{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T18:32:36Z","timestamp":1773513156385,"version":"3.50.1"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,5,8]],"date-time":"2021-05-08T00:00:00Z","timestamp":1620432000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,8]],"date-time":"2021-05-08T00:00:00Z","timestamp":1620432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61762090"],"award-info":[{"award-number":["61762090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61966036"],"award-info":[{"award-number":["61966036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61662086"],"award-info":[{"award-number":["61662086"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Data Sci. Eng."],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Multi-view clustering (MVC), which aims to explore the underlying structure of data by leveraging heterogeneous information of different views, has brought along a growth of attention. Multi-view clustering algorithms based on different theories have been proposed and extended in various applications. However, most existing MVC algorithms are shallow models, which learn structure information of multi-view data by mapping multi-view data to low-dimensional representation space directly, ignoring the nonlinear structure information hidden in each view, and thus, the performance of multi-view clustering is weakened to a certain extent. In this paper, we propose a deep multi-view clustering algorithm based on multiple auto-encoder, termed MVC-MAE, to cluster multi-view data. MVC-MAE adopts auto-encoder to capture the nonlinear structure information of each view in a layer-wise manner and incorporate the local invariance within each view and consistent as well as complementary information between any two views together. Besides, we integrate the representation learning and clustering into a unified framework, such that two tasks can be jointly optimized. Extensive experiments on six real-world datasets demonstrate the promising performance of our algorithm compared with 15 baseline algorithms in terms of two evaluation metrics.<\/jats:p>","DOI":"10.1007\/s41019-021-00159-z","type":"journal-article","created":{"date-parts":[[2021,5,8]],"date-time":"2021-05-08T13:02:43Z","timestamp":1620478963000},"page":"323-338","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":71,"title":["Deep Multiple Auto-Encoder-Based Multi-view Clustering"],"prefix":"10.1007","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8109-7152","authenticated-orcid":false,"given":"Guowang","family":"Du","sequence":"first","affiliation":[]},{"given":"Lihua","family":"Zhou","sequence":"additional","affiliation":[]},{"given":"Yudi","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Kevin","family":"L\u00fc","sequence":"additional","affiliation":[]},{"given":"Lizhen","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,8]]},"reference":[{"key":"159_CR1","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1016\/j.knosys.2018.10.022","volume":"163","author":"H Wang","year":"2019","unstructured":"Wang H, Yang Y, Liu B, Fujita H (2019) A study of graph-based system for multi-view clustering. Knowl-Based Syst 163:1009\u20131019","journal-title":"Knowl-Based Syst"},{"key":"159_CR2","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.patcog.2018.11.007","volume":"88","author":"S Huang","year":"2019","unstructured":"Huang S, Kang Z, Tsang IW, Xu Z (2019) Auto-weighted multi-view clustering via kernelized graph learning. Pattern Recogn 88:174\u2013184. https:\/\/doi.org\/10.1016\/j.patcog.2018.11.007","journal-title":"Pattern Recogn"},{"key":"159_CR3","doi-asserted-by":"crossref","unstructured":"Cao X, Zhang C, Fu H, Liu S, Zhang H (2015) Diversity-induced multi-view subspace clustering. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp 586\u2013594","DOI":"10.1109\/CVPR.2015.7298657"},{"key":"159_CR4","doi-asserted-by":"crossref","unstructured":"Liu J, Wang C, Gao J, Han J (2013) Multi-view clustering via joint nonnegative matrix factorization. In: Proceedings of the 2013 SIAM International Conference on Data Mining. SIAM 2013, pp 252\u2013260","DOI":"10.1137\/1.9781611972832.28"},{"key":"159_CR5","doi-asserted-by":"crossref","unstructured":"Wang Z, Kong X, Fu H, Li M, Zhang Y (2015) Feature extraction via multi-view non-negative matrix factorization with local graph regularization. In: 2015 IEEE International conference on image processing (ICIP). IEEE, pp 3500\u20133504","DOI":"10.1109\/ICIP.2015.7351455"},{"key":"159_CR6","unstructured":"Andrew G, Arora R, Bilmes J, Livescu K (2013) Deep canonical correlation analysis. In: International Conference on Machine Learning. pp 1247\u20131255"},{"key":"159_CR7","doi-asserted-by":"crossref","unstructured":"Chaudhuri K, Kakade SM, Livescu K, Sridharan K (2009) Multi-view clustering via canonical correlation analysis. In: Proceedings of the 26th annual international conference on machine learning. ACM, pp 129\u2013136","DOI":"10.1145\/1553374.1553391"},{"key":"159_CR8","unstructured":"Xie J, Girshick R, Farhadi A (2016) Unsupervised deep embedding for clustering analysis. In: International conference on machine learning. pp 478\u2013487"},{"key":"159_CR9","doi-asserted-by":"crossref","unstructured":"Zhao H, Ding Z, Fu Y (2017) Multi-view clustering via deep matrix factorization. In: Thirty-First AAAI Conference on Artificial Intelligence. AAAI press, pp 2921\u20132927","DOI":"10.1609\/aaai.v31i1.10867"},{"issue":"2","key":"159_CR10","doi-asserted-by":"publisher","first-page":"83","DOI":"10.26599\/BDMA.2018.9020003","volume":"1","author":"Y Yang","year":"2018","unstructured":"Yang Y, Wang H (2018) Multi-view clustering: A survey. Big Data Mining and Analytics 1(2):83\u2013107","journal-title":"Big Data Mining and Analytics"},{"key":"159_CR11","doi-asserted-by":"crossref","unstructured":"Luo S, Zhang C, Zhang W, Cao X (2018) Consistent and specific multi-view subspace clustering. In: Proceedings of the AAAI Conference on Artificial Intelligence. vol 1","DOI":"10.1609\/aaai.v32i1.11617"},{"key":"159_CR12","doi-asserted-by":"crossref","unstructured":"Xu C, Guan Z, Zhao W, Niu Y, Wang Q, Wang Z Deep (2018) Multi-View Concept Learning. In: the 28th International Joint Conference on Artificial Intelligence. pp 2898\u20132904","DOI":"10.24963\/ijcai.2018\/402"},{"issue":"11","key":"159_CR13","doi-asserted-by":"publisher","first-page":"3016","DOI":"10.1109\/TKDE.2015.2448542","volume":"27","author":"Z Guan","year":"2015","unstructured":"Guan Z, Zhang L, Peng J, Fan J (2015) Multi-view concept learning for data representation. IEEE Trans Knowl Data Eng 27(11):3016\u20133028","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"159_CR14","unstructured":"Kumar A, Rai P, Daume H (2011) Co-regularized multi-view spectral clustering. In: Advances in neural information processing systems. pp 1413\u20131421"},{"key":"159_CR15","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.inffus.2017.12.002","volume":"44","author":"L Houthuys","year":"2018","unstructured":"Houthuys L, Langone R, Suykens JAK (2018) Multi-View Kernel Spectral Clustering. Information Fusion 44:46\u201356","journal-title":"Information Fusion"},{"key":"159_CR16","unstructured":"Nie F, Jing L, Li X (2016) Parameter-free auto-weighted multiple graph learning: a framework for multiview clustering and semi-supervised classification. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence"},{"key":"159_CR17","doi-asserted-by":"crossref","unstructured":"Hinton GE, Salakhutdinov RR (2006) Reducing the dimensionality of data with neural networks. science 313 (5786):504\u2013507","DOI":"10.1126\/science.1127647"},{"key":"159_CR18","doi-asserted-by":"crossref","unstructured":"Wang D, Cui P, Zhu W (2016) Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining. pp 1225\u20131234","DOI":"10.1145\/2939672.2939753"},{"issue":"7","key":"159_CR19","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1016\/j.ijar.2008.11.006","volume":"50","author":"R Salakhutdinov","year":"2009","unstructured":"Salakhutdinov R, Hinton G (2009) Semantic hashing. Int J Approximate Reasoning 50(7):969\u2013978","journal-title":"Int J Approximate Reasoning"},{"issue":"8","key":"159_CR20","doi-asserted-by":"publisher","first-page":"1548","DOI":"10.1109\/TPAMI.2010.231","volume":"33","author":"D Cai","year":"2011","unstructured":"Cai D, He X, Han J, Huang TS (2011) 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"},{"issue":"6755","key":"159_CR21","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"},{"issue":"7","key":"159_CR22","doi-asserted-by":"publisher","first-page":"1527","DOI":"10.1162\/neco.2006.18.7.1527","volume":"18","author":"GE Hinton","year":"2006","unstructured":"Hinton GE, Osindero S, Teh Y-W (2006) A fast learning algorithm for deep belief nets. Neural Comput 18(7):1527\u20131554","journal-title":"Neural Comput"},{"key":"159_CR23","doi-asserted-by":"crossref","unstructured":"Xia R, Pan Y, Du L, Yin J (2014) Robust multi-view spectral clustering via low-rank and sparse decomposition. In: Brodley CE, StoneP (eds) Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence. 27\u201331, 2014, Qu \u0301ebec City, Qu \u0301ebec, Canada, AAAI Press, pp 2149\u2013215","DOI":"10.1609\/aaai.v28i1.8950"},{"issue":"4","key":"159_CR24","doi-asserted-by":"publisher","first-page":"1080","DOI":"10.1162\/neco_a_01055","volume":"30","author":"K Zhan","year":"2018","unstructured":"Zhan K, Shi J, Wang J, Wang H, Xie Y (2018) Adaptive structure concept factorization for multiview clustering. Neural Comput 30(4):1080\u20131103","journal-title":"Neural Comput"},{"issue":"10","key":"159_CR25","doi-asserted-by":"publisher","first-page":"2887","DOI":"10.1109\/TCYB.2017.2751646","volume":"48","author":"K Zhan","year":"2017","unstructured":"Zhan K, Zhang C, Guan J, Wang J (2017) Graph learning for multiview clustering. IEEE transactions on cybernetics 48(10):2887\u20132895","journal-title":"IEEE transactions on cybernetics"},{"key":"159_CR26","doi-asserted-by":"crossref","unstructured":"Nie F, Li J, Li X (2017) Self-weighted Multiview Clustering with Multiple Graphs. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence. pp 2564\u20132570","DOI":"10.24963\/ijcai.2017\/357"},{"issue":"1","key":"159_CR27","first-page":"3","volume":"30","author":"AL Maas","year":"2013","unstructured":"Maas AL, Hannun AY (2013) Ng AY Rectifier nonlinearities improve neural network acoustic models. ICML 30(1):3","journal-title":"ICML"},{"key":"159_CR28","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 information retrieval. ACM, pp 267\u2013273","DOI":"10.1145\/860435.860485"},{"key":"159_CR29","unstructured":"Maaten Lvd, Hinton G (2008) Visualizing data using t-SNE. Journal of machine learning research 9; 2579\u20132605"},{"key":"159_CR30","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.neucom.2019.08.002","volume":"370","author":"Z Li","year":"2019","unstructured":"Li Z, Tang C, Chen J, Wan C, Yan W, Liu X (2019) Diversity and consistency learning guided spectral embedding for multi-view clustering. Neurocomputing 370:128\u2013139","journal-title":"Neurocomputing"},{"key":"159_CR31","doi-asserted-by":"crossref","unstructured":"Wang, X., Guo, X., Lei, Z., Zhang, C., & Li, S. Z. (2017). Exclusivity-Consistency Regularized Multi-view Subspace Clustering. Paper presented at the Computer Vision & Pattern Recognition.","DOI":"10.1109\/CVPR.2017.8"},{"key":"159_CR32","doi-asserted-by":"publisher","first-page":"107015","DOI":"10.1016\/j.patcog.2019.107015","volume":"97","author":"S Huang","year":"2020","unstructured":"Huang S, Kang Z, Xu Z (2020) Auto-weighted multi-view clustering via deep matrix decomposition. Pattern Recogn 97:107015","journal-title":"Pattern Recogn"},{"key":"159_CR33","doi-asserted-by":"crossref","unstructured":"Chua TS, Tang J, Hong R, Li H, Luo Z (2009) NUS-WIDE: A real-world web image database from National University of Singapore. In: Acm International Conference on Image & Video Retrieval.","DOI":"10.1145\/1646396.1646452"},{"key":"159_CR34","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.neucom.2019.12.054","volume":"390","author":"J Li","year":"2020","unstructured":"Li J, Zhou G, Qiu Y, Wang Y, Zhang Y, Xie S (2020) Deep graph regularized non-negative matrix factorization for multi-view clustering. Neurocomputing 390:108\u2013116","journal-title":"Neurocomputing"},{"key":"159_CR35","first-page":"612","volume-title":"Asia-Pacific Web (APWeb) and Web-Age Information Management (WAIM) Joint International Conference on Web and Big Data","author":"G Du","year":"2020","unstructured":"Du G, Zhou L, Yang Y, L\u00fc K, Wang L (2020) Multi-view Clustering via Multiple Auto-Encoder. Asia-Pacific Web (APWeb) and Web-Age Information Management (WAIM) Joint International Conference on Web and Big Data. Springer, pp 612\u2013626"}],"container-title":["Data Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41019-021-00159-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41019-021-00159-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41019-021-00159-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T19:30:25Z","timestamp":1672083025000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41019-021-00159-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,8]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["159"],"URL":"https:\/\/doi.org\/10.1007\/s41019-021-00159-z","relation":{},"ISSN":["2364-1185","2364-1541"],"issn-type":[{"value":"2364-1185","type":"print"},{"value":"2364-1541","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,8]]},"assertion":[{"value":"21 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 May 2021","order":4,"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 known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"The datasets supporting the results of this article are included within the article and its additional files.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Availability of data and materials."}}]}}