Modern data are high-dimensional, for example, images with millions of pixels, text corpora with millions of words, gene sequences with billions of base pairs, etc. However, these data tend to concentrate on lower-dimensional, nonlinear subspaces known as manifolds. This class covers the mathematical theory of high-dimensional geometry and manifolds and the application of this geometry to machine learning and data analysis.
- Time: Tue/Thu 2:00 - 3:15 PM
- Location: Thornton E316 / Zoom
- Instructor: Tom Fletcher (ptf8v AT virginia DOT edu)
- Office Hours (over Zoom): Wednesdays, 11 AM - 12 noon
- TA: Yinzhu Jin (yj3cz AT virginia DOT edu)
- Office Hours (over Zoom): Mondays, 1 - 2 PM
- Prerequisites: You should have basic (undergraduate level) knowledge of Probability, Linear Algebra, Multivariate Calculus, and be comfortable programming in Python
- Software: All homeworks will be done in Jupyter
Manfredo do Carmo, Riemannian Geometry
Sigmundur Gudmundsson, Introduction to Riemannian Geometry
For those of you who are relatively new to Jupyter, here are a few notebooks that you might find useful (from my undergraduate course Foundations of Data Analysis.)