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arXiv · 1204.3873

A Cheeger Inequality for the Graph Connection Laplacian

Afonso S. Bandeira·Amit Singer·Daniel A. Spielman
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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.

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Afonso S. Bandeira, Amit Singer, Daniel A. Spielman. 2012-04-17. A Cheeger Inequality for the Graph Connection Laplacian. https://arxiv.org/abs/1204.3873

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