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

arXiv:2601.05263v1 Announce Type: new
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 $(T, Delta)$, 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.