Alternative c-means clustering algorithms
In this paper we propose a new metric to replace the Euclidean norm in c-means clustering procedures. On the basis of the robust statistic and the influence function, we claim that the proposed new metric is more robust than the Euclidean norm. We then create two new clustering methods called the al...
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| Published in | Pattern recognition Vol. 35; no. 10; pp. 2267 - 2278 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.10.2002
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0031-3203 1873-5142 |
| DOI | 10.1016/S0031-3203(01)00197-2 |
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| Abstract | In this paper we propose a new metric to replace the Euclidean norm in c-means clustering procedures. On the basis of the robust statistic and the influence function, we claim that the proposed new metric is more robust than the Euclidean norm. We then create two new clustering methods called the alternative hard c-means (AHCM) and alternative fuzzy c-means (AFCM) clustering algorithms. These alternative types of c-means clustering have more robustness than c-means clustering. Numerical results show that AHCM has better performance than HCM and AFCM is better than FCM. We recommend AFCM for use in cluster analysis. Recently, this AFCM algorithm has successfully been used in segmenting the magnetic resonance image of Ophthalmology to differentiate the abnormal tissues from the normal tissues. |
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| AbstractList | In this paper we propose a new metric to replace the Euclidean norm in c-means clustering procedures. On the basis of the robust statistic and the influence function, we claim that the proposed new metric is more robust than the Euclidean norm. We then create two new clustering methods called the alternative hard c-means (AHCM) and alternative fuzzy c-means (AFCM) clustering algorithms. These alternative types of c-means clustering have more robustness than c-means clustering. Numerical results show that AHCM has better performance than HCM and AFCM is better than FCM. We recommend AFCM for use in cluster analysis. Recently, this AFCM algorithm has successfully been used in segmenting the magnetic resonance image of Ophthalmology to differentiate the abnormal tissues from the normal tissues. |
| Author | Wu, Kuo-Lung Yang, Miin-Shen |
| Author_xml | – sequence: 1 givenname: Kuo-Lung surname: Wu fullname: Wu, Kuo-Lung – sequence: 2 givenname: Miin-Shen surname: Yang fullname: Yang, Miin-Shen email: msyang@math.cycu.edu.tw |
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| Keywords | Alternative c-means Hard c-means Robustness Noise Fixed-point iterations Fuzzy c-means |
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| References_xml | – year: 1976 ident: BIB11 publication-title: Principles of Mathematical Analysis – volume: 35 start-page: 73 year: 1964 end-page: 101 ident: BIB13 article-title: Robust estimation of a location parameter publication-title: Ann. Math. Statist. – reference: M.S. Yang, Y.J. Hu, K.C.R. Lin, C.C.L. Lin, Segmentation techniques for tissue differentiation in MRI of Ophthalmology using fuzzy clustering algorithms, Magnetic Resonance Imaging (2001) (in the first revision). – year: 1988 ident: BIB2 publication-title: Algorithm for Clustering Data – year: 1981 ident: BIB12 publication-title: Robust Statistics – volume: 1 start-page: 98 year: 1993 end-page: 110 ident: BIB15 article-title: A possibilistic approach to clustering publication-title: IEEE Trans. Fuzzy Systems – volume: 18 start-page: 1 year: 1993 end-page: 16 ident: BIB5 article-title: A survey of fuzzy clustering publication-title: Math. Comput. Modelling – year: 1981 ident: BIB6 publication-title: Pattern Recognition with Fuzzy Objective Function Algorithms – volume: 3 start-page: 32 year: 1974 end-page: 57 ident: BIB7 article-title: A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters publication-title: J. Cybernet. – volume: 11 start-page: 773 year: 1989 end-page: 781 ident: BIB8 article-title: Unsupervised optimal fuzzy clustering publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – year: 1973 ident: BIB1 publication-title: Pattern Classification and Scene Analysis – year: 1990 ident: BIB3 publication-title: Finding Groups in Data: An Introduction to Cluster Analysis – volume: 8 start-page: 338 year: 1965 end-page: 353 ident: BIB4 article-title: Fuzzy sets publication-title: Inf. Control – volume: 16 start-page: 343 year: 1990 end-page: 355 ident: BIB9 article-title: Fuzzy-shell clustering and applications to circle detection in digital images publication-title: Int. J. General Syst. – volume: 27 start-page: 1 year: 1997 end-page: 13 ident: BIB10 article-title: On cluster-wise fuzzy regression analysis publication-title: IEEE Trans. Systems, Man, Cybern. – volume: 8 start-page: 338 year: 1965 ident: 10.1016/S0031-3203(01)00197-2_BIB4 article-title: Fuzzy sets publication-title: Inf. Control doi: 10.1016/S0019-9958(65)90241-X – year: 1973 ident: 10.1016/S0031-3203(01)00197-2_BIB1 – volume: 16 start-page: 343 year: 1990 ident: 10.1016/S0031-3203(01)00197-2_BIB9 article-title: Fuzzy-shell clustering and applications to circle detection in digital images publication-title: Int. J. General Syst. doi: 10.1080/03081079008935087 – volume: 27 start-page: 1 year: 1997 ident: 10.1016/S0031-3203(01)00197-2_BIB10 article-title: On cluster-wise fuzzy regression analysis publication-title: IEEE Trans. Systems, Man, Cybern. doi: 10.1109/3477.552181 – volume: 1 start-page: 98 year: 1993 ident: 10.1016/S0031-3203(01)00197-2_BIB15 article-title: A possibilistic approach to clustering publication-title: IEEE Trans. Fuzzy Systems doi: 10.1109/91.227387 – year: 1981 ident: 10.1016/S0031-3203(01)00197-2_BIB6 – volume: 35 start-page: 73 year: 1964 ident: 10.1016/S0031-3203(01)00197-2_BIB13 article-title: Robust estimation of a location parameter publication-title: Ann. Math. Statist. doi: 10.1214/aoms/1177703732 – year: 1988 ident: 10.1016/S0031-3203(01)00197-2_BIB2 – volume: 11 start-page: 773 year: 1989 ident: 10.1016/S0031-3203(01)00197-2_BIB8 article-title: Unsupervised optimal fuzzy clustering publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.192473 – year: 1976 ident: 10.1016/S0031-3203(01)00197-2_BIB11 – ident: 10.1016/S0031-3203(01)00197-2_BIB14 doi: 10.1016/S0730-725X(02)00477-0 – year: 1990 ident: 10.1016/S0031-3203(01)00197-2_BIB3 – year: 1981 ident: 10.1016/S0031-3203(01)00197-2_BIB12 – volume: 18 start-page: 1 year: 1993 ident: 10.1016/S0031-3203(01)00197-2_BIB5 article-title: A survey of fuzzy clustering publication-title: Math. Comput. Modelling doi: 10.1016/0895-7177(93)90202-A – volume: 3 start-page: 32 year: 1974 ident: 10.1016/S0031-3203(01)00197-2_BIB7 article-title: A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters publication-title: J. Cybernet. doi: 10.1080/01969727308546046 |
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| Snippet | In this paper we propose a new metric to replace the Euclidean norm in c-means clustering procedures. On the basis of the robust statistic and the influence... |
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| SubjectTerms | Alternative c-means Fixed-point iterations Fuzzy c-means Hard c-means Noise Robustness |
| Title | Alternative c-means clustering algorithms |
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