The optimal hyperparameter for Bayesian clustering and its application to the evaluation of clustering results

In a probabilistic approach to cluster analysis, parametric models, such as a mixture of Gaussian distributions, are often used. Since the parameter is unknown, it is necessary to estimate both the parameter and the labels of the clusters. Recently, the statistical properties of Bayesian clustering have been studied. The theoretical accuracy has been analyzed, and it has been found to be better than the maximum-likelihood method, which is based on the expectation-maximization algorithm. However, the effect of a prior distribution on the clustering result remains unknown. In the present paper, we theoretically and experimentally investigate the behavior of the optimal hyperparameter, which is the parameter of the prior distribution, and we propose an evaluation method for the clustering result, based on the prior optimization.