将时间扭曲编辑距离推广到任意度量空间，拓展了其在非时序数据上的应用
A General Metric-Space Formulation of the Time Warp Edit Distance (TWED)
- 将时间与观测空间均视为度量空间，构建广义时间扭曲编辑距离
- 在合理假设下保持度量性质，经典TWED是其特例
- 适用于符号数据、流形或嵌入序列等非时间序列场景
本文提出时间扭曲编辑距离（TWED）的通用度量空间形式化。通过将观测域和时间域分别视为度量空间 $(X, d)$ 与 $(T, Δ)$，定义广义时间扭曲编辑距离（GTWED），在适度假设下仍为真度量。文中提供完整的性质证明，并表明当 $X = bR^d$、$T 뾻R$、$g(x) = x$ 时，可还原经典TWED。该形式化揭示了弹性距离可超越时序数据的理论基础，使类似TWED的度量适用于符号数据、流形或嵌入序列等任意域上的序列比较。
原文摘要 · Abstract (English)
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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