Estimating Walk-Based Similarities Using Random Walk

Shogo Murai, Yuichi Yoshida

Abstract: Measuring similarities between vertices is an important task in network analysis, which has numerous applications. One major approach to define a similarity between vertices is by accumulating weights of walks between them that encompasses personalized PageRank (PPR) and Katz similarity. Although many effective methods for PPR based on efficient simulation of random walks have been proposed, these techniques cannot be applied to other walk-based similarity notions because the random walk interpretation is only valid for PPR. In this paper, we propose a random-walk reduction method that reduces the computation of any walk-based similarity to the computation of a stationary distribution of a random walk. With this reduction, we can exploit techniques for PPR to compute other walk-based similarities. As a concrete application, we design an indexing method for walk-based similarities with which we can quickly estimate the similarity value of queried pairs of vertices, and theoretically analyze its approximation error. Our experimental results demonstrate that the instantiation of our method for Katz similarity is two orders of magnitude faster than existing methods on large real networks, without any deterioration in solution quality.