A Wasserstein-type distance in the space of Gaussian Mixture Models
About
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We derive a very simple discrete formulation for this distance, which makes it suitable for high dimensional problems. We also study the corresponding multi-marginal and barycenter formulations. We show some properties of this Wasserstein-type distance, and we illustrate its practical use with some examples in image processing.
Julie Delon, Agnes Desolneux• 2019
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Transport Map Estimation | sci-Plex human Belinostat (test) | Average Sinkhorn Divergence (Dε)8 | 5 | |
| Transport Map Estimation | human scRNA-seq Quisinostat sci-Plex (test) | Average Sinkhorn Divergence (Dε)8.8 | 5 | |
| Transport Map Estimation | human scRNA-seq Dacinostat sci-Plex (test) | Average Sinkhorn Divergence (Dε)8.9 | 5 | |
| Transport Map Estimation | human scRNA-seq Givinostat sci-Plex (test) | Average Sinkhorn Divergence (Dε)8.9 | 5 | |
| Transport Map Estimation | human scRNA-seq Hesperadin sci-Plex (test) | Avg Sinkhorn Divergence (Dε)8.1 | 5 | |
| Spatial gene expression imputation | MERFISH mouse brain (target slice) | Slc17a7 Score89 | 3 |
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