Gromov-Wasserstein Averaging in a Riemannian Framework

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Authors Tom Needham, Samir Chowdhury
Journal/Conference Name IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops
Paper Category
Paper Abstract We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is carried out under the lens of the Gromov-Wasserstein (GW) distance, and our methods translate the Riemannian framework of GW distances developed by Sturm into practical, implementable tools for network data analysis. Our methods are illustrated on datasets of letter graphs, asymmetric stochastic blockmodel networks, and planar shapes viewed as metric spaces. On the theoretical front, we supplement the work of Sturm by producing additional results on the tangent structure of this "space of spaces", as well as on the gradient flow of the Fr\'{e}chet functional on this space.
Date of publication 2019
Code Programming Language Jupyter Notebook

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