Efficient Processing Node Proximity via Random Walk with Restart

Abstract

Abstract. Graph is a useful tool to model complicated data structures. One important task in graph analysis is assessing node proximity based on graph topology. Recently, Random Walk with Restart (RWR) tends to pop up as a promising measure of node proximity, due to its proliferative applications in e.g. recommender systems, and image segmentation. However, the best-known algorithm for computing RWR resorts to a large LU matrix factorization on an entire graph, which is cost-inhibitive. In this paper, we propose hybrid techniques to efficiently compute RWR. First, a novel divide-and-conquer paradigm is designed, aiming to convert the large LU decomposition into small triangular matrix operations recursively on several partitioned subgraphs. Then, on every subgraph, a "sparse accelerator" is devised to further reduce the time of RWR without any sacrifice in accuracy. Our experimental results on real and synthetic datasets show that our approach outperforms the baseline algorithms by at least one constant factor without loss of exactness.

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“…The RWR approach has the benefit of capturing the global topology of a graph and representing a measure of proximity from all the nodes to the seed(s) based on the graph topology [55]. The measure of proximity between nodes is a relevant measure quantifying how closely connected a node is with the seeds and can be used to rank nodes [48,55,56]. In this study, nodes within each layer were ranked based on their measure of proximity to the seed nodes.…”