Effective Estimation of the Dimensions of a Manifold from Random Samples

Lucien Grillet; Juan Souto

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arXiv · 2209.01839

Effective Estimation of the Dimensions of a Manifold from Random Samples

Lucien Grillet·Juan Souto

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Abstract

We give explicit theoretical and heuristical bounds for how big does a data set sampled from a reach-1 submanifold M of euclidian space need to be, to be able to estimate the dimension of M with 90% confidence.

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Lucien Grillet, Juan Souto. 2022-09-05. Effective Estimation of the Dimensions of a Manifold from Random Samples. https://arxiv.org/abs/2209.01839

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