Cluster Stability for Finite Samples

Over the past few years, the notion of stability in data clustering has received growing attention as a cluster validation criterion in a sample-based framework. However, recent work has shown that as the sample size increases, any clustering model will usually become asymptotically stable. This led to the conclusion that stability is lacking as a theoretical and practical tool. The discrepancy between this conclusion and the success of stability in practice has remained an open ques- tion, which we attempt to address. Our theoretical approach is that stability, as used by cluster validation algorithms, is similar in certain respects to measures of generalization in a model-selection framework.