The Wasserstein Transform

Facundo Memoli, Zane Smith, Zhengchao Wan
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4496-4504, 2019.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-memoli19a, title = {The {W}asserstein Transform}, author = {Memoli, Facundo and Smith, Zane and Wan, Zhengchao}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {4496--4504}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/memoli19a/memoli19a.pdf}, url = {https://proceedings.mlr.press/v97/memoli19a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T The Wasserstein Transform %A Facundo Memoli %A Zane Smith %A Zhengchao Wan %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-memoli19a %I PMLR %P 4496--4504 %U https://proceedings.mlr.press/v97/memoli19a.html %V 97 %X 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.
APA
Memoli, F., Smith, Z. & Wan, Z.. (2019). The Wasserstein Transform. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:4496-4504 Available from https://proceedings.mlr.press/v97/memoli19a.html.

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