Evaluating DTW Measures via a Synthesis Framework for Time-Series Data

TL;DR

This work tackles the absence of guidelines for selecting Dynamic Time Warping (DTW) variants by introducing a controllable synthesis framework that generates realistic time-series pairs with known variations. The framework first creates plausible base signals and then applies structured deformations (scaling, Gaussian peaks, or combinations) to produce targets, enabling precise evaluation of DTW variants via ADM and ADT metrics. Through extensive synthetic experiments on signal alignment and classification, the authors derive practical guidelines on when standard DTW, WDTW, or derivative DTW variants perform best, and validate these insights on real-world tasks involving gamma-ray logs and flow streamline patterns. The results provide a useful framework for practitioners to choose DTW measures according to signal characteristics, with potential impact on time-series analysis across engineering and scientific domains.

Abstract

Time-series data originate from various applications that describe specific observations or quantities of interest over time. Their analysis often involves the comparison across different time-series data sequences, which in turn requires the alignment of these sequences. Dynamic Time Warping (DTW) is the standard approach to achieve an optimal alignment between two temporal signals. Different variations of DTW have been proposed to address various needs for signal alignment or classifications. However, a comprehensive evaluation of their performance in these time-series data processing tasks is lacking. Most DTW measures perform well on certain types of time-series data without a clear explanation of the reason. To address that, we propose a synthesis framework to model the variation between two time-series data sequences for comparison. Our synthesis framework can produce a realistic initial signal and deform it with controllable variations that mimic real-world scenarios. With this synthesis framework, we produce a large number of time-series sequence pairs with different but known variations, which are used to assess the performance of a number of well-known DTW measures for the tasks of alignment and classification. We report their performance on different variations and suggest the proper DTW measure to use based on the type of variations between two time-series sequences. This is the first time such a guideline is presented for selecting a proper DTW measure. To validate our conclusion, we apply our findings to real-world applications, i.e., the detection of the formation top for the oil and gas industry and the pattern search in streamlines for flow visualization.

Figures (16)

• Figure 1: Our time-series synthesis framework consists of two steps. The first step produces an initial series, while the second step deforms the initial series with the controllable variations to generate the second series.
• Figure 2: Time-Series Sequence Generator. (a) Sample a point between minimum and maximum magnitude; (b) Randomly sample another point between minimum and maximum magnitude and place it at random distance between maximum and minimum allowed distance between two peaks/valleys from first point; (c) Generate a random function like $y = c_1x^a + c_2x^b$ and fit it between these two points; (d) Add these sampled points to the signal array and repeat this process until the desired length is reached.
• Figure 3: Initial synthetic signal generation without (a) and with noise (b) inserted.
• Figure 4: Scaling the shaded region without length preservation.
• Figure 5: Length preserving scaling. Adjustment is made in the shaded region.