Hierarchical Overlapping Clustering on Graphs: Cost Function, Algorithm and Scalability

Overlap and hierarchy are two prevalent phenomena in clustering, and usually coexist in a single system. There are several studies on each of them separately, but it is unclear how to characterize and evaluate the hybrid structures yet. To address this issue, we initiate the study of hierarchical overlapping clustering on graphs by introducing a new cost function for it. We show the rationality of our cost function via several intuitive properties, and develop an approximation algorithm that achieves a constant approximation factor for its dual version. Our algorithm is a recursive process of overlapping bipartition based on local search, which makes a speed-up version of it extremely scalable. Our experiments demonstrate that the speed-up algorithm has significantly better performances than all the baseline methods in both effectiveness and scalability on synthetic and real datasets.