A possibilistic fuzzy c-means clustering algorithm
In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint...
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| Published in | IEEE transactions on fuzzy systems Vol. 13; no. 4; pp. 517 - 530 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.08.2005
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1063-6706 1941-0034 |
| DOI | 10.1109/TFUZZ.2004.840099 |
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| Abstract | In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification. |
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| AbstractList | Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification. In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification. |
| Author | Keller, J.M. Bezdek, J.C. Pal, N.R. Pal, K. |
| Author_xml | – sequence: 1 givenname: N.R. surname: Pal fullname: Pal, N.R. organization: Electron. & Commun. Sci. Unit, Indian Stat. Inst., Calcutta, India – sequence: 2 givenname: K. surname: Pal fullname: Pal, K. – sequence: 3 givenname: J.M. surname: Keller fullname: Keller, J.M. – sequence: 4 givenname: J.C. surname: Bezdek fullname: Bezdek, J.C. |
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| Cites_doi | 10.1109/91.531780 10.1109/91.531779 10.1109/IVELEC.2009.5193407 10.1016/j.fss.2003.11.009 10.1109/91.366564 10.1109/FUZZY.1997.616338 10.1007/978-1-4757-0450-1 10.1109/91.227387 10.1109/FUZZ.2002.1006721 10.1109/72.159055 |
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| Title | A possibilistic fuzzy c-means clustering algorithm |
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