标题： 通过加速交替投影的鲁棒多维缩放 显示英文标题

标题： Robust Multi-Dimensional Scaling via Accelerated Alternating Projections

摘要： 我们在这篇论文中考虑了鲁棒的多维缩放（RMDS）问题。 目标是从可能被异常值破坏的成对距离中定位点的位置。 受经典MDS理论和鲁棒主成分分析（RPCA）问题的非凸方法的启发，我们提出了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。 对于所提出的算法，如果异常值足够稀疏，我们可以在中心化和旋转对齐后建立重构点到原始点的线性收敛性。 数值实验验证了所提出算法的最先进性能。 显示英文摘要

摘要： 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.