Measuring distance or similarity between time-series data is a fundamental
aspect of many applications including classification and clustering. Existing
measures may fail to capture similarities due to local trends (shapes) and may
even produce misleading results. Our goal is to develop a measure that looks
for similar trends occurring around similar times and is easily interpretable
for researchers in applied domains. This is particularly useful for
applications where time-series have a sequence of meaningful local trends that
are ordered, such as in epidemics (a surge to an increase to a peak to a
decrease). We propose a novel measure, DTW+S, which creates an interpretable
"closeness-preserving" matrix representation of the time-series, where each
column represents local trends, and then it applies Dynamic Time Warping to
compute distances between these matrices. We present a theoretical analysis
that supports the choice of this representation. We demonstrate the utility of
DTW+S in ensemble building and clustering of epidemic curves. We also
demonstrate that our approach results in better classification compared to
Dynamic Time Warping for a class of datasets, particularly when local trends
rather than scale play a decisive role.

测量时间序列数据之间的距离或相似性是许多应用的基本方面，包括分类和聚类。我们的目标是开发一种可以查找相似时间点附近发生的相似趋势，并且对应用领域的研究人员易于解释的度量。我们提出了一种新颖的度量方法 DTW+S，它创建了一个可解释的时间序列 “接近保持” 矩阵表示，每一列代表局部趋势，然后应用动态时间规整来计算这些矩阵之间的距离。我们提供了支持该表示选择的理论分析。我们证明了 DTW+S 在集成构建和流行病曲线聚类中的实用性。此外，我们还证明了相对于动态时间规整在某类数据集上的分类效果更好，特别是当局部趋势而非尺度起决定性作用时。