Fast and Accurate Low Rank Approximation of Massive Graphs

In this paper we present a fast and accurate procedure called clustered low rank matrix approximation for massive graphs. The procedure involves a fast clustering of the graph and then approximating each cluster separately using existing methods, e.g. the singular value decomposition, or stochastic algorithms. The cluster-wise approximations are then extended to approximate the entire graph. This approach has several benefits: (1) important structure of the graph is preserved due to the clustering; (2) highly accurate low rank approximations are achieved; (3) the procedure is efficient both in terms of computational speed and memory usage. Further, we generalize stochastic algorithms into the clustered low rank approximation framework and present theoretical bounds for the approximation error. Finally, a set of experiments, using large scale and real world graphs, show that our methods drastically outperform standard low rank matrix approximation algorithms.