Tight lower bounds for dynamic time warping

Dynamic Time Warping (DTW) is a popular similarity measure for aligning and comparing time series. Due to DTW's high computation time, lower bounds are often employed to screen poor matches. Many alternative lower bounds have been proposed, providing a range of different trade-offs between tightness and computational efficiency. LB _KEOGH provides a useful trade-off in many applications. Two recent lower bounds, LB _IMPROVED and LB _ENHANCED , are substantially tighter than LB _KEOGH . All three have the same worst case computational complexity-linear with respect to series length and constant with respect to window size. We present four new DTW lower bounds in the same complexity class. LB _PETITJEAN is substantially tighter than LB _IMPROVED , with only modest additional computational overhead. LB _WEBB is more efficient than LB _IMPROVED , while often providing a tighter bound. LB _WEBB is always tighter than LB _KEOGH . The parameter free LB _WEBB is usually tighter than LB _ENHANCED . A parameterized variant, LB_WEBB_ENHANCED, is always tighter than LB _ENHANCED . A further variant, LB _WEBB^* , is useful for some constrained distance functions. In extensive experiments, LB _WEBB proves to be very effective for nearest neighbor search.