K-MACE and Kernel K-MACE Clustering

Determining the correct number of clusters (CNC) is an important task in data clustering and has a critical effect on nalizing the partitioning results. K-means is one of the popular methods of clustering that requires CNC. Validity index methods use an additional optimization procedure to estimate the CNC for K-means. We propose an alternative validity index approach denoted by k-Minimizing Average Central Error (KMACE). Average Central Error (ACE) is the average error between the unavailable cluster center and the estimated cluster center for each sample data. Kernel K-MACE is kernel K-means that is equipped with the proposed CNC estimator. In addition, kernel K-MACE includes an automatically tuned procedure for choosing the Gaussian kernel parameters. Simulation results for both synthetic and real data show superiority of K-MACE and kernel K-MACE over the conventional clustering methods not only in CNC estimation but also in the partitioning procedure.