A Cheeger Inequality for the Graph Connection Laplacian
Spectral Theory
2013-09-23 v2 Data Structures and Algorithms
Combinatorics
Abstract
The O(d) Synchronization problem consists of estimating a set of unknown orthogonal transformations O_i from noisy measurements of a subset of the pairwise ratios O_iO_j^{-1}. 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.
Cite
@article{arxiv.1204.3873,
title = {A Cheeger Inequality for the Graph Connection Laplacian},
author = {Afonso S. Bandeira and Amit Singer and Daniel A. Spielman},
journal= {arXiv preprint arXiv:1204.3873},
year = {2013}
}
Comments
To appear in the SIAM Journal on Matrix Analysis and Applications (SIMAX)