A tighter lower bound estimate for dynamic time warping

In this paper, we propose a new lower-bound estimate for speeding up dynamic time warping (DTW) on multivariate time sequences. It has several advantages as compared with the inner-product lower bound [1] recently proposed to eliminate a large number of DTW computations. First, we prove that it is tighter than the inner product lower bound while the computational complexity remains comparable. Second, the inner product lower bound is specifically designed for the inner product distance while the proposed lower bound is valid for any distance measure. Third, DTW search can be further speeded up since the distance matrix is calculated in advance at the lower bound estimation stage. Spoken term detection experiments on the TIMIT corpus show that the proposed lower bound estimate is able to reduce the computational requirements for DTW-KNN search by 54% as compared with the inner-product lower bound. in black ink.