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Manifold learning subsumes techniques conceived for problems where data of interest are assumed to lie on an embedded non-linear manifold within a higher-dimensional space.

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Is low rank finite-iteration manifold identification possible?

Yes. You can see results like this in the thesis of Jingwei Liang titled "Convergence Rates of First-Order Operator Splitting Methods" where they are called finite identification results (ch. 6, 7, 8) …
giorgi nguyen's user avatar