Structured Sampling for Robust Euclidean Distance Geometry

TL;DR

This paper introduces a new efficient algorithm combining Nyström method and robust PCA to accurately estimate point positions from corrupted distance measurements, especially in sensor and molecular data scenarios.

Contribution

The paper presents a novel algorithm that efficiently estimates point locations using only anchor distances and robustly handles sparse outliers, without needing target-to-target distances.

Findings

Achieves accurate localization with few anchors.

Handles high levels of sparse outliers effectively.

Performs well on synthetic and molecular datasets.

Abstract

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.