Hierarchical All-Pairs SimRank Calculation.

All-pairs SimRank calculation is a classic SimRank problem. However, all-pairs algorithms suffer from efficiency issues and accuracy issues. In this paper, we convert the non-linear simrank calculation into a new simple closed formulation of linear system. And we come up with a sequence of novel algorithms to efficiently solve the linear system with accuracy guarantees. To reduce the memory consumption and improve the computational efficiency, we build a hierarchical framework to calculate the all-pairs SimRank scores, which includes locally coarse calculation and globally refine calculation. We first solve the local linear systems generated from the subgraphs, then we refine the SimRank scores on the full graph from the residuals of the local structures. We also show that our algorithms outperform the state-of-the-art all-pairs SimRank computation algorithms on real graphs.