Learning Dictionaries over Datasets through Wasserstein Barycenters

Eduardo Fernandes Montesuma, Fred Maurice Ngole Mboula, Antoine Souloumiac

Keywords: Dictionary Learning, Optimal Transport, Domain Adaptation, Manifold Learning

TL;DR: We apply Wasserstein Dictionary Learning to datasets understood as empirical distributions.

Abstract: Dictionary learning consists of trying to represent objects in terms of basic elements (atoms) weighted by an importance factor (representation). Non-linear dictionary learning using optimal transport as a metric has been previously studied for normalized non-negative data on a fixed grid. We propose a new framework by using Wasserstein Dictionary Learning on datasets understood as empirical distributions. We leverage Wasserstein barycenters for learning a dictionary of virtual datasets and embeddings in a simplex. We apply our method for unsupervised domain adaptation, improving the state-of-the-art over 1.96% and 2.70%, respectively, and manifold learning of Gaussian distributions and color histograms.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Unsupervised and Self-supervised learning