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

TL;DR

The paper evaluates Multiscale Dubuc Distance (MDD), an envelope-based, non-point-mapping time-series similarity measure, against Dynamic Time Warping (DTW) across 95 UCR datasets and a real-world SWAN-SF task. MDD computes similarity over multiple scales using upper/lower envelopes and an IoU-inspired intersection ratio, yielding a (pseudo-)metric with linear-time complexity in series length. Optimized MDD (selecting a multiscale set $ ext{E}$) outperforms DTW in 41% of UCR datasets and delivers notable gains in average accuracy, while DTW remains superior for peak-alignment tasks; in SWAN-SF, MDD also achieves higher F1 and TSS. The results highlight complementary strengths of MDD and DTW and suggest practical utility in indexing and domain-specific time-series classification where point-wise matching is unreliable.

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.

Figures (12)

• Figure 1: The illustration shows how MDS (introduced in Sec. \ref{['sec:mdd-review']}) computes the similarity between two time series. From the UCR's SonyAIBORobotSurface1 dataset, time series indexed 82 is queried (green), and is matched with time series indexed 4 (red). Their corresponding envelopes created by $\varepsilon \in \{1, 2, 4, 8, 16\}$ is shown, individually (rows 1 and 2), as well as overlaid (row 3). One example of alignment (where $\varepsilon = 2$) is magnified for better visibility. The union and intersection used in Eq. \ref{['eq:union-and-inters']} are marked.
• Figure 2: The Sharpshooter plot compares the actual and expected accuracy gain of MDD over DTW ($g_{mdd,dtw}$, $\hat{g}_{mdd,dtw}$, respectively) for 95 datasets of UCR.
• Figure 3: Comparison of optimization approaches. These figures show the distribution of accuracy scores before and after optimizing MDD. The expected accuracy improves from 0.75 to 0.82, and the actual accuracy improves from 0.75 to 0.78. In the expected phase we show only the optimal accuracy scores.
• Figure 4: An example of a pair of time series (from the LargeKitchenAppliances dataset) for which DTW is most suited and MDD fails to capture the similarities.
• Figure 5: An example of a pair of time series (from UMD dataset) where both metrics perform similarly.