Theory and algorithms of Geometric and Topological Data Analysis, including : dimensionality reduction, manifold learning, nearest neighbors, density estimation, persistent homology and statistical topological inference. This course reviews fundamental constructions related to the manipulation of point clouds, mixing ideas from computational geometry and topology, statistics, and machine learning. The emphasis is on methods that not only come with theoretical guarantees, but also work well in practice. In particular, software references and example datasets will be provided to illustrate the constructions.
AI PhD Curriculum