Determining the number of states in dynamic functional connectivity using cluster validity indexes

Background: Clustering analysis is employed in brain dynamic functional connectivity (dFC) to cluster the data into a set of dynamic states. These states correspond to different patterns of functional connectivity that iterate through time. Although several cluster validity index (CVI) methods to determine the best clustering partition exists, the appropriateness of methods to apply in the case of dynamic connectivity analysis has not been determined. New Method: Currently employed indexes do not provide a crisp answer on what is the best number of clusters. In addition, there is a lack of CVI testing in the context of dFC data. This work tests a comprehensive set of twenty four cluster validity indexes applied to addiction data and suggest the best ones for clustering dynamic functional connectivity. Results: Out of the twenty four considered CVIs, Davies-Bouldin and Ray-Turi were the most suitable methods to find the number of clusters in both simulation and real data. The solution for these two CVIs is to find a local minimum critical point, which can be automated using computational algorithms. Comparison with Existing Methods: Elbow-Criterion, Silhouette and GAP-Statistic methods have been widely used in dFC studies. These methods are included among the tested CVIs where the performances of all twenty four CVIs are compared. Conclusions: Davies-Bouldin and Ray-Turi CVIs showed better performance among a group of twenty four CVIs in determining the number of clusters to use in dFC analysis.