Affine and Regional Dynamic Time Warping

Abstract

Time series are a ubiquitous form of data prevalent in everyday life, and their analysis has gathered immense interest in many domains. Pointwise matches between two time series are of great importance in time series analysis, and dynamic time warping (DTW) has been widely known to provide reasonable matches. There are situations where time series alignment should be invariant to scaling and offset in amplitude or certain regions of a time series should be strongly reflected in the pointwise matches. Two different variants of DTW, affine DTW (ADTW) and regional DTW (RDTW), are proposed to handle scaling and offset in amplitude and regional emphasis respectively. Furthermore, ADTW and RDTW can be combined in two different ways to generate alignments that incorporate advantages from both methods. In global-affine regional DTW (GARDTW), the affine model is applied globally to the entire time series with regional emphasis, whereas in local-affine regional DTW (LARDTW), the affine model is applied locally to each region which are then emphasized. Alignments produced by the proposed methods are evaluated on simulated datasets and their associated difference measures are tested on real datasets. The proposed methods are found to significantly outperform DTW when an evaluated dataset meets the models or preferences of the proposed methods.