Fuzzy c-Means Clustering Using Transformations into High Dimensional Spaces

Algorithms of fuzzy -means clustering with kernels employed in nonlinear transformations into high dimensional spaces in the support vector machines are studied. The objective functions in the standard method and the entropy based method are considered and iterative solutions in the alternate optimization algorithm are derived. Explicit cluster centers in the data space are not obtained by this method in general but fuzzy classification functions are useful which have much more information than crisp clusters in the hard -means. Numerical examples using radial basis kernel functions are given.