Geometric and Topological Methods in Machine Learning

Graduate / Professional

This course provides an introduction to geometric and topological methods in data science. Our starting point is the manifold hypothesis: that high dimensional data live on or near a much lower dimensional smooth manifold. We introduce tools to study the geometric and topological properties of this manifold in order to reveal relevant features and organization of the data. Topics include: metric space structures, curvature, geodesics, diffusion maps, eigenmaps, geometric model spaces, gradient descent, data embeddings and projections, and topological data analysis (TDA) in the form of persistence homology and their associated “barcodes.” We see applications of these methods in a variety of data types. Prerequisites: MATH 2250 or 2260 ; MATH 2550 or 2560 ; MATH 3020 ; and CPSC 1001 . TTh 11:35am-12:50pm