Corpus ID: 221090543

Lie PCA: Density estimation for symmetric manifolds

  title={Lie PCA: Density estimation for symmetric manifolds},
  author={Jameson Cahill and Dustin G. Mixon and H. Parshall},
  • 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.


    Publications referenced by this paper.
    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