English

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}
}
R2 v1 2026-06-23T17:45:28.220Z