Paper:
Generalized Fuzzy c-Means Clustering and its Property of Fuzzy Classification Function
Yuchi Kanzawa* and Sadaaki Miyamoto**
*Shibaura Institute of Technology
3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan
**University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
This study shows that a generalized fuzzy c-means (gFCM) clustering algorithm, which covers both standard and exponential fuzzy c-means clustering, can be constructed if a given fuzzified function, its derivative, and its inverse derivative can be calculated. Furthermore, our results show that the fuzzy classification function for gFCM exhibits a behavior similar to that of both standard and exponential fuzzy c-means clustering.
- [1] J. MacQueen, “Some Methods for Classification and Analysis of Multivariate Observations,” Proc. of the 5th Berkeley Symp. on Mathematical Statistics and Probability, pp. 281-297, 1967.
- [2] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.
- [3] K. Treerattanapitak and C. Jaruskulchai, “Membership Enhancement with Exponential Fuzzy Clustering for Collaborative Filtering,” Proc. of the 17th Int. Conf. on Neural Information Processing (ICONIP 2010), Part 1, pp. 559-566, 2010.
- [4] S. Miyamoto and K. Umayahara, “Methods in Hard and Fuzzy Clustering,” Z.-Q. Liu and S. Miyamoto (Eds.), “Soft Computing and Human-Centered Machines,” pp. 85-129, Springer, 2000.
- [5] T. A. Runkler and J. C. Bezdek, “Alternating cluster estimation: a new tool for clustering and function approximation,” IEEE Trans. on Fuzzy Systems, Vol.7, No.4, pp. 377-393, 1999.
- [6] S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications,” Springer, 2008.
- [7] V. Torra, “On Fuzzy c-Means and Membership Based Clustering,” Proc. of the 13th Int. Work-Conf. on Artificial Neural Networks (IWANN 2015), Part 1, pp. 597-607, 2015.
- [8] S. Miyamoto and N. Kurosawa, “Controlling cluster volume sizes in fuzzy c-means clustering,” Proc. of the Joint 2nd Int. Conf. on Soft Computing and Intelligent Systems and 5th Int. Symp. on Advanced Intelligent Systems (SCIS&ISIS2004), pp. 1-4, 2004.
- [9] H. Ichihashi, K. Honda, and N. Tani, “Gaussian mixture PDF approximation and fuzzy c-means clustering with entropy regularization,” Proc. of the 4th Asian Fuzzy System Symp., pp. 217-221, 2000.
- [10] I. S. Dhillon and D. S. Modha, “Concept Decompositions for Large Sparse Text Data Using Clustering,” Machine Learning, Vol.42, Issues 1-2, pp. 143-175, 2001.
- [11] S. Miyamoto and K. Mizutani, “Fuzzy Multiset Model and Methods of Nonlinear Document Clustering for Information Retrieval,” Proc. of the 1st Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI 2004), pp. 273-283, 2004.
- [12] K. Mizutani, R. Inokuchi, and S. Miyamoto, “Algorithms of nonlinear document clustering based on fuzzy multiset model,” Int. J. of Intelligent Systems, Vol.23, No.2, pp. 176-198, 2008.
- [13] Y. Kanzawa, “On Kernelization for a Maximizing Model of Bezdek-Like Spherical Fuzzy c-means Clustering,” Proc. of the 11th Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI 2014), pp. 108-121, 2014.
- [14] Y. Kanzawa, “A Maximizing Model of Bezdek-Like Spherical Fuzzy c-Means,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.5, pp. 662-669, 2015.
- [15] Y. Kanzawa, “A Maximizing Model of Spherical Bezdek-Type Fuzzy Multi-Medoids Clustering,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.6, pp. 738-746, 2015.
- [16] C.-H. Oh, K. Honda, and H. Ichihashi, “Fuzzy clustering for categorical multivariate data,” Proc. of the Joint 9th IFSA World Congress and 20th NAFIPS Int. Conf., Vol.4, pp. 2154-2159, 2001.
- [17] K. Honda, S. Oshio, and A. Notsu, “FCM-type fuzzy co-clustering by K-L information regularization,” Proc. of the 2014 IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE), pp. 2505-2510, 2014.
- [18] K. Honda, S. Oshio, and A. Notsu, “Item membership fuzzification in fuzzy co-clustering based on multinomial mixture concept,” Proc. of the 2014 IEEE Int. Conf. on Granular Computing (GrC), pp. 94-99, 2014.
- [19] Y. Kanzawa, “Fuzzy Co-Clustering Algorithms Based on Fuzzy Relational Clustering and TIBA Imputation,” J. Adv. Comput. Intell. Intell. Inform., Vol.18, No.2, pp. 182-189, 2014.
- [20] Y. Kanzawa, “On Possibilistic Clustering Methods Based on Shannon/Tsallis-Entropy for Spherical Data and Categorical Multivariate Data,” Proc. of the 12th Int. Conf. on Modelling Decisions for Artificial Intelligence (MDAI 2015), pp. 125-138, 2015.
- [21] Y. Kanzawa, “Bezdek-Type Fuzzified Co-Clustering Algorithm,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.6, pp. 852-860, 2015.
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