Externe Publikationen
Refine
Year of publication
- 2019 (2) (remove)
Document Type
- Article (2) (remove)
Language
- English (2)
Has Fulltext
- no (2)
Is part of the Bibliography
- no (2)
Keywords
- Time series (2) (remove)
Institute
Begutachtungsstatus
- peer-reviewed (2)
This article revisits an analysis on (in)accuracies of time series averaging under dynamic time warping (dtw) conducted by Niennattrakul and Ratanamahatana [16]. They proposed a correctness-criterion for dtw-averages and postulated that dtw-averages can drift out of the cluster of time series to be averaged. They claimed that dtw-averages are inaccurate if they violate the correctness-criterion or suffer from the drift-out phenomenon. Furthermore, they conjectured that such inaccuracies are caused by the lack of triangle inequality. In this article, we show that a rectified version of the correctness-criterion is unsatisfiable and that the concept of drift-out is geometrically and operationally inconclusive. Satisfying the triangle inequality is insufficient to achieve correctness and unnecessary to overcome the drift-out phenomenon. We place the concept of drift-out on a principled basis and show that Fréchet means never drift out. The adjusted drift-out is a way to test to which extent an approximated dtw-average is coherent. Empirical results show that approximations obtained by the state-of-the-art averaging methods are incoherent in over a third of all cases.
The literature postulates that the dynamic time warping (dtw) distance can cope with temporal variations but stores and processes time series in a form as if the dtw-distance cannot cope with such variations. To address this inconsistency, we first show that the dtw-distance is not warping-invariant—despite its name and contrary to its characterization in some publications. The lack of warping-invariance contributes to the inconsistency mentioned above and to a strange behavior. To eliminate these peculiarities, we convert the dtw-distance to a warping-invariant semi-metric, called time-warp-invariant (twi) distance. Empirical results suggest that the error rates of the twi and dtw nearest-neighbor classifier are practically equivalent in a Bayesian sense. However, the twi-distance requires less storage and computation time than the dtw-distance for a broad range of problems. These results challenge the current practice of applying the dtw-distance in nearest-neighbor classification and suggest the proposed twi-distance as a more efficient and consistent option.