BEAR: Block Elimination Approach for Random Walk with Restart on Large Graphs

Kijung Shin, Jinhong Jung, Lee Sael, U. Kang
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引用次数: 79

Abstract

Given a large graph, how can we calculate the relevance between nodes fast and accurately? Random walk with restart (RWR) provides a good measure for this purpose and has been applied to diverse data mining applications including ranking, community detection, link prediction, and anomaly detection. Since calculating RWR from scratch takes long, various preprocessing methods, most of which are related to inverting adjacency matrices, have been proposed to speed up the calculation. However, these methods do not scale to large graphs because they usually produce large and dense matrices which do not fit into memory. In this paper, we propose BEAR, a fast, scalable, and accurate method for computing RWR on large graphs. BEAR comprises the preprocessing step and the query step. In the preprocessing step, BEAR reorders the adjacency matrix of a given graph so that it contains a large and easy-to-invert submatrix, and precomputes several matrices including the Schur complement of the submatrix. In the query step, BEAR computes the RWR scores for a given query node quickly using a block elimination approach with the matrices computed in the preprocessing step. Through extensive experiments, we show that BEAR significantly outperforms other state-of-the-art methods in terms of preprocessing and query speed, space efficiency, and accuracy.
BEAR:大型图上随机行走的块消除方法
给定一个大的图,我们如何快速准确地计算节点之间的相关性?随机行走与重启(RWR)为这一目的提供了一个很好的度量,并已应用于各种数据挖掘应用,包括排名、社区检测、链接预测和异常检测。由于从头开始计算RWR需要很长时间,因此提出了各种预处理方法来加快计算速度,其中大多数与邻接矩阵反相关。然而,这些方法不能扩展到大的图,因为它们通常产生大而密集的矩阵,不适合内存。在本文中,我们提出了BEAR,一种快速,可扩展和准确的方法来计算大图上的RWR。BEAR包括预处理步骤和查询步骤。在预处理步骤中,BEAR对给定图的邻接矩阵进行重新排序,使其包含一个大且易于反转的子矩阵,并预先计算包括子矩阵的舒尔补在内的多个矩阵。在查询步骤中,BEAR使用预处理步骤中计算的矩阵,使用块消除方法快速计算给定查询节点的RWR分数。通过大量的实验,我们表明BEAR在预处理和查询速度、空间效率和准确性方面明显优于其他最先进的方法。
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