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Optim."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Common clustering methods, such as [Formula: see text]-means and convex clustering, group similar vector-valued observations into clusters. However, with the increasing prevalence of matrix-valued observations, which often exhibit low rank characteristics, there is a growing need for specialized clustering techniques for these data types. In this paper, we propose a low rank convex clustering model tailored for matrix-valued observations. Our approach extends the convex clustering model originally designed for vector-valued data to classify matrix-valued observations. Additionally, it serves as a convex relaxation of the low rank [Formula: see text]-means method proposed by Z. Lyu, and D. Xia [ J. R. Stat. Soc. Ser. B. Methodol., 88\u00a0(2026),\u00a0pp.\u00a043\u201365]. Theoretically, we establish exact cluster recovery for finite samples and asymptotic cluster recovery as the sample size approaches infinity. We also give a finite sample bound on prediction error in terms of centroid estimation, and further establish the prediction consistency. To make the model practically useful, we develop an efficient double-loop algorithm for solving it. Extensive numerical experiments are conducted to show the effectiveness of our proposed model.<\/jats:p>","DOI":"10.1137\/24m1721979","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T07:00:36Z","timestamp":1783926036000},"page":"1446-1475","source":"Crossref","is-referenced-by-count":0,"title":["Low Rank Convex Clustering for Matrix-Valued Observations"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9787-8586","authenticated-orcid":true,"given":"Meixia","family":"Lin","sequence":"first","affiliation":[{"name":"Institute of Statistics and Big Data, Renmin University of China, Beijing, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2679-3630","authenticated-orcid":true,"given":"Yangjing","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/080738970"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1145\/1970392.1970395"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2023.2197474"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1004228"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2014.948181"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-018-1300-6"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2006.08.017"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"M. 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