{"title":"On cluster validity for the fuzzy c-means model","authors":"N.R. Pal;J.C. Bezdek","doi":"10.1109/91.413225","DOIUrl":null,"url":null,"abstract":"Many functionals have been proposed for validation of partitions of object data produced by the fuzzy c-means (FCM) clustering algorithm. We examine the role a subtle but important parameter-the weighting exponent m of the FCM model-plays in determining the validity of FCM partitions. The functionals considered are the partition coefficient and entropy indexes of Bezdek, the Xie-Beni (1991), and extended Xie-Beni indexes, and the Fukuyama-Sugeno index (1989). Limit analysis indicates, and numerical experiments confirm, that the Fukuyama-Sugeno index is sensitive to both high and low values of m and may be unreliable because of this. Of the indexes tested, the Xie-Beni index provided the best response over a wide range of choices for the number of clusters, (2-10), and for m from 1.01-7. Finally, our calculations suggest that the best choice for m is probably in the interval [1.5, 2.5], whose mean and midpoint, m=2, have often been the preferred choice for many users of FCM.<\n<ETX>></ETX>","PeriodicalId":13212,"journal":{"name":"IEEE Transactions on Fuzzy Systems","volume":"3 3","pages":"370-379"},"PeriodicalIF":10.7000,"publicationDate":"1995-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1109/91.413225","citationCount":"1728","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Fuzzy Systems","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/413225/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 1728
Abstract
Many functionals have been proposed for validation of partitions of object data produced by the fuzzy c-means (FCM) clustering algorithm. We examine the role a subtle but important parameter-the weighting exponent m of the FCM model-plays in determining the validity of FCM partitions. The functionals considered are the partition coefficient and entropy indexes of Bezdek, the Xie-Beni (1991), and extended Xie-Beni indexes, and the Fukuyama-Sugeno index (1989). Limit analysis indicates, and numerical experiments confirm, that the Fukuyama-Sugeno index is sensitive to both high and low values of m and may be unreliable because of this. Of the indexes tested, the Xie-Beni index provided the best response over a wide range of choices for the number of clusters, (2-10), and for m from 1.01-7. Finally, our calculations suggest that the best choice for m is probably in the interval [1.5, 2.5], whose mean and midpoint, m=2, have often been the preferred choice for many users of FCM.<
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期刊介绍:
The IEEE Transactions on Fuzzy Systems is a scholarly journal that focuses on the theory, design, and application of fuzzy systems. It aims to publish high-quality technical papers that contribute significant technical knowledge and exploratory developments in the field of fuzzy systems. The journal particularly emphasizes engineering systems and scientific applications. In addition to research articles, the Transactions also includes a letters section featuring current information, comments, and rebuttals related to published papers.