Faster retrieval with a two-pass dynamic-time-warping lower bound

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. As an example, our approach is 2-3 times faster over random-walk and shape time series.

A Heuristic Based on the Intrinsic Dimensionality for Reducing the Number of Cyclic DTW Comparisons in Shape Classification and Retrieval Using AESA

“…We also used a synthetic corpus of sequences of several dimensions (1, 5, 10, 20 and 60). We generated 1000 sequences (for each number of dimensions) with a random walk (for each dimension of the sequence) defined by x i = x i−1 + N (0, 1) and x 1 = 0 as in [19].…”

“…since it is possible to find counterexamples where DTW does not satisfy it [14,19] (thus, CDTW is not a metric either). The correction of algorithms such as AESA (Figure 3) depends on having a metric distance and then it has to satisfy this property.…”

“…In [15], in 15 millions of triplets there were no cases where the triangular inequality was violated. In [19], the authors made experiments with synthetic time series (sequences of one dimension) of three types: white-noise, random-walk and cylinder-bell-funnel. The most problematic was random-walk where 20% of triplets violated the triangular inequality.…”

“…We performed an experiment similar to the one in [19], with random-walk sequences, but varying the number of dimensions (in [19] this experiment was done for just one dimension). We generated 1000 sequences for each number of dimensions, then we checked 1000000000 triplets.…”

High-performance DTW-based signals comparison for the brain electroencephalograms analysis

“…There are a number of ways to speed up the Dynamic Time Warping procedure, however, they either do not guarantee the finding of the optimal solution [6,[11][12][13][14], or the performance improvement is provided only in cases, when comparing close or sparse signals [15,16]. But such situations are rare in the analysis of electroencephalograms.…”