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 L
₁
, L
₂
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.