One major problem in duster 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-Kull-back 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.