{"ID":2845326,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.05263","arxiv_id":"2601.05263","title":"A General Metric-Space Formulation of the Time Warp Edit Distance (TWED)","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.","short_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...","url_abs":"https://arxiv.org/abs/2601.05263","url_pdf":"https://arxiv.org/pdf/2601.05263v1","authors":"[\"Zhen Yi Lau\"]","published":"2025-11-06T13:25:23Z","proceeding":"cs.IR","tasks":"[\"cs.IR\",\"cs.DS\"]","methods":"[]","has_code":false}