A Survey on Time-Series Distance Measures

TL;DR

This survey comprehensively reviews over 100 time-series distance measures, categorizing them and analyzing their mathematical frameworks, distinctions, and applications for univariate and multivariate data, aiding future research.

Contribution

It offers a detailed classification and comparison of existing distance measures, highlighting their differences and applications in time-series analysis.

Findings

Classified 100+ distance measures into 7 categories.

Provided mathematical frameworks for each category.

Analyzed applications for univariate and multivariate data.

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.