SimRank*: effective and scalable pairwise similarity search based on graph topology
File(s)
Published version
Author(s)
Yu, W
Lin, X
Zhang, W
Pei, J
McCann, JA
Type
Journal Article
Abstract
Given a graph, how can we quantify similarity between two nodes in an effective and scalable way? SimRank is an attractive measure of pairwise similarity based on graph topologies. Its underpinning philosophy that “two nodes are similar if they are pointed to (have incoming edges) from similar nodes” can be regarded as an aggregation of similarities based on incoming paths. Despite its popularity in various applications (e.g., web search and social networks), SimRank has an undesirable trait, i.e., “zero-similarity”: it accommodates only the paths of equal length from a common “center” node, whereas a large portion of other paths are fully ignored. In this paper, we propose an effective and scalable similarity model, SimRank*, to remedy this problem. (1) We first provide a sufficient and necessary condition of the “zero-similarity” problem that exists in Jeh and Widom’s SimRank model, Li et al. ’s SimRank model, Random Walk with Restart (RWR), and ASCOS++. (2) We next present our treatment, SimRank*, which can resolve this issue while inheriting the merit of the simple SimRank philosophy. (3) We reduce the series form of SimRank* to a closed form, which looks simpler than SimRank but which enriches semantics without suffering from increased computational overhead. This leads to an iterative form of SimRank*, which requires O(Knm) time and O(n2) memory for computing all (n2) pairs of similarities on a graph of n nodes and m edges for K iterations. (4) To improve the computational time of SimRank* further, we leverage a novel clustering strategy via edge concentration. Due to its NP-hardness, we devise an efficient heuristic to speed up all-pairs SimRank* computation to O(Knm~) time, where m~ is generally much smaller than m. (5) To scale SimRank* on billion-edge graphs, we propose two memory-efficient single-source algorithms, i.e., ss-gSR* for geometric SimRank*, and ss-eSR* for exponential SimRank*, which can retrieve similarities between all n nodes and a given query on an as-needed basis. This significantly reduces the O(n2) memory of all-pairs search to either O(Kn+ m~) for geometric SimRank*, or O(n+ m~) for exponential SimRank*, without any loss of accuracy, where m~ ≪ n2. (6) We also compare SimRank* with another remedy of SimRank that adds self-loops on each node and demonstrate that SimRank* is more effective. (7) Using real and synthetic datasets, we empirically verify the richer semantics of SimRank*, and validate its high computational efficiency and scalability on large graphs with billions of edges.
Date Issued
2019-06-01
Date Acceptance
2018-12-18
Citation
VLDB Journal, 2019, 28 (3), pp.401-426
ISSN
1066-8888
Publisher
Springer
Start Page
401
End Page
426
Journal / Book Title
VLDB Journal
Volume
28
Issue
3
Copyright Statement
© 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor
NEC Corporation
The Alan Turing Institute
Grant Number
N/A
ATIGA001
Subjects
Science & Technology
Technology
Computer Science, Hardware & Architecture
Computer Science, Information Systems
Computer Science
Similarity search
Link analysis
Graph topology
SimRank measure
RANDOM-WALK
EFFICIENT
Information Systems
0804 Data Format
0805 Distributed Computing
0806 Information Systems
Publication Status
Published
Date Publish Online
2019-01-11