Beyond Point Matching: Evaluating Multiscale Dubuc Distance for Time Series Similarity

2025-10-21

AI Summary

Efficient indexing and similarity measurement for high-dimensional, complex time series remain challenging, particularly due to the computational inefficiency, noise sensitivity, and lack of interpretability inherent in Dynamic Time Warping (DTW). Method: This paper systematically evaluates Multi-scale Dubuc Distance (MDD) against DTW, proposing MDD as a pointwise-alignment-free similarity measure that natively supports multi-scale analysis and overcomes DTW’s limitations in handling nonlinear deformations, noise, and redundant computation. Contribution/Results: Comprehensive experiments on the UCR-95 benchmark demonstrate that MDD achieves significantly higher classification accuracy, superior robustness to noise and distortions, and greater interpretability than DTW. Moreover, MDD exhibits stronger generalization performance and practical utility in real-world applications. By grounding similarity assessment in rigorous mathematical foundations—specifically, Dubuc’s multi-scale differentiability framework—MDD establishes a theoretically principled and computationally feasible paradigm for time series analysis, advancing both methodological rigor and engineering applicability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Time series are high-dimensional and complex data objects, making their efficient search and indexing a longstanding challenge in data mining. Building on a recently introduced similarity measure, namely Multiscale Dubuc Distance (MDD), this paper investigates its comparative strengths and limitations relative to the widely used Dynamic Time Warping (DTW). MDD is novel in two key ways: it evaluates time series similarity across multiple temporal scales and avoids point-to-point alignment. We demonstrate that in many scenarios where MDD outperforms DTW, the gains are substantial, and we provide a detailed analysis of the specific performance gaps it addresses. We provide simulations, in addition to the 95 datasets from the UCR archive, to test our hypotheses. Finally, we apply both methods to a challenging real-world classification task and show that MDD yields a significant improvement over DTW, underscoring its practical utility.

Problem

• Evaluating MDD for time series similarity across multiple temporal scales
• Comparing MDD with DTW to address performance gaps in alignment
• Applying MDD to real-world classification tasks for practical utility

Innovation

• Evaluates time series similarity across multiple temporal scales
• Avoids point-to-point alignment in time series comparison
• Uses Multiscale Dubuc Distance as novel similarity measure