Skip to content

1heart/math690-lecture-notes

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

6 Commits
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

Math 690 - Topics in Data Analysis and Computation

Lecture notes for Duke's MATH690 - Topics in Data Analysis and Computation. Folders by Topic.

Topics that will be covered:

  • Principal component analysis (PCA) in high dimension
    • Marcenko-Pastur law, random matrix theory and universality
    • Spiking model in covariance estimation
    • Eigen-shrinkage and matrix de-noising
  • Graph-based dimension reduction
    • Stochastic neighbor embedding (SNE), comparison with manifold learners (Isomap, LLE, diffusion map, etc) and multidimensional scaling (MDS)
    • Heat kernel on manifold, convergence of graph laplacian
  • Clustering on graphs
    • Review of spectral clustering and limitations
    • SDP relaxation: theory and computational issues
  • Estimation on graphs
    • De-noising functions by non-local means
    • Synchronization of group elements on graphs
    • Application: rotation registration in Cryo-electron microscopy (CryoEM)
  • Concentration of measure
    • Review of concentration inequalities
    • Application: the spectra of random graphs
    • Application: randomized fast low-rank matrix approximation
  • Representation learning by neural networks
    • Classifiers and “auto-encoders”
    • Representation by intermediate layers in a neural network
    • Convolutional neural networks and the instability in input
  • High dimensional two samples
    • Distance between two samples in one dimension
    • Kernel density estimation and limitations in high dimension
    • Application: evaluating deep generative neural networks

About

No description, website, or topics provided.

Resources

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published