Machine Learning on Graphs, Groups, and Manifolds

The emerging field of geometric deep learning has put a spotlight on the role of symmetry and low-dimensional latent structures in high-dimensional data analysis. In this course we start by discussing the curse of dimensionality which precludes high-dimensional learning without latent structure. We then exploit symmetry: we review the basics of group representation theory and design convolutional neural networks from first principles, starting with convnets on grids and progressing over homogeneous spaces (in particular the sphere) to graphs. Finally, we connect graphs and manifolds via the Laplace–Beltrami operator and discuss the basics of spectral graph theory and graph-based clustering and manifold learning algorithms.