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