An efficient algorithm extracts clusters to denoise distances to fixed accuracy in metric measure spaces under lower phi-regularity, with a non-efficient method for higher accuracy indicating a statistical-computational gap unlike the Riemannian case.
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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Denoising Distances in Metric Measure Spaces
An efficient algorithm extracts clusters to denoise distances to fixed accuracy in metric measure spaces under lower phi-regularity, with a non-efficient method for higher accuracy indicating a statistical-computational gap unlike the Riemannian case.
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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.