DTW+S: Shape-based Comparison of Time-series with Ordered Local Trend

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.