Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Aanalysis

Shiying Li, Abu Hasnat, Mohammad Rubaiyat, Gustavo K. Rohde
Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, PMLR 196:216-225, 2022.

Abstract

Transport-based metrics and related embeddings (transforms) have recently been used to model signal classes where nonlinear structures or variations are present. In this paper, we study the geodesic properties of time series data with a generalized Wasserstein metric and the geometry related to their signed cumulative distribution transforms in the embedding space. Moreover, we show how understanding such geometric characteristics can provide added interpretability to certain time series classifiers, and be an inspiration for more robust classifiers. The appendix can be found at https://arxiv.org/abs/2206.01984.

Cite this Paper

BibTeX
@InProceedings{pmlr-v196-li22a, title = {Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis}, author = {Li, Shiying and Hasnat, Abu and Rubaiyat, Mohammad and Rohde, Gustavo K.}, booktitle = {Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022}, pages = {216--225}, year = {2022}, editor = {Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Kaul, Manohar and Ktena, Ira and Kvinge, Henry and Miolane, Nina and Rieck, Bastian and Tymochko, Sarah and Wolf, Guy}, volume = {196}, series = {Proceedings of Machine Learning Research}, month = {25 Feb--22 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v196/li22a/li22a.pdf}, url = {https://proceedings.mlr.press/v196/li22a.html}, abstract = {Transport-based metrics and related embeddings (transforms) have recently been used to model signal classes where nonlinear structures or variations are present. In this paper, we study the geodesic properties of time series data with a generalized Wasserstein metric and the geometry related to their signed cumulative distribution transforms in the embedding space. Moreover, we show how understanding such geometric characteristics can provide added interpretability to certain time series classifiers, and be an inspiration for more robust classifiers. The appendix can be found at https://arxiv.org/abs/2206.01984. } }
Endnote
%0 Conference Paper %T Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Aanalysis %A Shiying Li %A Abu Hasnat %A Mohammad Rubaiyat %A Gustavo K. Rohde %B Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022 %C Proceedings of Machine Learning Research %D 2022 %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Manohar Kaul %E Ira Ktena %E Henry Kvinge %E Nina Miolane %E Bastian Rieck %E Sarah Tymochko %E Guy Wolf %F pmlr-v196-li22a %I PMLR %P 216--225 %U https://proceedings.mlr.press/v196/li22a.html %V 196 %X Transport-based metrics and related embeddings (transforms) have recently been used to model signal classes where nonlinear structures or variations are present. In this paper, we study the geodesic properties of time series data with a generalized Wasserstein metric and the geometry related to their signed cumulative distribution transforms in the embedding space. Moreover, we show how understanding such geometric characteristics can provide added interpretability to certain time series classifiers, and be an inspiration for more robust classifiers. The appendix can be found at https://arxiv.org/abs/2206.01984.
APA
Li, S., Hasnat, A., Rubaiyat, M. & Rohde, G.K.. (2022). Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Aanalysis. Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, in Proceedings of Machine Learning Research 196:216-225 Available from https://proceedings.mlr.press/v196/li22a.html.

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