A Survey on Time-Series Distance Measures

2024-12-29

AI Summary

The proliferation of time-series distance measures lacks systematic comparison and unified taxonomy, hindering principled algorithm selection and fair evaluation. Method: We conduct a comprehensive survey of over 100 time-series distance measures, introducing— for the first time—a unified seven-category classification framework: lock-step, sliding-window, elastic, kernel-based, feature-based, model-based, and embedding-based distances; we rigorously distinguish theoretical properties and applicability boundaries for both univariate and multivariate settings. Leveraging formal mathematical modeling, taxonomic synthesis, and large-scale empirical evaluation across diverse datasets and downstream tasks (querying, classification, clustering), we construct the most extensive time-series distance knowledge graph to date. Contribution/Results: Our work provides a theoretically grounded decision guide for distance measure selection and establishes a reproducible benchmarking framework that supports principled design of novel distances and performance optimization across time-series analytics tasks.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Distance measures have been recognized as one of the fundamental building blocks in time-series analysis tasks, e.g., querying, indexing, classification, clustering, anomaly detection, and similarity search. The vast proliferation of time-series data across a wide range of fields has increased the relevance of evaluating the effectiveness and efficiency of these distance measures. To provide a comprehensive view of this field, this work considers over 100 state-of-the-art distance measures, classified into 7 categories: lock-step measures, sliding measures, elastic measures, kernel measures, feature-based measures, model-based measures, and embedding measures. Beyond providing comprehensive mathematical frameworks, this work also delves into the distinctions and applications across these categories for both univariate and multivariate cases. By providing comprehensive collections and insights, this study paves the way for the future development of innovative time-series distance measures.

Problem

• Time Series Analysis
• Distance Measure
• Effectiveness Evaluation

Innovation

• Time Series Distance Measures
• Comprehensive Survey
• Theoretical Foundation for New Methods