Corpus ID: 221090543

Lie PCA: Density estimation for symmetric manifolds

@inproceedings{Cahill2020LiePD,
  title={Lie PCA: Density estimation for symmetric manifolds},
  author={Jameson Cahill and Dustin G. Mixon and H. Parshall},
  year={2020}
}
  • Jameson Cahill, Dustin G. Mixon, H. Parshall
  • Published 2020
  • Computer Science, Mathematics
  • 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. 

    Figures and Tables from this paper.

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 10 REFERENCES
    Density Estimation for Statistics and Data Analysis.
    • 4,934
    • PDF
    Group Invariant Scattering
    • 544
    • PDF
    Lie Groups
    • 1,688
    Invariant Scattering Convolution Networks
    • 514
    • PDF
    Matching Component Analysis for Transfer Learning
    • 1
    • PDF
    Best practices for convolutional neural networks applied to visual document analysis
    • 1,918
    • Highly Influential
    • PDF