Kernel based Fuzzy Clustering

Abstract

This chapter describes extended fuzzy cluster loadings obtained using the kernel method in a higher dimension space. It also shows the capability of kernel fuzzy cluster loading when used for the interpretation of the fuzzy clusters obtained from the fuzzy clustering result. The interpretation is estimated as a kernel fuzzy cluster loading which can show the relation between the obtained clusters and variables.We have mentioned fuzzy cluster loading in chapter 3. Conventional fuzzy cluster loading is estimated in the dimension of the observation space. However, kernel fuzzy cluster loading [47], [49] is estimated in the higher dimension space by applying the kernel method which is well known for a high discriminative performance in pattern recognition or classi- fication, and this method can avoid the noise in the given observation. The higher dimension space is related to the data space nonlinearly, so it seems to be adaptable for the dynamic spatial data where the data performs irregularly over the variables and times. We illustrate the better performance of the kernel based fuzzy cluster loading with numerical examples.