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On the Whitney near extension problem, BMO, alignment of data, best approximation in algebraic geometry, manifold learning and their beautiful connections: A modern treatment. (arXiv:2103.09748v6 [math.CA] UPDATED)
cs.CV updates on arXiv.org arxiv.org
This paper provides fascinating connections between several mathematical
problems which lie on the intersection of several mathematics subjects, namely
algebraic geometry, approximation theory, complex-harmonic analysis and high
dimensional data science. Modern techniques in algebraic geometry,
approximation theory, computational harmonic analysis and extensions develop
the first of its kind, a unified framework which allows for a simultaneous
study of labeled and unlabeled near alignment data problems in of $\mathbb R^D$
with the near isometry extension problem for discrete and non-discrete subsets …
alignment approximation arxiv data extension geometry manifold math near treatment