Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis

TL;DR

This paper explores the geometric properties of a generalized Wasserstein embedding for time series, revealing insights that enhance interpretability and robustness of classifiers using transport-based metrics.

Contribution

It analyzes the geodesic structure of time series under a generalized Wasserstein metric and its impact on interpretability and robustness of signal classification.

Findings

Geodesic properties of time series are characterized in the embedding space.

Understanding geometry improves interpretability of classifiers.

Insights can inspire more robust classification methods.

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.