Fast computation of General SimRank on heterogeneous information network

Similarity computation is a fundamental aspect of information network analysis, underpinning many research tasks including information retrieval, clustering, and recommendation systems. General SimRank (GSR), an extension of the well-known SimRank algorithm, effectively computes link-based global similarities incorporating semantic logic within heterogeneous information networks (HINs). However, GSR inherits the recursive nature of SimRank, making it computationally expensive to achieve convergence through iterative processes. While numerous rapid computation methods exist for SimRank, their direct application to GSR is impeded by differences in their underlying equations. To accelerate GSR computation, we introduce a novel approach based on linear systems. Specifically, we transform the pairwise surfer model of GSR on HINs into a new random walk model on a node-pair graph, establishing an equivalent linear system for GSR. We then develop a fast algorithm utilizing the local push technique to compute all-pair GSR scores with guaranteed accuracy. Additionally, we adapt the local push method for dynamic HINs and introduce a corresponding incremental algorithm. Experimental results on various real datasets demonstrate that our algorithms significantly outperform the traditional power method in both static and dynamic HIN contexts.