Samir Chowdhury

• 
  A Riemannian framework for Gromov-Wasserstein averaging with applications to neuroimaging
  Samir Chowdhury
  Geometric and topological data analysis methods are increasingly being used in human neuroimaging studies to derive insights into neurobiology and behavior. We will begin by describing a novel application of optimal transport toward predicting task performance, and go on to explain why reproducing such insights across clinical populations requires statistical learning techniques such as averaging and PCA across graphs without known node correspondences. We formulate this problem using the Gromov-Wasserstein (GW) distance and present a recently-developed Riemannian framework for GW-averaging and tangent PCA. This framework permits derived network representations beyond graph geodesic distances or adjacency matrices. As an application, we show that replacing the adjacency matrix formulation in state-of-the-art implementations with a spectral representation leads to improved accuracy and runtime in graph learning tasks. Joint work with Caleb Geniesse, Facundo Mémoli, Tom Needham, and Manish Saggar.