A review and evaluation of elastic distance functions for time series clustering

Abstract

Time series clustering is the act of grouping time series data without recourse to a label. Algorithms that cluster time series can be classified into two groups: those that employ a time series specific distance measure and those that derive features from time series. Both approaches usually rely on traditional clustering algorithms such as k-means. Our focus is on partitional clustering algorithms that employ elastic distance measures, i.e. distances that perform some kind of realignment whilst measuring distance. We describe nine commonly used elastic distance measures and compare their performance with k-means and k-medoids clusterer. Our findings, based on experiments using the UCR time series archive, are surprising. We find that, generally, clustering with DTW distance is not better than using Euclidean distance and that distance measures that employ editing in conjunction with warping are significantly better than other approaches. We further observe that using k-medoids clusterer rather than k-means improves the clusterings for all nine elastic distance measures. One function, the move–split–merge (MSM) distance, is the best performing algorithm of this study, with time warp edit (TWE) distance a close second. Our conclusion is that MSM or TWE with k-medoids clusterer should be considered as a good alternative to DTW for clustering time series with elastic distance measures. We provide implementations, extensive results and guidance on reproducing results on the associated GitHub repository.