Lie PCA: Density estimation for symmetric manifolds
Machine Learning
2020-09-15 v2 Optimization and Control
Machine Learning
Abstract
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.
Keywords
Cite
@article{arxiv.2008.04278,
title = {Lie PCA: Density estimation for symmetric manifolds},
author = {Jameson Cahill and Dustin G. Mixon and Hans Parshall},
journal= {arXiv preprint arXiv:2008.04278},
year = {2020}
}