Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis
This work addresses the problem of improving interpretability and robustness in time series classification for researchers and practitioners in signal processing and machine learning, but it appears incremental as it builds on existing transport-based metrics.
The paper studied the geodesic properties of time series data using a generalized Wasserstein metric and their signed cumulative distribution transforms in the embedding space, showing that this understanding can enhance interpretability and inspire more robust classifiers.
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.