Gromov-Wasserstein in a Riemannian framework with applications to neuroimaging


Event details

Date and time 29.09.2020 16:1517:15  
Speaker Samir  Chowdhury
Category Conferences - Seminars
Applied Topology Seminar

Speaker: Samir Chowdhury, Stanford University

Title: Gromov-Wasserstein in a Riemannian framework with applications to neuroimaging

Abstract: 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 pipeline that utilizes the Mapper algorithm to produce network representations of whole-brain activity during ongoing cognition. When applying this pipeline at scale across clinical populations, however, generating consistent insights requires the development of 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-based graph averaging, partitioning, and tangent PCA. This framework permits using derived network representations beyond graph geodesic distances or adjacency matrices. In particular, we show that compared to state-of-the-art implementations that use adjacency matrix formulations, a spectral network representation leads to improved accuracy and runtime in graph learning tasks. Additionally, we observe that the spectral approach to GW graph partitioning corresponds to a generalization of Fiedler bipartitioning, thus suggesting new avenues for rigorous analysis of the GW problem.

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Practical information

  • Informed public
  • Free


  • Applied Topology Seminar

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