Standard Dynamic Time Warping Research Articles

Large-Area Land-Cover Changes Monitoring With Time-Series Remote Sensing Images Using Transferable Deep Models

Dense time-series remote sensing images have transformed the traditional bitemporal land-cover change detection to continuous monitoring. Previous work mostly employs linear fitting, prediction, or decomposition methods, and the detection accuracy is not high. The latest progress of deep learning (DL) shows its advantages in time-series change monitoring. However, DL models are computationally expensive and require lots of labeled samples, resulting in often employed prediction-threshold-based unsupervised change detection method. However, the determination of a reasonable threshold has always been a big problem. Therefore, we proposed the similarity-measurement-based deep transfer learning for time-series adaptive change detection (SDTL-TSACD) model. First, a standard dynamic time warping (SDTW) distance was proposed and used to cluster large-scale time series into multiple subcategories with high time-series similarity. Second, a time convolutional network (TCN) was used for nonlinear time-series fitting and prediction, and an early stop strategy was used to prevent overfitting. Then, the trained TCN model would be transferred and performed pixel-by-pixel time-series prediction within the same category, and the SDTW was also used to evaluate the prediction accuracy. Finally, the Otsu adaptive threshold was used to detect change points, and the spatial neighbor relationship was used to eliminate the pseudo-change points. Change detection results using 132 benchmark datasets showed that the SDTL-TSACD performed well in both accuracy and efficiency. In addition, the MOD13Q1-EVI images from 2001 to 2020 were used to study the land-cover change of the Loess Plateau, and the SDTL-TSACD also showed a good ability to solve practical problems.

Bedding Angle Identification from BIF Marker Shales via Modified Dynamic Time Warping

When modelling a stratified orebody, accurately representing the dip and dip direction is important for accurate resource estimation. In the banded iron formation-hosted iron ore deposits in the Pilbara region of Western Australia, these quantities can be determined using marker shales from nearby holes. These marker shales are identified using natural gamma logs and are generally manually processed. Therefore, an automated method for matching natural gamma logs between holes is desirable. Dynamic time warping (DTW) can match two signals where there is stretching or distortion. This study presents a modified, iterative version of DTW for matching downhole natural gamma logs. This new method accounts for large differences in length of the two signals by comparing different segments of the signals. Several metrics were then used to rank potential matches between signals. The proposed iterative DTW method had an accuracy of 90%, compared with 67% for the standard DTW. Once matched, signals can be used to estimate the bedding angle at each hole. A point in one hole was matched to as many nearby holes as possible, creating a set of points located on the same surface. A localized plane was then fitted to these points. These bedding angles were used to reconstruct a surface representing the bedding. While the signal matching was accurate, the sparsity of correctly matched holes limits the accuracy of the calculated surface. Even with sparse gradient fields, a reasonable approximation of the bedding could be achieved.

Fast Constrained Dynamic Time Warping for Similarity Measure of Time Series Data

In this paper, we propose an efficient algorithm for reducing the computational complexity of dynamic time warping (DTW) for obtaining similarity measures between time series. The DTW technique exhibits superior classification accuracy compared to other algorithms but has a limitation of high computational complexity. To reduce the computational complexity of standard DTW, constrained DTW and fast DTW techniques have been proposed. The constrained DTW technique reduces the computational complexity of standard DTW by only considering limited alignments and prevent excessive alignments between two time series, which can reduce the overall classification accuracy. However, since the searching window for limited alignments is fixed, the computational complexity is still high when the length of time series is long. In contrast, fast DTW has a lower classification accuracy than the constrained DTW technique. However, fast DTW estimates the optimal alignment while considering only the alignments within an adaptive window; as two time series increase in length, the fast DTW technique more strongly reduces the computational complexity. Therefore, we propose a fast constrained DTW approach that applies the optimal alignment estimation of fast DTW within the limited alignments of constrained DTW. As the proposed fast constrained DTW operates within a fixed window area of the constrained DTW, which prevents excessive alignments, it has a classification accuracy similar to that of the constrained DTW. Also, in the fast constrained DTW, when the length of the time series is long, a low computational complexity is maintained by the influence of the adaptive window of the fast DTW. Experimental results on 19 UCR time series datasets show that the proposed fast constrained DTW method achieves computational complexity reductions of approximately 52.2% and 22.3% compared to the existing fast DTW and constrained DTW, while maintaining almost the same classification accuracy as the constrained DTW.

Modified Dynamic Time Warping for Hierarchical Clustering

Time series clustering is the process of grouping sequential correspondences in similar clusters. The key feature behind clustering time series data lies on the similarity/distance function used to identify the sequential matches. Dynamic Time Warping (DTW) is one of the common distance measures that have demonstrated competitive results compared to other functions. DTW aims to find the shortest path in the process of identifying sequential matches. DTW relies on dynamic programming to obtain the shortest path where the smaller distance is being computed. However, in the case of equivalent distances, DTW is selecting the path randomly. Hence, the selection could be misguided in such randomization process, which significantly affects the matching quality. This is due to randomization may lead to the longer path which drifts from obtaining the optimum path. This paper proposes a modified DTW that aims to enhance the dynamic selection of the shortest path when handling equivalent distances. Experiments were conducted using twenty UCR benchmark datasets. Also, the proposed modified DTW result has been compared with the state of the art competitive distance measures which is based on precision, recall and f-measure including the original DTW, Minkowski distance measure and Euclidean distance measure. The results showed that the proposed modified DTW reveal superior results in compared to the standard DTW, either using Minkowski or Euclidean. This can demonstrate the effectiveness of the proposed modification in which optimizing the shortest path has enhanced the performance of clustering. The proposed modified DTW can be used for having good clustering method for any time series data.

Evaluation of simulation models to mimic the distortions introduced into squiggles by nanopore sequencers and segmentation algorithms.

Nucleotides ratcheted through the biomolecular pores of nanopore sequencers generate raw picoamperage currents, which are segmented into step-current level signals representing the nucleotide sequence. These ‘squiggles’ are a noisy, distorted representation of the underlying true stepped current levels due to experimental and algorithmic factors. We were interested in developing a simulation model to support a white-box approach to identify common distortions, rather than relying on commonly used black box neural network techniques for basecalling nanopore signals. Dynamic time warped-space averaging (DTWA) techniques can generate a consensus from multiple noisy signals without introducing key feature distortions that occur with standard averaging. As a preprocessing tool, DTWA could provide cleaner and more accurate current signals for direct RNA or DNA analysis tools. However, DTWA approaches need modification to take advantage of the a-priori knowledge regarding a common, underlying gold-standard RNA / DNA sequence. Using experimental data, we derive a simulation model to provide known squiggle distortion signals to assist in validating the performance of analysis tools such as DTWA. Simulation models were evaluated by comparing mocked and experimental squiggle characteristics from one Enolase mRNA squiggle group produced by an Oxford MinION nanopore sequencer, and cross-validated using other Enolase, Sequin R1_71_1 and Sequin R2_55_3 mRNA studies. New techniques identified high inserted but low deleted base rates, generating consistent x1.7 squiggle event to base called ratios. Similar probability density and cumulative distribution functions, PDF and CDF, were found across all studies. Experimental PDFs were not the normal distributions expected if squiggle distortion arose from segmentation algorithm artefacts, or through individual nucleotides randomly interacting with individual nanopores. Matching experimental and mocked CDFs required the assumption that there are unique features associated with individual raw-current data streams. Z-normalized signal-to-noise ratios suggest intrinsic sensor limitations being responsible for half the gold standard and noisy squiggle DTW differences.

A large margin time series nearest neighbour classification under locally weighted time warps

Accuracy of the k-nearest neighbour ( $$k\hbox {NN}$$ ) classifier depends strongly on the ability of the used distance to induce k-nearest neighbours of the same class while keeping distant samples of different classes. For time series classification, $$k\hbox {NN}$$ based on dynamic time warping (dtw) measure remains among the most popular and competitive approaches. However, by assuming time series uniformly distributed, standard dtw may show some limitations to classify complex time series. In this paper, we show how to enhance the potential of $$k\hbox {NN}$$ under time warp measure by learning a locally weighted dynamic time warping. For that, first discriminative features are learned from the neighbourhoods, then used to weight time series elements to bring closer the k-nearest neighbours of the same class and move away the k-nearest neighbours of different classes. To evaluate the proposed method, a deep analysis and experimentation are conducted on 87 public datasets from different application domains, varying sizes and difficulty levels. The results obtained show significant improvement in the proposed weighted dtw for time series $$k\hbox {NN}$$ classification.

Modified Dynamic Time Warping Based on Direction Similarity for Fast Gesture Recognition

We propose a modified dynamic time warping (DTW) algorithm that compares gesture-position sequences based on the direction of the gestural movement. Standard DTW does not specifically consider the two-dimensional characteristic of the user’s movement. Therefore, in gesture recognition, the sequence comparison by standard DTW needs to be improved. The proposed gesture-recognition system compares the sequences of the input gesture’s position with gesture positions saved in the database and selects the most similar gesture by filtering out unrelated gestures. The suggested algorithm uses the cosine similarity of the movement direction at each moment to calculate the difference and reflects the characteristics of the gesture movement by using the ratio of the Euclidean distance and the proportional distance to the calculated difference. Selective spline interpolation assists in solving the issue of recognition-decline at instances of gestures. Through experiments with public databases (MSRC-12 and G3D), the suggested algorithm revealed an improved performance on both databases compared to other methods.

A new approach for image stitching technique using Dynamic Time Warping (DTW) algorithm towards scoliosis X-ray diagnosis

Consider a set of images of a single object, or scenery, taken from different viewpoints and time. Panorama image creation is the process of stitching such images into a single coordinate system to generate a wider viewing panoramic image. Image stitching consists of two processes which are image registration and image blending. In image registration, parts of two overlapping or consecutive images are considered to find an appropriate merging position and transformation to combine the images. In image blending, the intensities of pixels along the stitching line are modified so that they flow naturally without any noticeable break. In this paper, we propose a novel method that utilizes the Dynamic Time Warping (DTW) algorithm to match pairs of images for image stitching. We also perform a dimension reduction scheme that significantly reduces the computational complexity of the standard DTW without affecting its performance. The effectiveness of the proposed method is demonstrated in stitching 50 pairs of medical X-ray images and its performance is compared to those of normalized cross correlation (NCC), Minimum Average Correlation Energy (MACE) filters, sum-of-square-differences (SSD) and sum-of-absolute-differences (SAD). For the database used, the dimensionally reduced DTW outperforms the NCC, MACE, SSD and SAD methods in accuracy and average execution time. The method also outperforms two widely used stitching programs available on the internet called Hugin and Autostitch.

Method for investigating intradriver heterogeneity using vehicle trajectory data: A Dynamic Time Warping approach

After first extending Newell’s car-following model to incorporate time-dependent parameters, this paper describes the Dynamic Time Warping (DTW) algorithm and its application for calibrating this microscopic simulation model by synthesizing driver trajectory data. Using the unique capabilities of the DTW algorithm, this paper attempts to examine driver heterogeneity in car-following behavior, as well as the driver’s heterogeneous situation-dependent behavior within a trip, based on the calibrated time-varying response times and critical jam spacing. The standard DTW algorithm is enhanced to address a number of estimation challenges in this specific application, and a numerical experiment is presented with vehicle trajectory data extracted from the Next Generation Simulation (NGSIM) project for demonstration purposes. The DTW algorithm is shown to be a reasonable method for processing large vehicle trajectory datasets, but requires significant data reduction to produce reasonable results when working with high resolution vehicle trajectory data. Additionally, singularities present an interesting match solution set to potentially help identify changing driver behavior; however, they must be avoided to reduce analysis complexity.

Probability-based Dynamic Time Warping and Bag-of-Visual-and-Depth-Words for Human Gesture Recognition in RGB-D

We present a methodology to address the problem of human gesture segmentation and recognition in video and depth image sequences. A Bag-of-Visual-and-Depth-Words (BoVDW) model is introduced as an extension of the Bag-of-Visual-Words (BoVW) model. State-of-the-art RGB and depth features, including a newly proposed depth descriptor, are analysed and combined in a late fusion form. The method is integrated in a Human Gesture Recognition pipeline, together with a novel probability-based Dynamic Time Warping (PDTW) algorithm which is used to perform prior segmentation of idle gestures. The proposed DTW variant uses samples of the same gesture category to build a Gaussian Mixture Model driven probabilistic model of that gesture class. Results of the whole Human Gesture Recognition pipeline in a public data set show better performance in comparison to both standard BoVW model and DTW approach.

A DTW-based probability model for speaker feature analysis and data mining

This paper is a contribution to probabilistic data mining and pattern recognition. A DTW-based statistical model is proposed to explore the subspace structures of speaker feature space for feature evaluation, dimension reduction and inter-class information discovery in pattern space.We demonstrate its usefulness in isolated digits speaker identification, and the performance of the statistical model is compared with standard DTW recognition rate in the experiment. We argue that the probability model can be taken as data mining tools.

Auditory front end in DTW word recognition under noisy, reverberant, and multispeaker conditions.

In this report three front ends, a fixed Q cochlear filter (FQF), an adaptive Q cochlear filter (AQF), and a Bark DFT (DFT), are compared for use as the front end of a DTW system. The FQF is a conventional cascade/parallel-type cochlear filter that stimulates the asymmetrical filtering characteristics of a basilar membrane system. The AQF is a nonlinear cochlear filter that simulates three level-dependent characteristics of a basilar membrane system [T. Hirahara etal., Proc. ICASSP, 496–499 (1989)]. The DFT front end generates 64-channel Bark scale coefficients based on a 512-point DFT magnitude spectrum. These three front ends have 64 channels covering the frequency range from 1.5 to 19.5 Bark. Recognition performance for clean speech, degraded speech by adding noise and/or reverberation, and under multispeaker conditions, are compared. Four signal-to-noise ratios, S/N=∞, 40, 20, and 10 dB, are set by adding different levels of pink noise to speech data. As for reverberant speech, the impulse responses obtained in the ATR reverberation room, RT=0.2 and 1.1 s, are convolved with speech data. Speech data used in the experiments are 216 phoneme-balanced Japanese words uttered by two male and two female speakers. A standard dynamic time warping (DTW) system is used as a back end. The experiments results are as follows: (1) For noisy speech, AQF performance is equal to that of FQF but more robust than that of DFT. (2) For reverberant speech, AQF is affected more than DFT but the performance is better than that of FQF. (3) For speaker variation, AQF gives better performance than do FQF or DFT. While the advantage of the AQF front end is small with an HMM back end [T. Hirahara etal., Proc. ICSLP, 381–384 (1990)], these results show that the AQF is an excellent front end for a DTW recognition system.

Speaker-Independent English Consonant and Japanese Word Recognition by a Stochastic Dynamic Time Warping Method

In this paper, a stochastic dynamic time warping method for speaker-independent recognition is proposed and some considerations are described on speaker-independent consonant recognition and word recognition on a large vocabulary size. In this method, conditional probabilities were used instead of local distances in a standard dynamic time warping method, and transition probabilities instead of path costs. This is related to both the standard DTW method and the hidden Markov model. In word recognition, the whole word templates are constructed by the concatenation of syllable templates, which are taken from spoken words. And, we got the reference patterns from 216 words uttered by 30 male speakers and recognized the other 200 words uttered by the other 10 speakers. The standard dynamic time warping method for speaker-independent recognition on 200 words gave the average word recognition rate of 89.3%. The stochastic dynamic time warping method we proposed here improved the recognition rate to 92.9%.

A weighted cepstral distance measure for speech recognition

A weighted cepstral distance measure is proposed and is tested in a speaker-independent isolated word recognition system using standard DTW (dynamic time warping) techniques. The measure is a statistically weighted distance measure with weights equal to the inverse variance of the cepstral coefficients. The experimental results show that the weighted cepstral distance measure works substantially better than both the Euclidean cepstral distance and the log likelihood ratio distance measures across two different databases. The recognition error rate obtained using the weighted cepstral distance measure was about 1 percent for digit recognition. This result was less than one-fourth of that obtained using the simple Euclidean cepstral distance measure and about one-third of the results using the log likelihood ratio distance measure. The most significant performance characteristic of the weighted cepstral distance was that it tended to equalize the performance of the recognizer across different talkers.

Comparative study of several distortion measures for speech recognition

Local spectral distortion measures are commonly used to measure the similarity (or spectral distance) between two given short-time spectra. In this study we compared several different spectral distortion measures including the Itakura-Saito distortion measure, the log likelihood ratio (LLR) distortion measure, the likelihood ratio (LR) distortion measure, the cepstral (CEP) distortion measure, and two proposed perceptually based distortion measures, the weighted likelihood ratio (WLR) and the weighted slope metric (WSM) distortion measures, in terms of their effects on the performance of standard dynamic time warping (DTW) based, isolated word, speech recognizer. Two modifications of the basic forms of each measure were also investigated, namely a Bark-scale frequency warping and the incorporation of suprasegemental energy information. All distortion measures and their modifications were tested on an alpha-digit vocabulary, 4-talker, telephone recording data base. The results can be summarized as: (1) All LPC-based distortion measures performed reasonably well. The log likelihood ratio and weighted slope metric distortion measures gave the highest recognition accuracy, while the Itakura-Saito distortion measure gave the lowest score; (2) Whereas the addition of suprasegmental energy information helped the recognition performance, the use of gain and absolute loudness degraded the performance; (3) Bark-scale frequency warping did not, at least for the highly bandlimited telephone data base we tested, performed as well as its unwarped counterpart; (4) The weighted likelihood ratio distortion measure did not perform as well as its unweighted counterpart.

A vector-quantization-based preprocessor for speaker-independent isolated word recognition

In this paper, we propose a speaker-independent isolated ward recognition system whose performance is comparable to that of a conventional isolated word recognizer, but whose computation is greatly reduced. The structure of the proposed recognizer consists of a word-based vector quantization (VQ) preprocessor, followed by a conventional DTW postprocessor. The purpose of the preprocessor is essentially to eliminate from further consideration all words in the vocabulary which are unlikely recognition candidates. In some cases, the preprocessor will be able to eliminate all word candidates except one; for such cases, there is no further processing required for word recognition. In all other cases (i.e., when more than one word candidate is passed on), a dynamic time warping (DTW) processor is used to re-solve finer acoustical distinctions among the remaining word candidates. The performance of this type of recognizer (i.e., using a word-based preprocessor and a standard DTW comparison to make finer distinctions) is affected by a number of factors involved with the details of exactly how the system is implemented-e.g., the distortion measure used in the preprocessor and in the DTW comparison, the size of the VQ codebook for each vocabulary word, the decision thresholds of the preprocessor, etc. Several of these factors were studied experimentally using testing databases consisting of isolated digits and words from a vocabulary of 129 airline terms. The results show that the proposed preprocessor has the capability of reducing computation for recognition by up to an order of magnitude, while maintaining the same performance as that obtained using a DTW comparison without the pre-processor. A somewhat smaller reduction in memory over the straight DTW implementation is also obtained in the proposed approach.

Speaker‐independent recognition of isolated digits using a weighted cepstral distance

The cepstral distance has been one of the most efficient spectral distance measures in speech and speaker recognition [S. Furui, IEEE Trans. Acoust. Speech Signal Process. ASSP‐29, 254–272 (1981)]. A new weighted cepstral distance measure using LPC derived cepstrum coefficient variability was tested in a speaker‐independent English digit recognition system using standard DTW alignment techniques [L. R. Rubiner, S. E. Levinson, A. E. Rosenberg, and J. G. Wilpon, IEEE Trans. Acoust. Speech Signal Process. ASSP‐27, 134–141 (1979)]. The results show a recognition accuracy of > 99% for the digits [K. L. Shipley. A. E. Rosenberg, and D. E. Bock, J. Acoust. Soc. Am. Suppl. 1 72, S80 (1982)]. Recognition results using the same data base and the log likelihood LPC distance are about 97.4%. Hence there is a large improvement in performance with the new weighted cepstral distance.

An adaptive, ordered, graph search technique for dynamic time warping for isolated word recognition

The technique of dynamic time warping (DTW) is relied on heavily in isolated word recognition systems. The advantage of using DTW is that reliable time alignment between reference and test patterns is obtained. The disadvantage of using DTW is the heavy computational burden required to find the optimal time alignment path. Several alternative procedures have been proposed for reducing the computation of DTW algorithms. However, these alternative methods generally suffer from a loss of optimality or precision in defining points along the alignment path. In this paper we propose another alternative procedure for implementing a DTW algorithm. The procedure is based on the well-known class of techniques for a directed search through a grid to find the shortest path. An adaptive version of a directed search procedure is defined and shown to be capable of obtaining the exact DTW solution with reduced computation of distances but with increased overhead. It is shown that for machines where the time for distance computation is significantly larger than the time for combinatorics and overhead, a potential gain in speed of up to 3 : 1 can be realized with the directed search algorithm. Formal comparison of the directed search algorithm with a standard DTW method, in an isolated word recognition test, showed essentially no loss in recognition accuracy when the parameters of the directed search were selected to realize the 3:1 reduction in distance computation.