论文标题
$ \ mathrm {so}（d）$中的深度下降同步
Depth Descent Synchronization in $\mathrm{SO}(D)$
论文作者
论文摘要
我们为旋转组的同步提供了强大的恢复结果，$ \ mathrm {so}（d）$。特别是，我们考虑了一个对抗性腐败环境，其中有限的观察结果被任意腐败。我们给出了一种新颖的算法，该算法利用了切线空间中的Tukey深度，该算法准确地恢复了基础旋转，最高率为$ 1/（D（d-1）+2）$。这对应于$ \ mathrm {so}（2）$和$ 1/8 $的$ 1/4 $的离群分数，对于$ \ mathrm {so}（3）$。在$ d = 2 $的情况下，我们证明了该算法的一种变体线性收敛到地面真相旋转。我们通过讨论基于最小绝对偏差的更简单的非凸能最小化框架来讨论此结果，该框架表现出虚假的固定点。
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.
