A General Metric-Space Formulation of the Time Warp Edit Distance (TWED)

• URL: http://arxiv.org/abs/2601.05263v1
• Date: Thu, 06 Nov 2025 13:25:23 GMT
• Title: A General Metric-Space Formulation of the Time Warp Edit Distance (TWED)
• Abstract summary: We define a Generalized TWED (GTWED) that remains a true metric under mild assumptions.<n>This note focuses on the theoretical structure of GTWED and its implications for extending elastic distances beyond time series.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This short technical note presents a formal generalization of the Time Warp Edit Distance (TWED) proposed by Marteau (2009) to arbitrary metric spaces. By viewing both the observation and temporal domains as metric spaces $(X, d)$ and $(T, Δ)$, we define a Generalized TWED (GTWED) that remains a true metric under mild assumptions. We provide self-contained proofs of its metric properties and show that the classical TWED is recovered as a special case when $X = \mathbb{R}^d$, $T \subset \mathbb{R}$, and $g(x) = x$. This note focuses on the theoretical structure of GTWED and its implications for extending elastic distances beyond time series, which enables the use of TWED-like metrics on sequences over arbitrary domains such as symbolic data, manifolds, or embeddings.

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