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arXiv · 2306.02102

Accelerating Personalized PageRank Vector Computation

Zhen Chen·Xingzhi Guo·Baojian Zhou·Deqing Yang·Steven Skiena
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Abstract

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 approximates PPVs and has a sublinear rate of $O\big(\frac{1}{αε}\big)$. A recent study found that when high precision is required, FwdPush is similar to the power iteration method, and its run time is pessimistically bounded by $O\big(\frac{m}α \log\frac{1}ε\big)$. 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 $O\big(\tfrac{\text{vol}(S)}α \log\tfrac{1}ε\big)$ 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$\mathcal{O}\big(\tfrac{1}{\sqrtα}\big)$. Our experiments on six real-world graph datasets confirm the efficiency of FwdPushSOR and the acceleration methods for directed and undirected graphs, respectively.

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Zhen Chen, Xingzhi Guo, Baojian Zhou, Deqing Yang, Steven Skiena. 2023-06-06. Accelerating Personalized PageRank Vector Computation. https://arxiv.org/abs/2306.02102

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