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 the stability of our method under data perturbation and, when the dataset is assumed to be Euclidean, we also exhibit a precise connection between the Wasserstein transform and the mean shift family of algorithms. We then use this connection to prove that mean shift also inherits stability under perturbations. We study the performance of the Wasserstein transform method on different datasets as a preprocessing step prior to clustering and classification tasks.
Facundo Memoli (Ohio State University)
Zane Smith (University of Minnesota)
Zhengchao Wan (The Ohio State University)
Related Events (a corresponding poster, oral, or spotlight)
2019 Poster: The Wasserstein Transform »
Fri. Jun 14th 01:30 -- 04:00 AM Room Pacific Ballroom #112