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Lie PCA: Density estimation for symmetric manifolds
Jameson Cahill, Dustin G. Mixon, Hans Parshall · 2020-08-11 · via cs.LG updates on arXiv.org

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.

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