Some further studies on detection the number of clusters

To determine number of clusters in the unsupervised learning, a criterion based on the Bayesian-Kullback Ying-Yang machine learning scheme has recently been proposed (Xu, 1995), and has been proved by Theorem 1 of the paper by Xu (1996). As the condition presented in this theorem is hard to be directly checked in practice, in this paper we give one equivalent condition, which is easier to be examined for a given specific problem. Furthermore, since the implementation of the criterion requests a large quantity of computing costs to estimate parameters for each candidate cluster number k, here we also propose a heuristic algorithm for those data from mixture populations with the same priori probabilities and equal-and-isotropic variance, which can make the number of k as small as possible by selecting reasonable k´s instead of testing one by one. Preliminary experiments have shown that our proposed algorithm can save computing costs considerably