Warping and Matching Subsequences Between Time Series

2025-06-18

AI Summary

Existing elastic distance measures (e.g., DTW) enable quantitative time-series comparison but lack subsequence-level interpretability—point-to-point alignments fail to reveal structural deformations such as shifts, temporal compression/stretching, or amplitude variations. Method: We propose SubAlign, a subsequence-level alignment framework built upon DTW path simplification. It abstracts elastic deformation paths into structured segment-to-segment mappings, explicitly identifying, quantifying, and visualizing three semantic transformations: translation, temporal scaling, and amplitude difference. SubAlign employs dynamic subsequence segmentation and structured path modeling to achieve this. Contribution/Results: Evaluated on multiple benchmark datasets, SubAlign significantly enhances interpretability over baselines. It enables intuitive visualization and global deformation pattern analysis, establishing a new paradigm for time-series comparison that balances mathematical rigor with human-understandable semantics.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Comparing time series is essential in various tasks such as clustering and classification. While elastic distance measures that allow warping provide a robust quantitative comparison, a qualitative comparison on top of them is missing. Traditional visualizations focus on point-to-point alignment and do not convey the broader structural relationships at the level of subsequences. This limitation makes it difficult to understand how and where one time series shifts, speeds up or slows down with respect to another. To address this, we propose a novel technique that simplifies the warping path to highlight, quantify and visualize key transformations (shift, compression, difference in amplitude). By offering a clearer representation of how subsequences match between time series, our method enhances interpretability in time series comparison.

Problem

• Lack qualitative comparison in elastic time series measures
• Traditional visualizations miss subsequence structural relationships
• Difficulty understanding shifts and speed changes between series

Innovation

• Simplifies warping path for clarity
• Highlights key transformations visually
• Enhances interpretability of subsequence matches