Inaccuracies of Shape Averaging Method Using Dynamic Time Warping for Time Series Data

Abstract. Shape averaging or signal averaging of time series data is one of the prevalent subroutines in data mining tasks, where Dynamic Time Warping distance measure (DTW) is known to work exceptionally well with these time series data, and has long been demonstrated in various data mining tasks involving shape similarity among various domains. More specifically, in some tasks such as query refinement, template/pattern calculation, and k-means clustering, averaging a collection of time series is an essential subroutine. Therefore, DTW has been used to find the average shape of two time series according to the optimal mapping between them. Several methods have been proposed, some of which require the number of time series being averaged to be a power of two. In this work, we will demonstrate that these proposed methods cannot produce the real average of the time series. In fact, none of these publications have proved the correctness of their methods. This explains why current DTW averaging methods cannot be used in k-means clustering algorithm to achieve meaningful clustering results. We conclude with a suggestion of a method to potentially find the shape-based time series average