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.
Non-parametric estimation of manifolds from noisy data.arXiv preprint arXiv:2105.04754, 2021
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A review of manifold fitting that distinguishes it from embedding and denoising, covers its evolution from early nonparametric methods through mathematical insights to modern statistical approaches, and highlights applications in neural networks and bioinformatics.
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Denoising Distances in Metric Measure Spaces
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.
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Manifold Fitting: A Review of Methods and Applications
A review of manifold fitting that distinguishes it from embedding and denoising, covers its evolution from early nonparametric methods through mathematical insights to modern statistical approaches, and highlights applications in neural networks and bioinformatics.