Distance Function Selection for Multivariate Time-Series

This paper investigates the problem of optimal distance function selection to optimize the distance between multivariate time series. The dynamic time warping method of univariate time-series defines the warping path and uses its cost as the distance function. To find this path it uses various pairwise distances between time-series. This work examines a generalization of the time warping algorithm in case of multivariate time-series. The novelty of the paper is the comparison of various metrics between the multivariate values of time-series. The distances induced by L1, L2 norms and cosine distances are compared. This work also proposes the multivariate adaptation of the optimized time warping algorithm. The experiment runs subsequence search and clustering problems for multivariate time-series. The given cost functions are evaluated on three data sets: two data sets with labeled physical human activity data from wearable devices and coordinates and the pressing force in the process of writing characters.