Determining the correct number of clusters (CNC) is an important task in data clustering and has a critical effect on finalizing 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). K-means is one of the popular methods of clustering that requires CNC. Validity ACE is the average error between the true unavailable cluster center and the estimated cluster center for each sample data. Kernel K-MACE is kernel K-means that is equipped with an efficient CNC estimator. In addition, kernel K_MACE includes the first automatically tuned procedure for choosing the Gaussian kernel parameters. Simulation results for both synthetic and read 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.