Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gromov-Wasserstein Averaging in a Riemannian Framework   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.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin