Planted clique detection below the noise floor using low-rank sparse PCA

Alexis B. Cook, Benjamin A. Miller

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Detection of clusters and communities in graphs is useful in a wide range of applications. In this paper we investigate the problem of detecting a clique embedded in a random graph. Recent results have demonstrated a sharp detectability threshold for a simple algorithm based on principal component analysis (PCA). Sparse PCA of the graph's modularity matrix can successfully discover clique locations where PCA-based detection methods fail. In this paper, we demonstrate that applying sparse PCA to low-rank approximations of the modularity matrix is a viable solution to the planted clique problem that enables detection of small planted cliques in graphs where running the standard semidefinite program for sparse PCA is not possible.

Original languageEnglish
Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3726-3730
Number of pages5
ISBN (Electronic)9781467369978
DOIs
StatePublished - 4 Aug 2015
Externally publishedYes
Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
Duration: 19 Apr 201424 Apr 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2015-August
ISSN (Print)1520-6149

Conference

Conference40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Country/TerritoryAustralia
CityBrisbane
Period19/04/1424/04/14

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

  • community detection
  • graph analysis
  • planted clique detection
  • semidefinite programming
  • sparse principal component analysis

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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