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Geometric and topological data analysis methods are increasingly being used to derive insights from data arising in the empirical sciences. We start with a particular case where such techniques are applied to human neuroimaging data to obtain graphs which can then yield insights connecting neurobiology to human task performance. Reproducing such insights across 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. Beyond graph adjacency matrices, this framework permits consuming derived network representations such as distance or kernel matrices, and each choice leads to additional structure on the GW problem that can be exploited for theoretical and/or computational advantages. In particular, we show how replacing the adjacency matrix representation with a spectral representation leads to theoretical guarantees allowing efficient use of the Riemannian framework. Additionally we present numerics showing how the spectral representation achieves state of the art accuracy and runtime in graph learning tasks such as matching and partitioning on a variety of real and simulated datasets.

zoom info available https://sites.google.com/view/maddd After the talk, we will do virtual tea/coffee get-together at https://gather.town/KOoFj0aKT5GkEj40/Alder-Room