  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.
