More is simpler

Abstract

Similarity assessment is one of the core tasks in hyperlink analysis. Recently, with the proliferation of applications, e.g. , web search and collaborative filtering, SimRank has been a well-studied measure of similarity between two nodes in a graph. It recursively follows the philosophy that "two nodes are similar if they are referenced (have incoming edges) from similar nodes", which can be viewed as an aggregation of similarities based on incoming paths. Despite its popularity, SimRank has an undesirable property, i.e. , "zero-similarity": It only accommodates paths with equal length from a common "center" node. Thus, a large portion of other paths are fully ignored. This paper attempts to remedy this issue. (1) We propose and rigorously justify SimRank*, a revised version of SimRank, which resolves such counter-intuitive "zero-similarity" issues while inheriting merits of the basic SimRank philosophy. (2) We show that the series form of SimRank* can be reduced to a fairly succinct and elegant closed form, which looks even simpler than SimRank, yet enriches semantics without suffering from increased computational cost. This leads to a fixed-point iterative paradigm of SimRank* in O ( Knm ) time on a graph of n nodes and m edges for K iterations, which is comparable to SimRank. (3) To further optimize SimRank* computation, we leverage a novel clustering strategy via edge concentration. Due to its NP-hardness, we devise an efficient and effective heuristic to speed up SimRank* computation to O ( Kn m) time, where m is generally much smaller than m. (4) Using real and synthetic data, we empirically verify the rich semantics of SimRank*, and demonstrate its high computation efficiency.