ShapeDBA: Generating Effective Time Series Prototypes using ShapeDTW
  Barycenter Averaging
Ali Ismail-Fawaz Hassan Ismail Fawaz François Petitjean Maxime Devanne Jonathan Weber Stefano Berretti Geoffrey I. Webb Germain Forestier
Time series data can be found in almost every domain, ranging from the
medical field to manufacturing and wireless communication. Generating realistic
and useful exemplars and prototypes is a fundamental data analysis task. In
this paper, we investigate a novel approach to generating realistic and useful
exemplars and prototypes for time series data. Our approach uses a new form of
time series average, the ShapeDTW Barycentric Average. We therefore turn our
attention to accurately generating time series prototypes with a novel
approach. The existing time series prototyping approaches rely on the Dynamic
Time Warping (DTW) similarity measure such as DTW Barycentering Average (DBA)
and SoftDBA. These last approaches suffer from a common problem of generating
out-of-distribution artifacts in their prototypes. This is mostly caused by the
DTW variant used and its incapability of detecting neighborhood similarities,
instead it detects absolute similarities. Our proposed method, ShapeDBA, uses
the ShapeDTW variant of DTW, that overcomes this issue. We chose time series
clustering, a popular form of time series analysis to evaluate the outcome of
ShapeDBA compared to the other prototyping approaches. Coupled with the k-means
clustering algorithm, and evaluated on a total of 123 datasets from the UCR
archive, our proposed averaging approach is able to achieve new
state-of-the-art results in terms of Adjusted Rand Index.