Answering Why-Not Questions on Structural Graph Clustering

Abstract

Structural graph clustering is one fundamental problem in managing and analyzing graph data. As a fast and exact density based graph clustering algorithm, pSCAN is widely used to discover meaningful clusters in many different graph applications. The problem of explaining why-not questions on pSCAN is to find why an expected vertex is not included in the specified cluster of the pSCAN results. Obviously, the pSCAN results are sensitive to two parameters: (i) the similarity threshold $\epsilon$; and (ii) the density constraint $\mu$, when them are not set good enough, some expected vertices would be missing in the specified clusters. To tackle this problem, we firstly analyze that how the parameters affect the results of pSCAN, then we propose two novel explanation algorithms to explain why-not questions on pSCAN by offering some advices on how to refine the initial pSCAN with minimum penalty from two perspectives: (i) modifying the parameter $\epsilon$; and (ii) modifying the parameter $\mu$. Moreover, we present some constraints to ensure the original pSCAN results are retained as much as possible in the results of refined pSCAN. Finally, we conduct comprehensive experimental studies, which show that our approaches can efficiently return high-quality explanations for why-not questions on pSCAN.