Tangent Space and Dimension Estimation with the Wasserstein Distance

10/12/2021
by   Uzu Lim, et al.
0

We provide explicit bounds on the number of sample points required to estimate tangent spaces and intrinsic dimensions of (smooth, compact) Euclidean submanifolds via local principal component analysis. Our approach directly estimates covariance matrices locally, which simultaneously allows estimating both the tangent spaces and the intrinsic dimension of a manifold. The key arguments involve a matrix concentration inequality, a Wasserstein bound for flattening a manifold, and a Lipschitz relation for the covariance matrix with respect to the Wasserstein distance.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset