An exhaustive comparison of distance measures in the classification of time series with 1NN method

Time series classification is an important and challenging problem in data analysis. With the increase in time series data availability, hundreds of algorithms have been proposed. A huge effort over the past two decades caused a significant improvement in both the efficiency and effectiveness of time series classification. There is a belief in the community that the best method is a surprisingly simple one. Even though there exist many algorithms outperforming the nearest neighbor (NN) classifier, the popularity of the latter remains stable - due to its simplicity and high performance in many domains, especially with dynamic time warping (DTW) as the distance measure. In the paper, we present an exhaustive study in which we compare the performance of different similarity measures relying on the 1NN classifier. We used the most highly cited time series distance measures used in classification (in total we compared 56 distance measures). We evaluate methods on all datasets from the UCR Time Series Classification Archive. Additionally, we perform extensive statistical comparison of the examined methods. We show that none of the distance measures is the best for all datasets, however, there is a group performing statistically significantly better than the others.