A General Metric-Space Formulation of the Time Warp Edit Distance (TWED) · arXivDesk
2601.05263Nov 6, 202520 pages, 1 algorithm, small technical note on the generalization of the Time Warp Edit Distance (TWED) to arbitrary metric spaces
A General Metric-Space Formulation of the Time Warp Edit Distance (TWED)
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=Rd
Nearby in the stack
,
T⊂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.