抄録
Kernel functions are widely known to be useful tools in many areas of data analysis, while it has not yet shown that fuzzy models have close relation to kernel functions. We propose three basic functions derived from fuzzy c-means and possibilistic clustering. And then, we prove that the functions are able to be kernel functions, because those functions are positive-definite. The proof is based on the completely monotone function defined by Schoenberg. To verify that the present functions are useful to classify data sets with nonlinear cluster boundaries, we conduct vector quantization clustering based on the kernel functions. Moreover, we compare performances of kernel algorithms of vector quantization with different choices of the present kernel functions and their parameters.
