Accuracy Estimation of Link-Based Similarity Measures and Its Application

Abstract

Link-based similarity measures play significant role in many graph based applications. Consequently, measuring nodes similarity in a graph is a fundamental problem of graph data mining. Personalized PageRank (PPR) and SimRank (SR) have emerged as the most popular and influential link-based similarity measures. In practice, PPR and SR scores are achieved by iterative computing. With increasing of iterations, the computations incur heavy overhead. The ideal solution is that computing similarity within the minimum number of iterations is sufficient to guarantee a desired accuracy. However, the existing upper bounds are too coarse to be useful in general. Therefore, we focus on designing accurate and tight upper bounds of PPR and SR in the paper. Our upper bounds are designed based on following human intuition: “the smaller the difference between the two consecutive iteration step results is, the smaller the difference between iterative similarity scores and theoretical ones is”. Furthermore, we demonstrate effectiveness of our novel upper bounds in the scenario of top-k similar nodes query, where our upper bounds accelerate speed of the query. At last, we run a comprehensive set of experiments on real data sets to verify effectiveness and efficiency of our upper bounds