An area-based shape distance measure of time series

Abstract

For any two one-dimensional time series of equal or non-equal length, we propose a new method to determine their shape distance. Each of the original time series is represented by a sequence of linear segments which are produced by l1 trend filtering. As the dimensionality of this representation ranges between time series, dynamic time warping (DTW) method is used to calculate the distance between time series. In contrast to the standard dynamic time warping method, here the element of the new distance matrix concerns the distance between two linear segments instead of two elements of the original time series. More specifically, the distance between the two linear segments is calculated as the area of a triangle which is formed by the two linear segments after their translation and connection. In brief, the new measure can be regarded as the dynamic time warping distance computed in a piecewise linear space. Furthermore, we show that new distance measure quantitatively reflects the shape's difference between two one-dimensional time series. The simulation experiments presented in this paper illustrate the performance of the proposed method.