# Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis

arXiv: https://arxiv.org/abs/2206.01984 · HTML: https://mlsanity.com/paper/2206.01984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 4 Jun 2022.

## Builds on (most cited first, 8 of 8)

- [A review on distance based time series classification](https://mlsanity.com/paper/1806.04509/) (2018)
- [Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations](https://mlsanity.com/paper/2008.09165/) (2020)
- [Partitioning signal classes using transport transforms for data analysis and machine learning](https://mlsanity.com/paper/2008.03452/) (2020)
- [Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning](https://mlsanity.com/paper/2204.06645/) (2022)
- [Radon cumulative distribution transform subspace modeling for image classification](https://mlsanity.com/paper/2004.03669/) (2020)
- [The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification](https://mlsanity.com/paper/2106.02146/) (2021)
- [End-to-End Signal Classification in Signed Cumulative Distribution Transform Space](https://mlsanity.com/paper/2205.00348/) (2022)
- [Nearest Subspace Search in The Signed Cumulative Distribution Transform Space for 1D Signal Classification](https://mlsanity.com/paper/2110.05606/) (2021)

## 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.