# Lie PCA: Density estimation for symmetric manifolds

arXiv: https://arxiv.org/abs/2008.04278 · HTML: https://mlsanity.com/paper/2008.04278/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 4 of 4)

- [Dimensionless machine learning: Imposing exact units equivariance](https://mlsanity.com/paper/2204.00887/) (2022)
- [Approximately Equivariant Graph Networks](https://mlsanity.com/paper/2308.10436/) (2023)
- [A tradeoff between universality of equivariant models and learnability of symmetries](https://mlsanity.com/paper/2210.09444/) (2022)
- [LieDetect: Detection of representation orbits of compact Lie groups from point clouds](https://mlsanity.com/paper/2309.03086/) (2023)

## Abstract (arXiv)

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.