Agglomerative Hierarchical Clustering and Fuzzy c-Means Using Kernel Functions Based on Complete Monotonicity

Abstract

Recently, kernel functions are incorporated into many clustering methods. There are, for example, Gaussian kernel, polynomial kernel, perceptron kernel and sigmoid kernel as representative kernels. There are, however, many data where we do not have adequate results of clustering by these kernels. It is necessary to research a new kernel that replaces existing kernels. In this paper, we study two kernels derived from fuzzy c-means and compare these kernels with conventional ones. We investigate classification performance and calculation time of the proposed kernels using illustrative examples.