k-MACE Clustering for Gaussian Clusters

<p>Conventional clustering approaches require a preprocessing step that estimates the correct number of cluster prior to the cluster center allocation step. In these approaches, the preprocessing step minimizes one objective function while the second step concentrates on optimization of another objective function. Inspired by MACE-means, we use a single objective function to simultaneously estimate the Correct Number of Cluster (CNC) and acquire the cluster centers. Similarly, we use the Average Central Error (ACE) as ourcost function. The proposed method, denoted by k-minimum ACE (k-MACE), improves MACE-means by rigorous calculation of probabilistic estimate of ACE. While MACE-means (Minimum ACE) only concentrates on Independent Indentically Distributed (IID) clusters, k �� MACE is a solution for Gaussian clusters with any covariance structure. Simulation results show superiority of k �� MACE over MACE means and over conven- tional clustering methods such as G-means, DBSCAN, and validity indices methods such as Calinkski Harabaz, Silhoutte, and gap index. Performance is evaluated in terms of</p>