Knee Point Detection on Bayesian Information Criterion

Abstract

The main challenge of cluster analysis is that the number of clusters or the number of model parameters is seldom known, and it must therefore be determined before clustering. Bayesian Information Criterion (BIC) often serves as a statistical criterion for model selection, which can also be used in solving model-based clustering problems, in particular for determining the number of clusters. Conventionally, a correct number of clusters can be identified as the first decisive local maximum of BIC; however, this is intractable due to the overtraining problem and inefficiency of clustering algorithms. To circumvent this limitation, we proposed a novel method for identifying the number of clusters by detecting the knee point of the resulting BIC curve instead. Experiments demonstrated that the proposed method is able to detect the correct number of clusters more robustly and accurately than the conventional approach.