The geometry and metric structure of data
Published:
Much of my current work asks how faithfully we can represent complex data with simple geometric structure — trees, hyperbolic spaces, and metric spaces — and what happens when we cannot. This includes metric repair, large-scale metric-constrained optimization, low-dimensional and hyperbolic embeddings, multidimensional scaling, and graph rewiring for machine learning.
Representative work: Project and Forget (JMLR 2023), Fitting trees to ℓ1 hyperbolic distances (NeurIPS 2023), How can classical multidimensional scaling go wrong? (NeurIPS 2021), Tree! I am no Tree! (NeurIPS 2020), and Generalized Metric Repair on Graphs (SWAT 2020).
Students interested in the geometry of data, embeddings, and optimization on metric constraints are welcome to get in touch.