The Wasserstein transform
This method addresses dataset quality issues for researchers in machine learning and data analysis, but appears incremental as it builds on existing optimal transportation and mean shift ideas.
The authors tackled the problem of enhancing and denoising datasets on metric spaces by introducing the Wasserstein transform, which connects to mean shift algorithms and shows stability under data perturbation.
We introduce the Wasserstein transform, a method for enhancing and denoising datasets defined on general metric spaces. The construction draws inspiration from Optimal Transportation ideas. We establish precise connections with the mean shift family of algorithms and establish the stability of both our method and mean shift under data perturbation.