{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:03:30Z","timestamp":1778601810218,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T00:00:00Z","timestamp":1523491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Macau RC MYRG2015-00148-FST, Science and Technology Development Fund, Macao S.A.R","award":["097\/2015\/A3"],"award-info":[{"award-number":["097\/2015\/A3"]}]},{"name":"National Nature Science Foundation of China","award":["61673405"],"award-info":[{"award-number":["61673405"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Ensemble clustering combines different basic partitions of a dataset into a more stable and robust one. Thus, cluster ensemble plays a significant role in applications like image segmentation. However, existing ensemble methods have a few demerits, including the lack of diversity of basic partitions and the low accuracy caused by data noise. In this paper, to get over these difficulties, we propose an efficient fuzzy cluster ensemble method based on Kullback\u2013Leibler divergence or simply, the KL divergence. The data are first classified with distinct fuzzy clustering methods. Then, the soft clustering results are aggregated by a fuzzy KL divergence-based objective function. Moreover, for image segmentation problems, we utilize the local spatial information in the cluster ensemble algorithm to suppress the effect of noise. Experiment results reveal that the proposed methods outperform many other methods in synthetic and real image-segmentation problems.<\/jats:p>","DOI":"10.3390\/e20040273","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T12:19:27Z","timestamp":1523535567000},"page":"273","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4184-3701","authenticated-orcid":false,"given":"Huiqin","family":"Wei","sequence":"first","affiliation":[{"name":"Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0184-5446","authenticated-orcid":false,"given":"Long","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1109\/TMI.2013.2255309","article-title":"Attributed relational graphs for cell nucleus segmentation in fluorescence microscopy images","volume":"32","author":"Arslan","year":"2013","journal-title":"IEEE Trans. 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