## Partial Gromov-Wasserstein with Applications on Positive-Unlabeled Learning

**L. Chapel, M. Z. Alaya, G. Gasso**

*NeurIPS*, 2020

Optimal Transport (OT) framework allows defining similarity between probability distributions and provides metrics such as the Wasserstein and Gromov-Wasserstein discrepancies. Classical OT problem seeks a transportation map that preserves the total mass, requiring the mass of the source and target distributions to be the same. This may be too restrictive in certain applications such as color or shape matching, since the distributions may have arbitrary masses or that only a fraction of the total mass has to be transported. Several algorithms have been devised for computing unbalanced Wasserstein metrics but when it comes with the Gromov-Wasserstein problem, no partial formulation is available yet. **Read more**