Determine the number of clusters by data augmentation

Determining the number of clusters is crucial for the successful application of clustering. In this paper, we propose a new order-determination method called the data augmentation estimator (DAE), for the general model-based clustering. The estimator is based on a novel idea that augments data with an independently generated small cluster, which enables us to justify how the instability of clustering changes with the number of clusters assumed in clustering. The pattern of instability provides an alternative characterization of the true number of clusters to the commonly used goodness-of-fit measure. By combining the two sources of information appropriately, the proposed estimator reaches asymptotic consistency under general conditions and is easily implementable. It is also more efficient than the conventional BIC-type approaches that use the goodness-of-fit measure only. These properties are illustrated by the simulation studies and real data examples at the end.