This paper addresses the problem of estimating the positions of points from distance measurements corrupted by sparse outliers. Specifically, we consider a setting with two types of nodes: anchor nodes, for which exact distances to each other are known, and target nodes, for which complete but corrupted distance measurements to the anchors are available. To tackle this problem, we propose a novel algorithm powered by Nystr\"om method and robust principal component analysis. Our method is computationally efficient as it processes only a localized subset of the distance matrix and does not require distance measurements between target nodes. Empirical evaluations on synthetic datasets, designed to mimic sensor localization, and on molecular experiments, demonstrate that our algorithm achieves accurate recovery with a modest number of anchors, even in the presence of high levels of sparse outliers.

翻译：本文研究了从受稀疏异常值干扰的距离测量中估计点位置的问题。具体而言，我们考虑包含两类节点的场景：锚节点（其相互间的精确距离已知）与目标节点（可获得其与锚节点之间完整但受干扰的距离测量）。为解决此问题，我们提出了一种基于Nyström方法与鲁棒主成分分析的新型算法。该算法仅处理距离矩阵的局部子集，且无需目标节点间的距离测量，因而计算效率较高。在模拟传感器定位的合成数据集及分子实验上的实证评估表明，即使存在高比例的稀疏异常值，本算法仅需少量锚节点即可实现精确恢复。