Dynamic Information Networks: Geometry, Topology and Statistical Learning for the Articulation of Structure

: The research objectives of this project were to create new mathematical tools for understanding different kinds of information networks, especially the dynamics thereof and also to import tools from geometry to analyze network dynamics. In particular, we aimed to create new mathematical frameworks for visualizing and teasing apart multiscale network dynamics. We see this as extremely relevant for the analysis of large document corpora. The primary technical approach exploits ideas from linear algebra, markov processes, diffusion networks, differential geometry, and machine learning.