The performance of a combined distance between time series - Cardoso, M. G. M. S.; Martins, A. A. A. F. (XXV Congress of the Portuguese Statistical Society, 2021)
The use of dissimilarity measures between time series is critical in several data analysis tasks which range from simple querying to classification, clustering and anomaly detection. Recently, we proposed a new dissimilarity measure, a convex combination of four (normalized) distance measures which offer complementary perspectives on the differences between two time series: the Euclidean distance which captures differences in scale; a Pearson correlation based measure that takes into account linear increasing and decreasing trends over time; a Periodogram based measure that expresses the dissimilarities between frequencies or cyclical components of the series; and a distance between estimated autocorrelation structures, comparing the series in terms of their dependence on past observations. We conduct an experimental analysis, to evaluate the comparative performance of this combined distance measure, resorting to the UCR Time-Series Archive that includes time series data sets from a wide variety of application domains. We follow a methodology suggested in previous studies [?] that were conducted to compare several dissimilarity measures and their variants: we use one nearest neighbor (1NN) classifier on labelled data to evaluate the efficacy of the distance measures. In fact, since the distance measure used is critical to 1NN accuracy, this indicator directly reflects the effectiveness of the dissimilarity measure used. We conclude that the proposed combined measure is competitive in several settings. Finally, we suggest further research taking into account normalization methods.