Effective Estimation of the Dimensions of a Manifold from Random Samples

TL;DR

This paper provides explicit bounds on the sample size needed from a manifold with reach 1 to reliably estimate its dimension with high confidence, aiding data analysis and manifold learning.

Contribution

It introduces theoretical and heuristic bounds for sample size requirements to accurately estimate manifold dimension from random samples.

Findings

Derived explicit bounds for sample size based on confidence levels.

Provided both theoretical and heuristic estimates for practical use.

Enhanced understanding of sample complexity in manifold dimension estimation.

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.