Learning on incomparable spaces using Optimal Transport

How to learn from multiple graphs or images of different resolutions? In this talk, I will present some strategies based on Optimal Transport theory (OT) that allows to define geometric notions of distance between probability distributions and to find correspondences, relations, between sets of points. I will present the Gromov-Wassertsein (GW) framework and show how it can be useful for dealing with structured data such as graphs. On the image side, I will present the problem of CO Optimal Transport (COOT) whose goal is to align both samples and features of two different datasets. I will present applications of COOT in heterogeneous domain adaptation and co-clustering/data summarization.