Community detection in sparse networks via Grothendieck's inequality

Abstract : We present a simple and flexible method to prove consistency of semidefinite optimization problems on random graphs. The method is based on Grothendieck's inequality. Unlike the previous uses of this inequality that lead to constant relative accuracy, we achieve any given relative accuracy by leveraging randomness. We illustrate the method with the problem of community detection in sparse networks, those with bounded average degrees. We demonstrate that even in this regime, various natural semidefinite programs can be used to recover the community structure up to an arbitrarily small fraction of misclas-sified vertices. The method is general; it can be applied to a variety of stochastic models of networks and semidefinite programs.
Document type :
Journal articles
Complete list of metadatas

Cited literature [66 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-01262623
Contributor : Olivier Guédon <>
Submitted on : Tuesday, January 26, 2016 - 10:17:29 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:04 PM
Long-term archiving on : Wednesday, April 27, 2016 - 1:19:47 PM

Files

gv-sdp-revision2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01262623, version 1

Citation

Olivier Guédon, Roman Vershynin. Community detection in sparse networks via Grothendieck's inequality. Probability Theory and Related Fields, Springer Verlag, 2016, 165 (3-4), pp.1025-1049. ⟨hal-01262623⟩

Share

Metrics

Record views

129

Files downloads

168