{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T19:12:50Z","timestamp":1781291570073,"version":"3.54.1"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,8,8]],"date-time":"2019-08-08T00:00:00Z","timestamp":1565222400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation for Scientific and Technological Project of Henan Province","award":["172102210279"],"award-info":[{"award-number":["172102210279"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Electrical and Computer Engineering"],"published-print":{"date-parts":[[2019,8,8]]},"abstract":"<jats:p>Because traditional fuzzy clustering validity indices need to specify the number of clusters and are sensitive to noise data, we propose a validity index for fuzzy clustering, named CSBM (compactness separateness bipartite modularity), based on bipartite modularity. CSBM enhances the robustness by combining intraclass compactness and interclass separateness and can automatically determine the optimal number of clusters. In order to estimate the performance of CSBM, we carried out experiments on six real datasets and compared CSBM with other six prominent indices. Experimental results show that the CSBM index performs the best in terms of robustness while accurately detecting the number of clusters.<\/jats:p>","DOI":"10.1155\/2019\/2719617","type":"journal-article","created":{"date-parts":[[2019,8,8]],"date-time":"2019-08-08T19:30:23Z","timestamp":1565292623000},"page":"1-9","source":"Crossref","is-referenced-by-count":18,"title":["A Validity Index for Fuzzy Clustering Based on Bipartite Modularity"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0540-865X","authenticated-orcid":true,"given":"Yongli","family":"Liu","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, Henan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0391-7829","authenticated-orcid":true,"given":"Xiaoyang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, Henan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8866-0219","authenticated-orcid":true,"given":"Jingli","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, Henan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6700-9446","authenticated-orcid":true,"given":"Hao","family":"Chao","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, Henan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"issue":"4","key":"2","first-page":"197","volume":"36","year":"2017","journal-title":"International Journal of Emerging Trends & Technology in Computer Science"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1142\/s0218213017300022"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2016.06.012"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0197499"},{"key":"7","year":"2017"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/jstars.2015.2444405"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/tii.2017.2684807"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.4316\/aece.2017.03014"},{"issue":"1171","key":"11","first-page":"203","volume":"22","year":"1987","journal-title":"Advanced Applications in Pattern Recognition"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.12.013"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/bf02339490"},{"issue":"3","key":"16","first-page":"58","volume":"3","year":"1974","journal-title":"Journal of Cybernetics"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8655(96)00026-8"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/34.85677"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2004.11.022"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2010.04.025"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.69.026113"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1038\/nbt.2530"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/s10334-010-0205-z"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.76.066102"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.76.036102"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7932-3_7"}],"container-title":["Journal of Electrical and Computer Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jece\/2019\/2719617.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jece\/2019\/2719617.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jece\/2019\/2719617.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,8]],"date-time":"2019-08-08T19:30:35Z","timestamp":1565292635000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jece\/2019\/2719617\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,8]]},"references-count":22,"alternative-id":["2719617","2719617"],"URL":"https:\/\/doi.org\/10.1155\/2019\/2719617","relation":{},"ISSN":["2090-0147","2090-0155"],"issn-type":[{"value":"2090-0147","type":"print"},{"value":"2090-0155","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,8]]}}}