Year: 2026
Type: preprint
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
Source: arXiv (Cornell University)
Authors: Mixon, Dustin G., Needham, Tom, Willey, Nathan
Institutions: The Ohio State University, Florida State University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222997938