Work

A Cheeger Inequality for the Graph Connection Laplacian

Year: 2013

Type: article

Abstract: The $O(d)$ synchronization problem consists of estimating a set of $n$ unknown orthogonal $d\times d$ matrices $O_1,\ldots,O_n$ 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.

Source: SIAM Journal on Matrix Analysis and Applications

DOI: 10.1137/120875338

Authors: Afonso S. Bandeira, Amit Singer, Daniel A. Spielman

Institutions: Princeton University, Yale University

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, National Institute of General Medical Sciences, Air Force Office of Scientific Research