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

TL;DR

This paper evaluates the Multiscale Dubuc Distance (MDD) for time series similarity, demonstrating its advantages over Dynamic Time Warping (DTW) across multiple scales and in real-world classification tasks.

Contribution

It introduces and thoroughly assesses MDD, a novel similarity measure that operates across multiple temporal scales without point-to-point alignment, outperforming DTW in various scenarios.

Findings

MDD outperforms DTW in many simulated and real-world datasets.

MDD provides significant improvements in classification accuracy.

The method effectively captures multi-scale temporal features.

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.