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Data"],"published-print":{"date-parts":[[2019,2,28]]},"abstract":"<jats:p>Ensemble Clustering (EC) is an important topic for data cluster analysis. It targets to integrate multiple Basic Partitions (BPs) of a particular dataset into a consensus partition. Among previous works, one promising and effective way is to transform EC as a graph partitioning problem on the co-association matrix, which is a pair-wise similarity matrix summarized by all the BPs in essence. However, most existing EC methods directly utilize the co-association matrix, yet without considering various noises (e.g., the disagreement between different BPs and the outliers) that may exist in it. These noises can impair the cluster structure of a co-association matrix, and thus mislead the final graph partitioning process. To address this challenge, we propose a novel Robust Spectral Ensemble Clustering (RSEC) algorithm in this article. Specifically, we learn low-rank representation (LRR) for the co-association matrix to uncover its cluster structure and handle the noises, and meanwhile, we perform spectral clustering with the learned representation to seek for a consensus partition. These two steps are jointly proceeded within a unified optimization framework. In particular, during the optimizing process, we leverage consensus partition to iteratively enhance the block-diagonal structure of LRR, in order to assist the graph partitioning. To solve RSEC, we first formulate it by using nuclear norm as a convex proxy to the rank function. Then, motivated by the recent advances in non-convex rank minimization, we further develop a non-convex model for RSEC and provide it a solution by the majorization--minimization Augmented Lagrange Multiplier algorithm. Experiments on 18 real-world datasets demonstrate the effectiveness of our algorithm compared with state-of-the-art methods. Moreover, several impact factors on the clustering performance of our approach are also explored extensively.<\/jats:p>","DOI":"10.1145\/3278606","type":"journal-article","created":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T18:36:36Z","timestamp":1547058996000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":49,"title":["Robust Spectral Ensemble Clustering via Rank Minimization"],"prefix":"10.1145","volume":"13","author":[{"given":"Zhiqiang","family":"Tao","sequence":"first","affiliation":[{"name":"Northeastern University, Boston, MA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongfu","family":"Liu","sequence":"additional","affiliation":[{"name":"Brandeis University, Waltham, MA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1205-8632","authenticated-orcid":false,"given":"Sheng","family":"Li","sequence":"additional","affiliation":[{"name":"University of Georgia, Athens, GA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengming","family":"Ding","sequence":"additional","affiliation":[{"name":"Indiana University - Purdue University Indianapolis, Indianapolis, IN"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"Fu","sequence":"additional","affiliation":[{"name":"Northeastern University, Boston, MA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,1,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.1138"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2010.231"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/080738970"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"E. 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