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• W3104633905 abstract "We give robust recovery results for synchronization on the rotation group, $mathrm{SO}(D)$. In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We give a novel algorithm that exploits Tukey depth in the tangent space, which exactly recovers the underlying rotations up to an outlier percentage of $1/(D(D-1)+2)$. This corresponds to an outlier fraction of $1/4$ for $mathrm{SO}(2)$ and $1/8$ for $mathrm{SO}(3)$. In the case of $D=2$, we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We finish by discussing this result in relation to a simpler nonconvex energy minimization framework based on least absolute deviations, which exhibits spurious fixed points." @default.
• W3104633905 created "2020-11-23" @default.
• W3104633905 creator A5082234176 @default.
• W3104633905 creator A5088795209 @default.
• W3104633905 date "2020-02-13" @default.
• W3104633905 modified "2023-09-27" @default.
• W3104633905 title "Depth Descent Synchronization in $mathrm{SO}(D)$" @default.
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• W3104633905 hasPublicationYear "2020" @default.
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