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arXiv · 2610.24191

Certifiably Correct Fréchet Means in Orbit Spaaces

Dustin G. Mixon·Tom Needham·Nathan Willey
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Abstract

We study Fréchet means in orbit spaces of finite orthogonal group actions. Since computing these means is NP-hard in general, we take inspiration from group synchronization to develop tractable spectral and semidefinite relaxations. Pairwise alignment certifies global optimality and we develop a semidefinite certificate that can extend beyond this condition. For Gaussian data modulo sign, we prove that our certificate succeeds in a high-noise regime where alignment fails. Numerical experiments evaluate these methods in various settings, including summarizing ensembles of districting plans and clustering time series

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Dustin G. Mixon, Tom Needham, Nathan Willey. 2026-10-16. Certifiably Correct Fréchet Means in Orbit Spaaces. https://arxiv.org/abs/2610.24191

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