On the Optimal Hyperparameter Behavior in Bayesian Clustering

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 of the label estimation 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. The prior distribution has the parameter, which is the hyperparameter. In the present paper, we theoretically and experimentally investigate the behavior of the optimal hyperparameter, and we propose an evaluation method for the clustering result, based on the prior optimization.