Tangent Space and Dimension Estimation with the Wasserstein Distance

Understand

Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space.

• We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of that manifold with high confidence.
• The algorithm for this estimation is Local PCA, a local version of principal component analysis.
• Our results accommodate for noisy non-uniform data distribution with the noise that may vary across the manifold, and allow simultaneous estimation at multiple points.