doi-asserted-by":"crossref","DOI":"10.1016\/j.cosrev.2021.100423","article-title":"A survey on deep matrix factorizations","volume":"42","author":"De Handschutter","year":"2021","journal-title":"Comput. Sci. Rev."},{"key":"10.1016\/j.patcog.2026.114086_b19","unstructured":"Kenji Kawaguchi, Deep learning without poor local minima, in: Proceedings of the 30th International Conference on Neural Information Processing Systems, ISBN: 9781510838819, 2016, pp. 586\u2013594."},{"key":"10.1016\/j.patcog.2026.114086_b20","unstructured":"George Trigeorgis, Konstantinos Bousmalis, Stefanos Zafeiriou, Bj\u00f6rn W. Schuller, A deep semi-NMF model for learning hidden representations, in: Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32, 2014, pp. II\u20131692\u2013II\u20131700."},{"key":"10.1016\/j.patcog.2026.114086_b21","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1142\/S0129065707001275","article-title":"Multilayer nonnegative matrix factorization using projected gradient approaches","volume":"17","author":"Cichocki","year":"2008","journal-title":"Int. J. Neural Syst."},{"issue":"3","key":"10.1016\/j.patcog.2026.114086_b22","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1109\/TPAMI.2016.2554555","article-title":"A deep matrix factorization method for learning attribute representations","volume":"39","author":"Trigeorgis","year":"2017","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"6","key":"10.1016\/j.patcog.2026.114086_b23","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1109\/TPAMI.2019.2962679","article-title":"Deep non-negative matrix factorization architecture based on underlying basis images learning","volume":"43","author":"Zhao","year":"2021","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"7","key":"10.1016\/j.patcog.2026.114086_b24","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1109\/LGRS.2018.2823425","article-title":"Sparsity-constrained deep nonnegative matrix factorization for hyperspectral unmixing","volume":"15","author":"Fang","year":"2018","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"10.1016\/j.patcog.2026.114086_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2025.110715","article-title":"Orthogonal diversity nonnegative matrix factorization for multi-view clustering","volume":"152","author":"Zhang","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.patcog.2026.114086_b26","doi-asserted-by":"crossref","DOI":"10.1016\/j.patcog.2023.110179","article-title":"Deep asymmetric nonnegative matrix factorization for graph clustering","volume":"148","author":"Hajiveiseh","year":"2024","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.patcog.2026.114086_b27","series-title":"Intelligent Computing Methodologies","first-page":"378","article-title":"BP neural network-based deep non-negative matrix factorization for image clustering","author":"Zeng","year":"2020"},{"key":"10.1016\/j.patcog.2026.114086_b28","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2024.123645","article-title":"Deep nonnegative matrix factorization with joint global and local structure preservation","volume":"249","author":"Saberi-Movahed","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.patcog.2026.114086_b29","doi-asserted-by":"crossref","DOI":"10.1016\/j.patcog.2022.109102","article-title":"A consistent and flexible framework for deep matrix factorizations","volume":"134","author":"De Handschutter","year":"2023","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.patcog.2026.114086_b30","doi-asserted-by":"crossref","unstructured":"Yoshua Bengio, Pascal Lamblin, Dan Popovici, Hugo Larochelle, Greedy layer-wise training of deep networks, in: Proceedings of the 20th International Conference on Neural Information Processing Systems, 2006, pp. 153\u2013160.","DOI":"10.7551\/mitpress\/7503.003.0024"},{"issue":"15","key":"10.1016\/j.patcog.2026.114086_b31","first-page":"16135","article-title":"Creating coherence in federated non-negative matrix factorization","volume":"39","author":"Dalleiger","year":"2025","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"10.1016\/j.patcog.2026.114086_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.ins.2024.120585","article-title":"Cluster structure augmented deep nonnegative matrix factorization with low-rank tensor learning","volume":"670","author":"Zhong","year":"2024","journal-title":"Inform. Sci."},{"key":"10.1016\/j.patcog.2026.114086_b33","doi-asserted-by":"crossref","DOI":"10.1016\/j.patcog.2022.108984","article-title":"Progressive deep non-negative matrix factorization architecture with graph convolution-based basis image reorganization","volume":"132","author":"Zhao","year":"2022","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.patcog.2026.114086_b34","series-title":"Proceedings of the 32nd ACM International Conference on Multimedia","first-page":"1130","article-title":"Multi-view clustering based on deep non-negative tensor factorization","author":"Feng","year":"2024"},{"issue":"6","key":"10.1016\/j.patcog.2026.114086_b35","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1109\/TETCI.2025.3572129","article-title":"Robust low-rank tensor constrained orthogonal symmetric non-negative matrix factorization for multi-layer networks community detection","volume":"9","author":"Zhou","year":"2025","journal-title":"IEEE Trans. Emerg. Top. Comput. Intell."},{"key":"10.1016\/j.patcog.2026.114086_b36","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.neucom.2021.08.152","article-title":"A survey of deep nonnegative matrix factorization","volume":"491","author":"Chen","year":"2022","journal-title":"Neurocomputing"},{"issue":"8","key":"10.1016\/j.patcog.2026.114086_b37","doi-asserted-by":"crossref","first-page":"5042","DOI":"10.1109\/TII.2019.2951011","article-title":"A deep nonnegative matrix factorization approach via autoencoder for nonlinear fault detection","volume":"16","author":"Ren","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"10.1016\/j.patcog.2026.114086_b38","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2020.106846","article-title":"Structural deep nonnegative matrix factorization for community detection","volume":"97","author":"Zhang","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.patcog.2026.114086_b39","article-title":"Symmetric non-negative matrix factorization-based deep representation algorithm for multi-view clustering","volume":"139","author":"Deng","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"6","key":"10.1016\/j.patcog.2026.114086_b40","doi-asserted-by":"crossref","first-page":"2882","DOI":"10.1109\/TSP.2012.2190406","article-title":"NeNMF: An optimal gradient method for nonnegative matrix factorization","volume":"60","author":"Guan","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.patcog.2026.114086_b41","series-title":"Proceedings of the 26th International Joint Conference on Artificial Intelligence","first-page":"1965","article-title":"Variational deep embedding: an unsupervised and generative approach to clustering","author":"Jiang","year":"2017"},{"key":"10.1016\/j.patcog.2026.114086_b42","doi-asserted-by":"crossref","unstructured":"Xifeng Guo, Long Gao, Xinwang Liu, Jianping Yin, Improved Deep Embedded Clustering with Local Structure Preservation, in: International Joint Conference on Artificial Intelligence, 2017, pp. 1753\u20131759.","DOI":"10.24963\/ijcai.2017\/243"},{"key":"10.1016\/j.patcog.2026.114086_b43","first-page":"8547","article-title":"Contrastive clustering","volume":"vol. 35, no. 10","author":"Li","year":"2021"},{"issue":"8","key":"10.1016\/j.patcog.2026.114086_b44","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1109\/TPAMI.2010.231","article-title":"Graph regularized nonnegative matrix factorization for data representation","volume":"33","author":"Cai","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."}],"container-title":["Pattern Recognition"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0031320326010514?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0031320326010514?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T20:14:31Z","timestamp":1780344871000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0031320326010514"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":44,"alternative-id":["S0031320326010514"],"URL":"https:\/\/doi.org\/10.1016\/j.patcog.2026.114086","relation":{},"ISSN":["0031-3203"],"issn-type":[{"value":"0031-3203","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Hierarchical Dynamic Self-Supervised Learning for Robust Deep Non-negative Matrix Factorization in clustering tasks","name":"articletitle","label":"Article Title"},{"value":"Pattern Recognition","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.patcog.2026.114086","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"114086"}}