Overlapping Attributed Graph Clustering using Mixed strategy games

Abstract

Unlike a simple network with just nodes and edges in between them, the real-world networks can contain much more, such as a set of attributes associated with every node in the network. These networks opened up a new avenue in community detection called attributed graph clustering (AGC). Furthermore, the clusters in real-world are not usually disjoint, as compared to most of the work that has been carried out in the field of AGC. This raises a need for AGC with fuzzy clusters. In this work, we try to comprehend the problem of attributed graph clustering with the help of a game-theoretic approach called dynamic cluster formation game (DCFG). To address the possibility of fuzzy clusters in a network, we model the problem of AGC as a series of coupled games involving mixed strategies, in contrast to the previous work that was primarily focused on pure strategy equilibrium. We discuss the convergence of the proposed game and the existence of Nash equilibrium at convergence. We also propose a clustering algorithm which uses a game-theoretic approach to partition a network into fuzzy clusters, giving a solution balanced in terms of topology and node attributes. We compare the the results of our work to the state-of-the-art clustering methods available in the literature.