Provable Non-Convex Euclidean Distance Matrix Completion: Geometry, Reconstruction, and Robustness

ArXi:2508.00091v3 Announce Type: replace-cross The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network localization, molecular conformation, and manifold learning. In this paper, we propose a Riemannian optimization framework for solving the EDMC problem by formulating it as a low-rank matrix completion task over the space of positive semi-definite Gram matrices.