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