Random walk with restart over dynamic graphs

Yu, Weiren and McCann, Julie (2017). Random walk with restart over dynamic graphs. IN: Proceedings: 16th IEEE International Conference on Data Mining, ICDM 2016. Bonchi, Francesco; Domingo-Ferrer, Josep; Baeza-Yates, Ricardo and et al (eds) Proceedings. IEEE International Conference on Data Mining . Piscataway, NJ (US): IEEE.

Abstract

Random Walk with Restart (RWR) is an appealing measure of proximity between nodes based on graph structures. Since real graphs are often large and subject to minor changes, it is prohibitively expensive to recompute proximities from scratch. Previous methods use LU decomposition and degree reordering heuristics, entailing O(|V|3) time and O(|V|2) memory to compute all (|V|2) pairs of node proximities in a static graph. In this paper, a dynamic scheme to assess RWR proximities is proposed: (1) For unit update, we characterize the changes to all-pairs proximities as the outer product of two vectors. We notice that the multiplication of an RWR matrix and its transition matrix, unlike traditional matrix multiplications, is commutative. This can greatly reduce the computation of all-pairs proximities from O(|V|3) to O(|Δ|) time for each update without loss of accuracy, where |Δ| (<<|V|2) is the number of affected proximities. (2) To avoid O(|V|2) memory for all pairs of outputs, we also devise efficient partitioning techniques for our dynamic model, which can compute all pairs of proximities segment-wisely within O(l|V|) is a user-controlled trade-off between  memory an I/O costs. (3) For bulk update, we also devise aggregation and hashing methods, which can discard many unneccessary updates further and handle chuncks of unit updates simultaneously. Our experimental results on various datasets demonstrate that our methods can be 1-2 orders of magnitude faster than other competitors while securing scalability and exactness...

Publication DOI: https://doi.org/10.1109/ICDM.2016.0070
Divisions: Engineering & Applied Sciences
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Event Title: 16th IEEE International Conference on Data Mining and Workshops
Event Type: Other
Event Location: World Trade Center
Event Dates: 2016-12-12 - 2016-12-15
Uncontrolled Keywords: time measurement,loss measurement,Symmetric matrices,noise measurement,computational modeling ,matrix decomposition,matrix converters,Engineering(all)
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
Published Date: 2017
Authors: Yu, Weiren
McCann, Julie

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