TPA: Two Phase Approximation for Random Walk with Restart

Given a large graph, how can we determine similarity between nodes in a fast and accurate way? Random walk with restart (RWR) is a popular measure for this purpose and has been exploited in numerous data mining applications including ranking, anomaly detection, link prediction, and community detection. However, previous methods for computing exact RWR require prohibitive storage sizes and computational costs, and alternative methods which avoid such costs by computing approximate RWR have limited accuracy, especially in ranking. In this paper, we propose TPA, a fast, scalable, and highly accurate method for computing approximate RWR on large graphs. TPA exploits two important properties in RWR: 1) Nodes close to a seed node are likely to be revisited in following steps due to block-wise structure of many real graphs, and 2) RWR scores of nodes which reside far from the seed node are proportional to their PageRank scores. Based on these two properties, TPA divides approximate RWR problem into two subproblems called neighbor approximation and stranger approximation. In the neighbor approximation, TPA estimates RWR scores of nodes close to the seed based on scores of few early steps from the seed. In the stranger approximation, TPA estimates RWR scores for nodes far from the seed using their PageRank. The stranger and neighbor approximations are conducted in the preprocessing phase and the online phase, respectively. Through extensive experiments, we show that TPA requires 1140 times less time with 20 times less memory space than other state-of-the-art methods for the preprocessing phase. In the online phase, TPA computes approximate RWR up to 150 times faster than existing methods with 6 times lower L1 norm error and 3.5 times lower rank error.