Dynamic Time Warping Calculation Research Articles

An end-to-end machine learning approach with explanation for time series with varying lengths

AbstractAn accurate prediction of complex product quality parameters from process time series by an end-to-end learning approach remains a significant challenge in machine learning. A special difficulty is the application of industrial batch process data because many batch processes generate variable length time series. In the industrial application of such methods, explainability is often desired. In this study, a 1D convolutional neural network (CNN) algorithm with a masking layer is proposed to solve the problem for time series of variable length. In addition, a novel combination of 1D CNN and class activation mapping (CAM) technique is part of this study to better understand the model results and highlight some regions of interest in the time series. As a comparative state-of-the-art unsupervised machine learning method, the One-Nearest Neighbours (1NN) algorithm combined with dynamic time warping (DTW) was used. Both methods are investigated as end-to-end learning methods with balanced and unbalanced class distributions and with scaled and unscaled input data, respectively. The FastDTW and DTAIDistance algorithms were investigated for the DTW calculation. The data set is made up of sensor signals that was collected during the production of plastic parts. The objective was to predict a quality parameter of plastic parts during production. For this research, the quality parameter will be a difficult or only destructively measurable parameter and both methods will be investigated for their applicability to this prediction task. The application of the proposed approach to an industrial facility for producing plastic products shows a prediction accuracy of 83.7%. It can improve the reverence method by approximately 1.4%. In addition to the slight increase in accuracy, the CNN training time was significantly reduced compared to the DTW calculation.

Exact Dynamic Time Warping calculation for weak sparse time series

The Dynamic Time Warping (DTW) technique is widely used in time series data mining. However, it should be pointed out that the calculation complexity of DTW is very high. In this paper, we propose an accurate and fast DTW calculation algorithm on weak sparse time series (WSTS). The algorithm takes the advantage of the weak sparse property, and it shows a remarkable time saving in DTW calculation. In addition, it should be emphasized that this algorithm for DTW calculation is an accurate one, which is one of the main contributions of this paper. The mathematical proof is also given to prove the accuracy of this algorithm. Several examples with different practical prospects are given to show the effectiveness of the proposed accurate and fast DTW calculation algorithm.

Identification of Urban Functional Regions in Chengdu Based on Taxi Trajectory Time Series Data

Overall scientific planning of urbanization layout is an important component of the new period of land spatial planning policies. Defining the main functions of different spaces and dividing urban functional areas are of great significance for optimizing the land development pattern. This article identifies and analyses urban functional areas from the perspective of data mining. The results of this method are consistent with the actual situation. In this paper, representative taxi trajectory data are selected as the research basis of urban functional areas. First, based on trajectory data from Didi Chuxing within the high-speed road surrounding Chengdu, we generated trajectory time sequence data and used the dynamic time warping (DTW) algorithm to generate a time series similarity matrix. Second, we utilized the K-medoid clustering algorithm to generate preliminary results of land clustering and selected the results with high classification accuracy as the training samples. Then, the k-nearest neighbour (KNN) classification algorithm based on DTW was performed to classify and identify the urban functional areas. Finally, with the help of point-of-interest (POI) auxiliary analysis, the final functional layout in Chengdu was obtained. The results show that the spatial structure of Chengdu is complex and that the urban functions are interlaced, but there are still rules that are followed. Moreover, traffic volume and inflow data can better reflect the travel rules of residents than simple taxi on–off data. The original DTW calculation method has high temporal complexity, which can be improved by normalization and the reduction of time series dimensionality. The semi-supervised learning classification method is also applicable to trajectory data, and it is best to select training samples from unsupervised learning. This method can provide a theoretical basis for urban land planning and has auxiliary and guiding value for urbanization layout in the context of land spatial planning policies in the new era.

Speeding up similarity search under dynamic time warping by pruning unpromising alignments

Similarity search is the core procedure for several time series mining tasks. While different distance measures can be used for this purpose, there is clear evidence that the Dynamic Time Warping (DTW) is the most suitable distance function for a wide range of application domains. Despite its quadratic complexity, research efforts have proposed a significant number of pruning methods to speed up the similarity search under DTW. However, the search may still take a considerable amount of time depending on the parameters of the search, such as the length of the query and the warping window width. The main reason is that the current techniques for speeding up the similarity search focus on avoiding the costly distance calculation between as many pairs of time series as possible. Nevertheless, the few pairs of subsequences that were not discarded by the pruning techniques can represent a significant part of the entire search time. In this work, we adapt a recently proposed algorithm to improve the internal efficiency of the DTW calculation. Our method can speed up the UCR suite, considered the current fastest tool for similarity search under DTW. More important, the longer the time needed for the search, the higher the speedup ratio achieved by our method. We demonstrate that our method performs similarly to UCR suite for small queries and narrow warping constraints. However, it performs up to five times faster for long queries and large warping windows.

Asymptotic Dynamic Time Warping calculation with utilizing value repetition

Dynamic Time Warping (DTW) is a popular method for measuring the similarity of time series. It is widely used in various domains. A major drawback of DTW is that it has a high computational complexity. To address this problem, pruning techniques to calculate the exact DTW distance, as well as DTW approximation methods, have become important approaches. In this paper, we introduce Blocked Dynamic Time Warping (BDTW), a new similarity measure which works on run-length encoded time series representation. BDTW utilizes any repetitive values (zero and nonzero) in time series to reduce DTW computation time. BDTW closely approximates DTW distance, and it is significantly faster than traditional DTW for time series with high levels of value repetition. Moreover, BDTW can be combined with time series representation methods which provide constant segments, to serve as a close approximation method even for the time series without value repetition. Constrained BDTW, BDTW upper bound and BDTW lower bound are discussed as variations of BDTW. BDTW upper bound and BDTW lower bound are presented as a new DTW upper bound and lower bound which can be efficiently applied on time series with high levels of value repetition for pruning unhopeful alignments and matches in the exact DTW calculation. We show the effectiveness of BDTW and its variations on different applications using the following datasets: Almanac of Minutely Power, Refit Smart Homes, as well as the 85 datasets from the University of California, Riverside time series classification archive (UCR archive).

Similarity search for numerous patterns over multiple time series streams under dynamic time warping which supports data normalization

A huge challenge in nowadays' data mining is similarity search in streaming time series under Dynamic Time Warping (DTW). In the similarity search, data normalization is a must to obtain accurate results. However, data normalization on the fly and the DTW calculation cost a great deal of computational time and memory space. In the paper, we present two methods, SUCR-DTW and ESUCR-DTW, which conduct similarity search for numerous prespecified patterns over multiple time-series streams under DTW supporting data normalization. These two methods utilize a combination of techniques to mitigate the aforementioned costs. The efficient methods inherit the cascading lower bounds introduced in UCR-DTW, a state-of-the-art method of similarity search in the static time series, to admissibly prune off unpromising subsequences. To be adaptive in the streaming setting, SUCR-DTW performs incremental updates on the envelopes of new-coming time-series subsequences and incremental data normalization on time-series data. However, like UCR-DTW, SUCR-DTW retrieves only similar subsequences that have the same length as the patterns. ESUCR-DTW, an extension of SUCR-DTW, can find similar subsequences whose lengths are different from those of the patterns. Furthermore, our proposed methods exploit multi-threading to have a fast response to high-speed time-series streams. The experimental results show that SUCR-DTW obtains the same precision as UCR-DTW and has lower wall clock time. Besides, the experimental results of SUCR-DTW and ESUCR-DTW reveal that the extended method has higher accuracy in spite of longer wall clock time. Also, the paper evaluates the influence of incremental z-score normalization and incremental min---max normalization on the obtained results.

Early abandon to accelerating exactly warping matching of time series

Dynamic Time Warping(DTW)is one of the important distance measures in similarity searching of time series;however,the exact calculation has become a bottleneck.An approach named EA_DTW was proposed.The method checked if value of the cell in cumulative distance matrix exceeded the threshold and if so,it would terminate the calculation of other related cells.The theoretical analysis on the process of EA_DTW was made.The empirical experimental results show that EA_DTW outperforms the dynamic DTW calculation in terms of calculation time,and is much better when the threshold is below the real DTW distance.