Dynamic Time Warping with Boundaries Constraint Relaxation

2004

The dynamic time warping (DTW) algorithm is able to find the optimal alignment between two time series. It is often used to determine time series similarity, classification, and to find corresponding regions between two time series. DTW has a quadratic time and space complexity that limits its use to only small time series data sets. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a multilevel approach that recursively projects a solution from a coarse resolution and refines the projected solution.

arXiv (Cornell University), 2021

Dynamic Time Warping (DTW), and its constrained (CDTW) and weighted (WDTW) variants, are time series distances with a wide range of applications. They minimize the cost of non-linear alignments between series. CDTW and WDTW have been introduced because DTW is too permissive in its alignments. However, CDTW uses a crude step function, allowing unconstrained flexibility within the window, and none beyond it. WDTW's multiplicative weight is relative to the distances between aligned points along a warped path, rather than being a direct function of the amount of warping that is introduced. In this paper, we introduce Amerced Dynamic Time Warping (ADTW), a new, intuitive, DTW variant that penalizes the act of warping by a fixed additive cost. Like CDTW and WDTW, ADTW constrains the amount of warping. However, it avoids both abrupt discontinuities in the amount of warping allowed and the limitations of a multiplicative penalty. We formally introduce ADTW, prove some of its properties, and discuss its parameterization. We show on a simple example how it can be parameterized to achieve an intuitive outcome, and demonstrate its usefulness on a standard time series classification benchmark. We provide a demonstration application in C++ [1].

Proceedings of the 2001 SIAM International Conference on Data Mining, 2001

2012

We present a new space-efficient approach, (SparseDTW), to compute the Dynamic Time Warping (DTW) distance between two time series that always yields the optimal result. This is in contrast to other known approaches which typically sacrifice optimality to attain space efficiency. The main idea behind our approach is to dynamically exploit the existence of similarity and/or correlation between the time series. The more the similarity between the time series the less space required to compute the DTW between them. To the best of our knowledge, all other techniques to speedup DTW, impose apriori constraints and do not exploit similarity characteristics that may be present in the data. We conduct experiments and demonstrate that SparseDTW outperforms previous approaches.

2019

In time series classification the most commonly used approach is k Nearest Neighbor classification, where k = 1, coupled with Dynamic Time Warping (DTW) similarity checking. A challenge is that the DTW process is computationally expensive. This paper presents a new approach for speeding-up the DTW process, Sub-Sequence-Based DTW, which offers the additional benefit of improving accuracy. This paper also presents an analysis of the impact of the Sub-Sequence-Based method in terms of efficiency and effectiveness in comparison with standard DTW and the Sakoe-Chiba Band technique.

2019

k Nearest Neighbour classification techniques, where \(k=1\), coupled with Dynamic Time Warping (DTW) are the most effective and most frequently used approaches for time series classification. However, because of the quadratic complexity of DTW, research efforts have been directed at methods and techniques to make the DTW process more efficient. This paper presents a new approach to efficient DTW, the Sub-Sequence-Based DTW approach. Two variations are considered, fixed length sub-sequence segmentation and fixed number sub-sequence segmentation. The reported experiments indicate that the technique improvs efficiency, compared to standard DTW, without adversely affecting effectiveness.

Third Workshop on Mining Temporal …, 2004

The Dynamic Time Warping (DTW) distance measure is a technique that has long been known in speech recognition community. It allows a non-linear mapping of one signal to another by minimizing the distance between the two. A decade ago, DTW was introduced into Data Mining community as a utility for various tasks for time series problems including classification, clustering, and anomaly detection. The technique has flourished, particularly in the last three years, and has been applied to a variety of problems in various disciplines.

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1987

Recently, some new and promising methods have been proposed to reduce the number of Dynamic Time Warping (DTW) computations in Isolated Word Recognition. For these methods to be properly applicable, the verification of the Triangle Inequality (TI) by the DTW-based Dissimilarity Measure utilized seems to be an important prerequisite.

International Journal of Data Mining, Modelling and Management, 2016

Dynamic time warping (DTW) consists at finding the best alignment between two time series. It was introduced into pattern recognition and data mining, including many tasks for time series such as clustering and classification. DTW has a quadratic time complexity. Several methods have been proposed to speed up its computation. In this paper, we propose a new variant of DTW called dynamic warping window (DWW). It gives a good approximation of DTW in a competitive CPU time. The accuracy of DWW was evaluated to prove its efficiency. Then the KNN classification was applied for several distance measures (dynamic time warping, derivative dynamic time warping, fast dynamic time warping and DWW). Results show that DWW gives a good compromise between computational speed and accuracy of KNN classification.

Dynamic Time Warping (DTW) is an established method for finding a global alignment between two feature sequences. However, having a computational complexity that is quadratic in the input length, memory consumption becomes a major issue when dealing with long feature sequences. Various strategies have been proposed to reduce the memory requirements of DTW. For example, online alignment approaches often have a constant memory consumption by applying forward path estimation strategies. However, this comes at the cost of robustness. Efficient offline DTW based on multiscale strategies constitutes another approach. While methods built on this principle are usually robust, their memory requirements are still dependent on the input length. By combining ideas from online alignment approaches and offline multiscale strategies, we introduce a novel alignment procedure that allows for specifying a constant upper bound on its memory requirements. This is an important aspect when working on devices with limited computational resources. Experiments show that when restricting the memory consumption of our proposed procedure to eight megabytes, it basically yields the same alignments as the standard DTW procedure.