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A Cheeger Inequality for the Graph Connection Laplacian
classification
🧮 math.SP
cs.DSmath.CO
keywords
inequalityproblemconnectiongraphlaplaciansolvesynchronizationcase
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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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