Lie PCA: Density estimation for symmetric manifolds
Jameson Cahill, Dustin G. Mixon, Hans Parshall · arXiv (Cornell University) · 2020
We introduce an extension to local principal component analysis for learning symmetric manifolds. In particular, we use a spectral method to approximate the Lie algebra corresponding to the symmetry group of the underlying manifold. We derive the sample complexity of our method for a variety of manifolds before applying it to various data sets for improved density estimation.