A Game-theoretic Approach for Enumerating Dominant Sets

Recently, a novel graph-theoretic notion of a cluster has been proposed, i.e., the “dominant set”, which captures the two basic requirements of a cluster, namely internal coherency and external incoherency. In this paper, we tackle the problem of finding several dominant sets using the replicator dynamics. Specifically, we adopt a game-theoretic perspective to this iterative extraction: Game dynamics are used to locate individual dominant sets, and after each extraction the similarity matrix is transformed in such a way as to make the located cluster unstable under the dynamics, without affecting the remaining groups. This guarantees that once found, a cluster will not be extracted again.