Syllabus

The following topics will be covered, subject to changes. See the course web page for a detailed schedule.

• Introduction to Manifolds
  • Manifold definition, coordinate charts
  • Tangent spaces
  • Metrics, geodesics
  • Curvature
  • Lie groups and symmetric spaces
• Manifold-valued Data
  • Directional data
  • Matrix data
  • Shape data
• Statistical Analysis of Manifold-valued Data
  • Means, medians on manifolds
  • Principal component analysis on manifolds
  • Regression on manifolds
• Manifold Learning
  • Multi-dimensional scaling
  • Principal curves and manifolds
  • Local linear embedding
  • Diffusion maps
  • Gaussian process latent variable models
  • Autoenconders

• Information Geometry

• Manifolds in Deep Learning and AI Application
  • Supervised Learning
  • Unsupervised Learning
  • Graph Learning
  • Self-supervised Learning
  • Generative Modeling