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• W3102664621 startingPage "935" @default.
• W3102664621 abstract "In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various compact groups. Spectral Group Synchronization is a commonly used, robust algorithm for solving group synchronization problems, which relies on diagonalization of a block matrix whose blocks are matrix representations of the measured pairwise differences. Assuming uniformly distributed measurement errors, we present a rigorous analysis of the accuracy and noise sensitivity of spectral group synchronization algorithms over any compact group, up to the rounding error. We identify a Baik-Ben Arous-P'ech'e type phase transition in the noise level, beyond which spectral group synchronization necessarily fails. Below the phase transition, spectral group synchronization succeeds in recovering the unknown group elements, but its performance deteriorates with the noise level. We provide asymptotically exact formulas for the accuracy of spectral group synchronization below the phase transition, up to the rounding error. We also provide a consistent risk estimate, allowing practitioners to estimate the method's accuracy from available measurements." @default.
• W3102664621 created "2020-11-23" @default.
• W3102664621 creator A5013235677 @default.
• W3102664621 creator A5039600520 @default.
• W3102664621 date "2020-11-01" @default.
• W3102664621 modified "2023-10-14" @default.
• W3102664621 title "The Noise-sensitivity phase transition in spectral group synchronization over compact groups" @default.
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• W3102664621 doi "https://doi.org/10.1016/j.acha.2019.05.002" @default.
• W3102664621 hasPublicationYear "2020" @default.
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