Accelerating Personalized PageRank Vector Computation

Personalized PageRank Vectors are widely used as fundamental graph-learning tools for detecting anomalous spammers, learning graph embeddings, and training graph neural networks. The well-known local FwdPush algorithm[5] approximates PPVs and has a sublinear rate of O(1 over αε). A recent study [51] found that when high precision is required, FwdPush is similar to the power iteration method, and its run time is pessimistically bounded by O(m over α log 1 over ε). This paper looks closely at calculating PPVs for both directed and undirected graphs. By leveraging the linear invariant property, we show that FwdPush is a variant of Gauss-Seidel and propose a Successive Over-Relaxation based method, FwdPushSOR to speed it up by slightly modifying FwdPush. Additionally, we prove FwdPush has local linear convergence rate O(vol (S) over α log 1 over ε) enjoying advantages of two existing bounds. We also design a new local heuristic push method that reduces the number of operations by 10-50 percent compared to FwdPush. For undirected graphs, we propose two momentum-based acceleration methods that can be expressed as one-line updates and speed up non-acceleration methods by O (1 / √ α). Our experiments on six real-world graph datasets confirm the efficiency of FwdPushSOR and the acceleration methods for directed and undirected graphs, respectively.