A Novel and Fast SimRank Algorithm

SimRank is a widely adopted similarity measure for objects modeled as nodes in a graph, based on the intuition that two objects are similar if they are referenced by similar objects. The recursive nature of SimRank definition makes it expensive to compute the similarity score even for a single pair of nodes. This defect limits the applications of SimRank. To speed up the computation, some existing works replace the original model with an approximate model to seek only rough solution of SimRank scores. In this work, we propose a novel solution for computing all-pair SimRank scores. In particular, we propose to convert SimRank to the problem of solving a linear system in matrix form, and further prove that the system is non-singular, diagonally dominate, and symmetric definite positive (for undirected graphs). Those features immediately lead to the adoption of Conjugate Gradient (CG) and Bi-Conjugate Gradient (BiCG) techniques for efficiently computing SimRank scores. As a result, a significant improvement on the convergence rate can be achieved; meanwhile, the sparsity of the adjacency matrix is not damaged all the time. Inspired by the existing common neighbor sharing strategy, we further reduce the computational complexity of the matrix multiplication and resolve the scalable issues. The experimental results show our proposed algorithms significantly outperform the state-of-the-art algorithms.