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Random walk with restart over dynamic graphs

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Yu, Weiren and McCann, Julie (2017) Random walk with restart over dynamic graphs. In: 2016 IEEE 16th International Conference on Data Mining (ICDM), Barcelona, Spain, 12-15 Dec 2016. Published in: 2016 IEEE 16th International Conference on Data Mining (ICDM) pp. 589-598. ISSN 2374-8486. doi:10.1109/ICDM.2016.0070

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Official URL: http://dx.doi.org/10.1109/ICDM.2016.0070

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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(|ν| 3 ) time and O(|ν| 2 ) memory to compute all (|ν| 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(|ν| 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(I|V|) memory and O([|V|/l]) I/O costs, where 1 ≤ I ≤ |V| is a user-controlled trade-off between memory and I/O costs. (3) For bulk updates, we also devise aggregation and hashing methods, which can discard many unnecessary updates further and handle chunks 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.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Random walks (Mathematics), Graph algorithms, Proximity matrices
Journal or Publication Title: 2016 IEEE 16th International Conference on Data Mining (ICDM)
Publisher: IEEE
ISSN: 2374-8486
Book Title: 2016 IEEE 16th International Conference on Data Mining (ICDM)
Official Date: 2 February 2017
Dates:
DateEvent
2 February 2017Published
12 December 2016UNSPECIFIED
Page Range: pp. 589-598
DOI: 10.1109/ICDM.2016.0070
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: © 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.
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIEDNEC Corporationhttp://dx.doi.org/10.13039/501100013422
619795European Commissionhttp://dx.doi.org/10.13039/501100000780
Conference Paper Type: Paper
Title of Event: 2016 IEEE 16th International Conference on Data Mining (ICDM)
Type of Event: Conference
Location of Event: Barcelona, Spain
Date(s) of Event: 12-15 Dec 2016

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