An algorithm extracts large localized clusters in metric measure spaces to denoise distances with near-linear time for fixed error r, plus sharp info-theoretic scales for vanishing r suggesting statistical-computational gaps beyond Riemannian cases.
Localization from incomplete noisy distance measurements
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Riemannian gradient descent on rank-r Gram matrices for EDMC achieves linear convergence with high probability for sampling probability p ≥ O(ν² r² log(n)/n) and a hard-thresholding initialization under a weaker rate.
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Provable Non-Convex Euclidean Distance Matrix Completion: Geometry, Reconstruction, and Robustness
Riemannian gradient descent on rank-r Gram matrices for EDMC achieves linear convergence with high probability for sampling probability p ≥ O(ν² r² log(n)/n) and a hard-thresholding initialization under a weaker rate.