用少量锚点和局部距离数据，抗噪定位目标点位置
Structured Sampling for Robust Euclidean Distance Geometry
- 基于奈氏方法与鲁棒PCA，仅处理距离矩阵局部子集
- 在稀疏异常值下，用少量锚点实现高精度定位
- 适合传感器网络与分子结构重建等场景
本文研究从受稀疏异常值污染的距离测量中估计点的位置问题。考虑两种节点：已知彼此精确距离的锚点，以及相对于锚点有完整但被污染的距离测量的目标点。提出一种新算法，结合奈氏方法与鲁棒主成分分析，计算高效，仅需处理距离矩阵的局部子集，无需目标点间距离数据。在模拟传感器定位的合成数据集和分子实验上验证，即使在高稀疏异常值下，也能用较少锚点实现高精度恢复。
原文摘要 · Abstract (English)
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 Nyström 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.
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