{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T17:33:27Z","timestamp":1723570407847},"reference-count":59,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,12]],"date-time":"2022-12-12T00:00:00Z","timestamp":1670803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["11501435","61976130"]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2022KRM170"],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015401","name":"key research and development projects of Shaanxi Province","doi-asserted-by":"publisher","award":["2018KW-021"],"id":[{"id":"10.13039\/501100015401","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"Multi-view clustering algorithms based on matrix factorization have gained enormous development in recent years. Although these algorithms have gained impressive results, they typically neglect the spatial structures that the latent data representation should have, for example, the ideal data representation owns a block structure just like the indicator matrix has. To address this issue, a new algorithm named latent multi-view semi-nonnegative matrix factorization with block diagonal constraint (LMSNB) is proposed. First, latent representation learning and Semi-NMF are combined to get a lower-dimensional representation with consistent information from different views. Second, the block diagonal constraint is able to capture the global structure of original data. In addition, the graph regularization is considered in our model to preserve the local structure. LMSNB can deal with negative data matrix and be applied to more fields. Although the low dimensional representation from semi-nonnegative matrix factorization loses some valuable information, it still has same structure as original data with the help of block diagonal constraint and graph regularization. Finally, an iterative optimization algorithm is proposed for our objective problem. Experiments on several multi-view benchmark datasets demonstrate the effectiveness of our approach against other state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/axioms11120722","type":"journal-article","created":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T08:32:32Z","timestamp":1670920352000},"page":"722","source":"Crossref","is-referenced-by-count":1,"title":["Latent Multi-View Semi-Nonnegative Matrix Factorization with Block Diagonal Constraint"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-0705-7969","authenticated-orcid":false,"given":"Lin","family":"Yuan","sequence":"first","affiliation":[{"name":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710084, China"}]},{"given":"Xiaofei","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710084, China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8765-1233","authenticated-orcid":false,"given":"Zhiwei","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710084, China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3356-7535","authenticated-orcid":false,"given":"Yingcang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710084, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,12]]},"reference":[{"key":"ref_1","first-page":"100","article-title":"Algorithm AS 136: A k-means clustering algorithm","volume":"28","author":"Hartigan","year":"1979","journal-title":"J. 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