Graph clustering using early-stopped random walks

Abstract

Very fast growth of empirical graphs demands clustering algorithms with nearly-linear time complexity. We propose a novel approach to clustering, based on random walks. The idea is to relax the standard spectral method and replace eigenvectors with vectors obtained by running early-stopped random walks. We abandoned iterating the random walk algorithm to convergence but instead stopped it after the time that is short compared with the mixing time. The computed vectors constitute a local approximation of the leading eigenvectors. The algorithm performance is competitive to the traditional spectral solutions in terms of computational complexity.We empirically evaluate the proposed approach against other exact and approximate methods. Experimental results show that the use of the early stop procedure does not influence the quality of the clustering on the tested real world data sets.