Consistent selection of the number of clusters via crossvalidation

In cluster analysis, one of the major challenges is to estimate the number of clusters. Most existing approaches attempt to minimize some distance-based dissimilarity measure within clusters. This article proposes a novel selection criterion that is applicable to all kinds of clustering algorithms, including distance based or non-distance based algorithms. The key idea is to select the number of clusters that minimizes the algorithm's instability, which measures the robustness of any given clustering algorithm against the randomness in sampling.Anovel estimation scheme for clustering instability is developed based on crossvalidation. The proposed selection criterion's effectiveness is demonstrated on a variety of numerical experiments, and its asymptotic selection consistency is established when the dataset is properly split.