Geometry of Data


Modern data are high-dimensional, multi-modal, and large-scale, 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. Learning and sampling from this real distribution, hence, is of tremendous value. This class covers the mathematical theory of high-dimensional geometry and manifolds and how it applies to the latest advances in artificial intelligence.


Additional Reading

Manfredo do Carmo, Riemannian Geometry

Sigmundur Gudmundsson, Introduction to Riemannian Geometry

Example Jupyter Notebooks

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.)