Kernel K-Mace Clustering

Abstract

We propose a kernel k-means based unsupervised clustering algorithm. The kernel k-means approaches require finding not only the Correct Number of Clusters (CNC) but also the optimum kernel function parameters in the clustering procedure. Existing index validation approaches use a criterion different from the k-means criterion to find the optimum CNC and also choose kernel parameter by trial and error. The proposed algorithm denoted by kernel k-Minimum Average Central Error (Kernel k-MACE), estimates the CNC while simultaneously providing the optimum value of the Gaussian kernel parameter. The advantage of the method in theory is in its consistency in using only one criterion for all the three steps of clustering, CNC estimation, and kernel function parameter estimation. A novel cluster initialization technique enables Kernel k-MACE to converge in less iterations compared to the existing approaches. Simulation results illustrate superiority of Kernel K-MACE over multiple state-of-the-art unsupervised clustering methods for both real data sets and self-generated data sets having 10%-50% overlap. The method outperforms the existing methods by not only providing more accurate CNC estimates, but also by providing better clustering results evaluated by Adjusted Random Index (ARI) and Normalized Variation Index (NVI).