A Fuzzy Clustering Validity Index Induced by Triple Center Relation

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dc.authoridTang, Yiming/0000-0002-0917-2277
dc.authorwosidTang, Yiming/AAL-6708-2020
dc.contributor.authorTang, Yiming
dc.contributor.authorHuang, Jiajia
dc.contributor.authorPedrycz, Witold
dc.contributor.authorLi, Bing
dc.contributor.authorRen, Fuji
dc.date.accessioned2024-05-19T14:40:12Z
dc.date.available2024-05-19T14:40:12Z
dc.date.issued2023
dc.departmentİstinye Üniversitesien_US
dc.description.abstractThe existing clustering validity indexes (CVIs) show some difficulties to produce the correct cluster number when some cluster centers are close to each other, and the separation processing mechanism appears simple. The results are imperfect in case of noisy data sets. For this reason, in this study, we come up with a novel CVI for fuzzy clustering, referred to as the triple center relation (TCR) index. The originality of this index is twofold. On the one hand, a new fuzzy cardinality is built on the strength of the maximum membership degree, and a novel compactness formula is constructed by combining it with the within-class weighted squared error sum. On the other hand, starting from the minimum distance between different cluster centers, the mean distance as well as the sample variance of cluster centers in the statistical sense are further integrated. These three factors are combined by means of product to form a triple characterization of the relationship between cluster centers, and hence a 3-D expression pattern of separability is formed. Subsequently, the TCR index is put forward by combining the compactness formula with the separability expression pattern. By virtue of the degenerate structure of hard clustering, we show an important property of the TCR index. Finally, based on the fuzzy C-means (FCMs) clustering algorithm, experimental studies were conducted on 36 data sets (incorporating artificial and UCI data sets, images, the Olivetti face database). For comparative purposes, 10 CVIs were also considered. It has been found that the proposed TCR index performs best in finding the correct cluster number, and has excellent stability.en_US
dc.description.sponsorshipNational Natural Science Foundation of China [62176083, 62277014, 62176084]; Key Research and Development Program of Anhui Province [202004d07020004]; Natural Science Foundation of Anhui Province [2108085MF203]en_US
dc.description.sponsorshipThis work was supported in part by the National Natural Science Foundation of China under Grant 62176083, Grant 62277014, and Grant 62176084; in part by the Key Research and Development Program of Anhui Province under Grant 202004d07020004; and in part by the Natural Science Foundation of Anhui Province under Grant 2108085MF203.en_US
dc.identifier.doi10.1109/TCYB.2023.3263215
dc.identifier.endpage5036en_US
dc.identifier.issn2168-2267
dc.identifier.issn2168-2275
dc.identifier.issue8en_US
dc.identifier.pmid37040251en_US
dc.identifier.scopus2-s2.0-85153351984en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage5024en_US
dc.identifier.urihttps://doi.org10.1109/TCYB.2023.3263215
dc.identifier.urihttps://hdl.handle.net/20.500.12713/4922
dc.identifier.volume53en_US
dc.identifier.wosWOS:000973197700001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherIeee-Inst Electrical Electronics Engineers Incen_US
dc.relation.ispartofIeee Transactions on Cyberneticsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmz20240519_kaen_US
dc.subjectClustering Validity Index (Cvi)en_US
dc.subjectCompactnessen_US
dc.subjectFuzzy Clusteringen_US
dc.subjectFuzzy C-Means (Fcms)en_US
dc.subjectSeparabilityen_US
dc.titleA Fuzzy Clustering Validity Index Induced by Triple Center Relationen_US
dc.typeArticleen_US

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