Families of Optimal Transport Kernels for Cell Complexes

TMLR Paper4736 Authors

Abstract: Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the Wasserstein distance between cell complex signal distributions in terms of a Hodge-Laplacian matrix. This leads to a structurally meaningful measure to compare CW complexes and define the optimal transportation map. In order to simultaneously include both feature and structure information, we extend the Fused Gromov-Wasserstein distance to CW complexes. Finally, we introduce novel kernels over the space of probability measures on CW complexes based on the dual formulation of optimal transport.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Pierre_Ablin2

Submission Number: 4736