Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis

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 thei...

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Hauptverfasser:	Li, Shiying, Rubaiyat, Abu Hasnat Mohammad, Rohde, Gustavo K
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Sprache:	eng
Schlagworte:	Computer Science - Learning Mathematics - Geometric Topology
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creator	Li, Shiying Rubaiyat, Abu Hasnat Mohammad Rohde, Gustavo K
description	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.
doi_str_mv	10.48550/arxiv.2206.01984
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title	Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis
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