Determine the number of clusters by data augmentation

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