Faster Sequential Search with a Two-Pass Dynamic-Time-Warping Lower Bound

TL;DR

This paper introduces a faster sequential search method for time series using a new tighter lower bound for Dynamic Time Warping, significantly improving search speed over previous bounds.

Contribution

It proposes a two-pass approach utilizing a tighter lower bound (LB_Improved) for DTW, enhancing the efficiency of nearest neighbor search in time series data.

Findings

LB_Improved-based search is 3 times faster than previous methods.

Derived a tight triangle inequality for DTW.

Showed DTW reduces to l_1 distance under certain conditions.

Abstract

The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensive lower bound (LB_Keogh). We compare LB_Keogh with a tighter lower bound (LB_Improved). We find that LB_Improved-based search is faster for sequential search. As an example, our approach is 3 times faster over random-walk and shape time series. We also review some of the mathematical properties of the DTW. We derive a tight triangle inequality for the DTW. We show that the DTW becomes the l_1 distance when time series are separated by a constant.