Fundamental network science
Foundational network science research includes: study of topological data analysis on graphs, reinforcement learning on complex networks, graph embedding and representation learning, scalable algorithms for mining graphs, and anomaly detection. We are also working on a collection of studies developing rigorous approaches to latent-geometric network models, maximum entropy ensembles of random graphs, and their navigability, with applications ranging from neuroscience to quantum gravity and cosmology.
Generalized word shift graphs: a method for visualizing and explaining pairwise comparisons between texts
Network comparison and the within-ensemble graph distance
Who Says What with Whom: Using Bi-Spectral Clustering to Organize and Analyze Social Media Protest Networks
In our project on Scalable Graph Distances, we explore measurements of graph distance in metric spaces, which are required for many graph mining tasks (eg, clustering, anomaly detection). This project explores a formal mathematical foundation covering a family of graph distance measures that overcome common limitations, such as their inability to scale up to millions of nodes and reliance on heuristics. In another collection of studies on latent geometry, we rigorously establish conditions for a given (real) network to have latent geometry. This geometry can then be reliably used in applications ranging from explaining the structure of (optimal) information flows in the brain to providing new approaches to the dark energy problem in cosmology.