Different Objective Functions in Fuzzy c-Means Algorithms and Kernel-Based Clustering

An overview of fuzzy c-means clustering algorithms is given where we focus on different objective functions: they use regularized dissimilarity, entropy- based function, and function for possibilistic clustering. Classification functions for the objective functions and their properties are studied. Fuzzy c-means algorithms using kernel functions is also discussed with kernelized cluster validity measures and numerical experiments. New kernel functions derived from the classification functions are moreover studied.

[1]  I. J. Schoenberg.  Metric spaces and completely monotone functions , 1938 .

[2]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[3]  Enrique H. Ruspini,et al.  A New Approach to Clustering , 1969, Inf. Control..

[4]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[5]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[6]  J. Dunn.  Well-Separated Clusters and Optimal Fuzzy Partitions , 1974 .

[7]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[8]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[9]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[10]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[11]  Isak Gath,et al.  Unsupervised Optimal Fuzzy Clustering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  宮本 定明.  Fuzzy sets in information retrieval and cluster analysis , 1990 .

[13]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[14]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[15]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[16]  Rui-Ping Li,et al.  A maximum-entropy approach to fuzzy clustering , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[17]  Sadaaki Miyamoto,et al.  Fuzzy c-means as a regularization and maximum entropy approach , 1997 .

[18]  Rajesh N. Davé,et al.  Robust clustering methods: a unified view , 1997, IEEE Trans. Fuzzy Syst..

[19]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[20]  J. C. Peters,et al.  Fuzzy Cluster Analysis : A New Method to Predict Future Cardiac Events in Patients With Positive Stress Tests , 1998 .

[21]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[22]  James M. Keller,et al.  Fuzzy Models and Algorithms for Pattern Recognition and Image Processing , 1999 .

[23]  Masao Mukaidono,et al.  Gaussian clustering method based on maximum-fuzzy-entropy interpretation , 1999, Fuzzy Sets Syst..

[24]  Hidetomo Ichihashi,et al.  Gaussian Mixture PDF Approximation and Fuzzy c-Means Clustering with Entropy Regularization , 2000 .

[25]  L. Jain,et al.  Fuzzy sets and their application to clustering and training , 2000 .

[26]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[27]  Mark A. Girolami,et al.  Mercer kernel-based clustering in feature space , 2002, IEEE Trans. Neural Networks.

[28]  Sadaaki Miyamoto,et al.  Fuzzy c-Means Clustering Using Kernel Functions in Support Vector Machines , 2003, J. Adv. Comput. Intell. Intell. Informatics.

[29]  Sadaaki Miyamoto,et al.  Algorithms of Hard c-Means Clustering Using Kernel Functions in Support Vector Machines , 2003, J. Adv. Comput. Intell. Intell. Informatics.

[30]  Kenneth G. Manton,et al.  Fuzzy Cluster Analysis , 2005 .

[31]  Alexander Zien,et al.  Semi-Supervised Learning , 2006 .

[32]  Fusheng Yu,et al.  Partially Horizontal Collaborative Fuzzy C-Means , 2007 .

[33]  Xia Li,et al.  Semi-supervised kernel-based fuzzy C-means with pairwise constraints , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[34]  Sadaaki Miyamoto,et al.  Algorithms for Fuzzy Clustering - Methods in c-Means Clustering with Applications , 2008, Studies in Fuzziness and Soft Computing.

[35]  Sadaaki Miyamoto,et al.  Comparison and Evaluation of Different Cluster Validity Measures Including Their Kernelization , 2009, J. Adv. Comput. Intell. Intell. Informatics.

[36]  Ching-Chih Tsai,et al.  Behavior-Based Navigation Using Heuristic Fuzzy Kohonen Clustering Network for Mobile Service Robots , 2010 .

[37]  Sadaaki Miyamoto,et al.  Kernel Functions Derived from Fuzzy Clustering and Their Application to Kernel Fuzzy c-Means , 2011, J. Adv. Comput. Intell. Intell. Informatics.