Cluster number selection for a small set of samples using the Bayesian Ying-Yang model

One major problem in cluster analysis is the determination of the number of clusters. In this paper, we describe both theoretical and experimental results in determining the cluster number for a small set of samples using the Bayesian-Kullback Ying-Yang (BYY) model selection criterion. Under the second-order approximation, we derive a new equation for estimating the smoothing parameter in the cost function. Finally, we propose a gradient descent smoothing parameter estimation approach that avoids complicated integration procedure and gives the same optimal result.