A cheeger inequality for the graph connection laplacian

Afonso Bandeira, Amit Singer, Daniel A. Spielman

Research output: Contribution to journalArticle

Abstract

The O(d) synchronization problem consists of estimating a set of n unknown orthogonal d × d matrices O1, ... , On from noisy measurements of a subset of the pairwise ratios OiO-1 j . We formulate and prove a Cheeger-type inequality that relates a measure of how well it is possible to solve the O(d) synchronization problem with the spectra of an operator, the graph connection Laplacian. We also show how this inequality provides a worst-case performance guarantee for a spectral method to solve this problem.

Original languageEnglish (US)
Pages (from-to)1611-1630
Number of pages20
JournalSIAM Journal on Matrix Analysis and Applications
Volume34
Issue number4
DOIs
StatePublished - 2013

Fingerprint

Synchronization
Graph in graph theory
Worst-case Performance
Performance Guarantee
Spectral Methods
Pairwise
Unknown
Subset
Operator

Keywords

  • Cheeger inequality
  • Graph connection Laplacian
  • O(d) synchronization
  • Vector diffusion maps

ASJC Scopus subject areas

  • Analysis

Cite this

A cheeger inequality for the graph connection laplacian. / Bandeira, Afonso; Singer, Amit; Spielman, Daniel A.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 4, 2013, p. 1611-1630.

Research output: Contribution to journalArticle

Bandeira, Afonso ; Singer, Amit ; Spielman, Daniel A. / A cheeger inequality for the graph connection laplacian. In: SIAM Journal on Matrix Analysis and Applications. 2013 ; Vol. 34, No. 4. pp. 1611-1630.
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