提出加速投影法，从含异常值的距离数据中精准恢复点位置。
Robust Multi-Dimensional Scaling via Accelerated Alternating Projections
- 基于交替投影与切空间加速，提升鲁棒性
- 稀疏异常值下可线性收敛到真实位置
- 适合高精度点云重建与异常干扰场景
本文研究鲁棒多维尺度变换（RMDS）问题，目标是从可能被异常值污染的成对距离中恢复点的位置。受经典MDS理论和鲁棒主成分分析（RPCA）非凸方法启发，提出一种基于交替投影的算法，并通过切空间投影技术进一步加速。当异常值足够稀疏时，该算法可实现重构点在中心化与旋转对齐后对原始点的线性收敛。数值实验验证了该算法在性能上达到当前最优水平。
原文摘要 · Abstract (English)
We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the robust principal component analysis (RPCA) problem, we propose an alternating projection based algorithm that is further accelerated by the tangent space projection technique. For the proposed algorithm, if the outliers are sparse enough, we can establish linear convergence of the reconstructed points to the original points after centering and rotation alignment. Numerical experiments verify the state-of-the-art performances of the proposed algorithm.
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