Speeding Up All-Pairwise Dynamic Time Warping Matrix Calculation

Abstract

Dynamic Time Warping (DTW) is certainly the most relevant distance for time series analysis. However, its quadratic time complexity may hamper its use, mainly in the analysis of large time series data. All the recent advances in speeding up the exact DTW calculation are confined to similarity search. However, there is a significant number of important algorithms including clustering and classification that require the pairwise distance matrix for all time series objects. The only techniques available to deal with this issue are constraint bands and DTW approximations. In this paper, we propose the first exact approach for speeding up the all-pairwise DTW matrix calculation. Our method is exact and may be applied in conjunction with constraint bands. We demonstrate that our algorithm reduces the runtime in approximately 50% on average and up to one order of magnitude in some datasets.

An accurate and rapid continuous wavelet dynamic time warping algorithm for unbalanced global mapping in nanopore sequencing

“…DTW is the original method that finds the optimal mapping between the two signal sequences by dynamic programming, whereas FastDTW is the state-of-the-art multi-level DTW method which approximates DTW in linear time-and space-complexity. Other representative DTW algorithms, such as PrunedDTW [12], were designed to measure the similarity between two sequences. They implicitly assume that the lengths of the two sequences to be mapped are comparable and thus cannot handle the unbalanced sequences in the two nanopore datasets.…”

“…Though DTW has been well-established, the original DTW has O(L 1 L 2 ) time complexity and needs a matrix D with L 1 × L 2 dimension, which is too inefficient and memory-costly for long sequences, such as the ones from nanopore sequencing. To apply DTW in challenging applications, various versions of improved DTW have been proposed, such as FastDTW [10], PrunedDTW [12], SparseDTW [11], and MultiscaleDTW [16,17]. CWT representation is the initial step that runs a continuous wavelet transform on each input signal sequence to obtain an informative representation, followed by peak and nadir picking to produce the low-resolution signals with reduced lengths.…”

“…To accelerate the analysis of long sequences, a variety of improved DTW have been proposed, which can be roughly categorized into three classes: constrained DTW, coarsening DTW, and multi-level DTW. Constrained DTW (e.g., SparseDTW [11] and PrunedDTW [12]), whose accuracy lies on the strategy of bounding, casts an arbitrary or a predefined boundary to reduce the search space. Coarsening DTW (e.g., PDTW [13], IDDTW [14] and COW [15]) speeds up DTW by operating on a reduced representation of the signals, which is often produced by down-sampling or equal averaging, and then projecting the low-resolution warping path to the full resolution.…”

Prediction of Intention during Interaction with iCub with Probabilistic Movement Primitives

“…The calculation speed of DTW is improved using different methods, such as FastDTW, Lucky Time Warping, or FTW. An explanation and comparison of these methods are presented in Silva and Batista (2016), where they add their own computation speed improvement by using a method called Pruned Warping Paths. This method allows the deletion of unlikely data.…”

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.…”