On triangular versus edge representations - Towards scalable modeling of networks

Qirong Ho, Junming Yin, Eric P. Xing

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Scopus citations

Abstract

In this paper, we argue for representing networks as a bag of triangular motifs, particularly for important network problems that current model-based approaches handle poorly due to computational bottlenecks incurred by using edge representations. Such approaches require both 1-edges and 0-edges (missing edges) to be provided as input, and as a consequence, approximate inference algorithms for these models usually require Ω(N2) time per iteration, precluding their application to larger real-world networks. In contrast, triangular modeling requires less computation, while providing equivalent or better inference quality. A triangular motif is a vertex triple containing 2 or 3 edges, and the number of such motifs is Θ(Σ i Di2) (where Di is the degree of vertex i), which is much smaller than N2 for low-maximum-degree networks. Using this representation, we develop a novel mixed-membership network model and approximate inference algorithm suitable for large networks with low max-degree. For networks with high maximum degree, the triangular motifs can be naturally subsampled in a node-centric fashion, allowing for much faster inference at a small cost in accuracy. Empirically, we demonstrate that our approach, when compared to that of an edge-based model, has faster runtime and improved accuracy for mixed-membership community detection. We conclude with a large-scale demonstration on an N ≈ 280, 000-node network, which is infeasible for network models with (N2) inference cost.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Pages2132-2140
Number of pages9
StatePublished - Dec 1 2012
Externally publishedYes
Event26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States
Duration: Dec 3 2012Dec 6 2012

Publication series

NameAdvances in Neural Information Processing Systems
Volume3
ISSN (Print)1049-5258

Other

Other26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
CountryUnited States
CityLake Tahoe, NV
Period12/3/1212/6/12

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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  • Cite this

    Ho, Q., Yin, J., & Xing, E. P. (2012). On triangular versus edge representations - Towards scalable modeling of networks. In Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 (pp. 2132-2140). (Advances in Neural Information Processing Systems; Vol. 3).