On the Unification of k-Harmonic Means and Fuzzy c-Means Clustering Problems under Kernelization

This paper presents a common algorithm for the kernel k-harmonic means (KKHM) and the kernel fuzzy c-means (KFCM) clustering problems. We incorporate kernel functions in a generalized fuzzy c- means cost function, forming the cost function of a kernelized general fuzzy c-means (KGFCM) problem, and design an algorithm to locally minimize this cost function. The KGFCM cost function has two parameters: the exponent p of the Euclidean distance, and the fuzzy weighting exponent m. By setting proper values for p and m in our algorithm, one can execute the KKHM or the KFCM algorithm. Using the algorithm for KKHM, we compare its clustering performance with the popular kernel k-means and KFCM algorithms. Experiments performed on real-world and synthetic datasets show the superior clustering capabilities of KKHM. We also show that KKHM retains the advantages of the original KHM algorithm, resulting in better clustering performance when high number of clusters are present.