Constrained local graph clustering by colored random walk

Detecting local graph clusters is an important problem in big graph analysis. Given seed nodes in a graph, local clustering aims at finding subgraphs around the seed nodes, which consist of nodes highly relevant to the seed nodes. However, existing local clustering methods either allow only a single seed node, or assume all seed nodes are from the same cluster, which is not true in many real applications. Moreover, the assumption that all seed nodes are in a single cluster fails to use the crucial information of relations between seed nodes. In this paper, we propose a method to take advantage of such relationship. With prior knowledge of the community membership of the seed nodes, the method labels seed nodes in the same (different) community by the same (different) color. To further use this information, we introduce a color-based random walk mechanism, where colors are propagated from the seed nodes to every node in the graph. By the interaction of identical and distinct colors, we can enclose the supervision of seed nodes into the random walk process. We also propose a heuristic strategy to speed up the algorithm by more than 2 orders of magnitude. Experimental evaluations reveal that our clustering method outperforms state-of-the-art approaches by a large margin.