Gromov-Wasserstein Averaging in a Riemannian Framework

CVPRW 2020 pp. 3676-3684

doi:10.1109/CVPRW50498.2020.00429 /cvprw/2020/chowdhury2020cvprw-gromovwasserstein/

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 Fréchet functional on this space.

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Cite

Text

Chowdhury and Needham. "Gromov-Wasserstein Averaging in a Riemannian Framework." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2020. doi:10.1109/CVPRW50498.2020.00429

Markdown

[Chowdhury and Needham. "Gromov-Wasserstein Averaging in a Riemannian Framework." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2020.](https://mlanthology.org/cvprw/2020/chowdhury2020cvprw-gromovwasserstein/) doi:10.1109/CVPRW50498.2020.00429

BibTeX

@inproceedings{chowdhury2020cvprw-gromovwasserstein,
  title     = {{Gromov-Wasserstein Averaging in a Riemannian Framework}},
  author    = {Chowdhury, Samir and Needham, Tom},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops},
  year      = {2020},
  pages     = {3676-3684},
  doi       = {10.1109/CVPRW50498.2020.00429},
  url       = {https://mlanthology.org/cvprw/2020/chowdhury2020cvprw-gromovwasserstein/}
}