Lie PCA: Density estimation for symmetric manifolds

08/10/2020

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by   Jameson Cahill, et al.

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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.