Clustering with varying risks of false assignments in discrete latent variable model

In clustering problems, to model the intrinsic structure of unlabeled data, the latent variable models are frequently used. These model-based clustering methods often provide a clustering rule minimizing the total false assignment error. However, in many clustering applications, it is desirable to treat false assignment errors for a certain cluster differently. In this paper, we introduce the false assignment rate for clustering and estimate it by using the extended likelihood approach. We propose VRclust, a novel clustering rule that controls various errors differently across clusters. Real data examples illustrate the usage of estimation of false assignment rate and a simulation study shows that error controls are consistent as the sample size increases.