Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis
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Abstract (arXiv)
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.
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References · 8
- 2018A review on distance based time series classificationcited by 40
- 2020Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbationscited by 37
- 2020Partitioning signal classes using transport transforms for data analysis and machine learningcited by 15
- 2022Wassmap: Wasserstein Isometric Mapping for Image Manifold Learningcited by 15
- 2020Radon cumulative distribution transform subspace modeling for image classificationcited by 14
- 2021The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classificationcited by 9
- 2022End-to-End Signal Classification in Signed Cumulative Distribution Transform Spacecited by 7
- 2021Nearest Subspace Search in The Signed Cumulative Distribution Transform Space for 1D Signal Classificationcited by 5
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