Two rounds of linear-sum assignment identify near neighbors, a three-equation system estimates per-point noise, and subtracting the estimates from corrupted distances yields provably consistent Euclidean distances.
The metric nearness problem.SIAM Journal on Matrix Analysis and Applications, 30(1):375–396, 2008
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Euclidean Distance Deflation Under High-Dimensional Heteroskedastic Noise
Two rounds of linear-sum assignment identify near neighbors, a three-equation system estimates per-point noise, and subtracting the estimates from corrupted distances yields provably consistent Euclidean distances.