Lie PCA: Density estimation for symmetric manifolds
This work addresses density estimation for symmetric manifolds, which is incremental as it builds on local PCA with a spectral extension.
The authors tackled the problem of density estimation for symmetric manifolds by extending local PCA with a spectral method to approximate the Lie algebra of the symmetry group, resulting in improved density estimation on various datasets.
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.