Dynamic Time Warping Method Research Articles

On analyzing GNSS displacement field variability of Taiwan: Hierarchical Agglomerative Clustering based on Dynamic Time Warping technique

We investigate the feasibility of using the Dynamic Time Warping (DTW) technique to cluster continuous GNSS displacements in Taiwan. Using the DTW distance as the measure for waveform similarity, we combine the DTW method with the Hierarchical Agglomerative Clustering (HAC) algorithm. This is in contrast to the conventional clustering approach that uses the Euclidean distance, considering the average long-term crustal motion, but inherently neglects full-waveform temporal variations. Here we apply the DTW-based HAC algorithm adopting DTW distance as the waveform similarity measure on 11 years worth of 3-D displacement data from 115 continuous GNSS network stations in Taiwan. We demonstrate the efficacy of the DTW-based HAC method in distinguishing the GNSS spatiotemporal variabilities that are consistent with the known, complex tectonic behavior of the region. An open-source Python package has been developed and made available to perform the HAC analysis.

Green Bonds as an Instrument for Financing Ecological Investments in the V4 Countries

The aim of this paper is to characterise the green bond market in the Visegrad Group of countries (V4) and to identify the determinants and benefits of issuing green bonds. The specific objective is a spatial–temporal analysis of the green bond yield in V4 countries. The following research methods were used in the paper: a source literature analysis and report analysis, statistical data analysis (from international financial markets), and the Dynamic Time Warping method (DTW). DTW comprises a class of algorithms that are used to compare both equal and unequal time series. The DTW method allows the smallest distance between two time series of different lengths to be found while allowing for the transformation over time of both series. As the method is highly efficient, it is used to provide a thorough spatial–temporal analysis of green bonds. The research process confirmed that green bonds are an instrument with potential in the global debt market. Among the most important stimulants for the issuance of green government bonds are capital mobilisation, the development of the green financial market, investor demand, and reputational benefits.

Shape Dynamic Time Warping for Seismic Waveform Inversion

ABSTRACT We illustrate shape dynamic time warping (ShapeDTW) for 1D structure waveform inversion with examples from Tanzania, East Africa, and Northeastern Oklahoma. Seismograms of the Mw 5.9 Lake Rukwa, Tanzania, earthquake (18 August 1994) recorded by regional broadband seismographic stations of the Tanzania Broadband Seismic Experiment are used to demonstrate the method. We also test the inversion through solving for 1D crustal velocity structure of the Cherokee Platform in Oklahoma using seismograms of the 2011 Mw 5.7 Prague, Oklahoma, earthquake recorded by the EarthScope Transportable Array. Dynamic time warping (DTW) bypasses the time expense required for manual identification of seismic phases and shows potential for linking discrete seismic phases between two similar waveforms. ShapeDTW improves inversion performance by characterizing the character of the time series near each amplitude point. Applying Sakoe-Chiba band limits to ShapeDTW and an additional amplitude constraint improves the overfitting problem that occurs with the classic DTW method. We apply ShapeDTW to estimate optimal time shifts between observed and synthetic waveforms with time shifts reduced through inversion. The crustal velocity model of Tanzania found using ShapeDTW is close to that found using “phase time inversion” of numerous regional seismic phases observed in the three-component waveforms in a previous study but avoids the necessity of isolating and interpreting different seismic phases in the waveforms. Reducing the ShapeDTW functional misfits can overcome the cycle-skipping problem that often occurs with direct comparison of amplitudes in waveform inversion. This method may be useful in generating starting models for other 1D and 3D inversion methods.

Landslide Displacement Prediction Based on a Two-Stage Combined Deep Learning Model under Small Sample Condition

The widely distributed “Step-type” landslides in the Three Gorges Reservoir (TGR) area have caused serious casualties and heavy economic losses. The prediction research of landslide displacement will be beneficial to the establishment of local geological hazard early warning systems for the realization of scientific disaster prevention and mitigation. However, the number of observed data like landslide displacement, rainfall, and reservoir water level in this area is very small, which results in difficulties for the training of advanced deep learning model to obtain more accurate prediction results. To solve the above problems, a Two-stage Combined Deep Learning Dynamic Prediction Model (TC-DLDPM) for predicting the typical “Step-type” landslides in the TGR area under the condition of small samples is proposed. The establishment process of this method is as follows: (1) the Dynamic Time warping (DTW) method is used to enhance the small samples of cumulative displacement data obtained by the Global Positioning System (GPS); (2) A Difference Decomposition Method (DDM) based on sequence difference is proposed, which decomposes the cumulative displacement into trend displacement and periodic displacement, and then the cubic polynomial fitting method is used to predict the trend displacement; (3) the periodic displacement component is predicted by the proposed TC-DLDPM model combined with external environmental factors such as rainfall and reservoir water level. The TC-DLDPM model combines the advantages of Convolutional Neural Network (CNN), Attention mechanism, and Long Short-term Memory network (LSTM) to carry out two-stage learning and parameter transfer, which can effectively realize the construction of a deep learning model for high-precision under the condition of small samples. A variety of advanced prediction models are compared with the TC-DLDPM model, and it is verified that the proposed method can accurately predict landslide displacement, especially in the case of drastic changes in external factors. The TC-DLDPM model can capture the spatio-temporal characteristics and dynamic evolution characteristics of landslide displacement, reduce the complexity of the model, and the number of model training calculations. Therefore, it provides a better solution and exploration idea for the prediction of landslide displacement under the condition of small samples.

Classification of volcano-seismic events using waveforms in the method of k-means clustering and dynamic time warping

In most volcano observatories classification of seismic events is made as a routine work to get some information on eruptive activities. Automating the classification with artificial intelligence (AI) techniques is a current issue but many AI techniques are not directly applicable to waveforms because they consist of individually different data lengths. This study develops a simple method in which the distance between waveforms with different lengths is evaluated by dynamic time warping and waveforms are classified by k-means clustering. In this method each of the classified groups is specified by a prototype, one of the waveforms that may represent the group best and good classifications are selected considering high generality and good fitting to the members. The seismic events of Sakurajima volcano are classified in this method and waveforms, spectra, time sequences and source locations are compared among groups for some good classifications. It is revealed that one of the groups consisting of tremor-like waveforms has an intimate connection with a magma ascent event beneath the active crater of the volcano.

Relationship between the COVID-19 pandemic and currency exchange rates studied by means of the Dynamic Time Warping method

The COVID-19 pandemic affected the entire global economic system, including currency exchange rates. The main objective of this study is to assess the similarity between time series of currency exchange rates before and during the COVID-19 crisis. In addition, the study aims to examine the relationship between the exchange rates of currencies and the COVID-19 time series in particular countries. The Dynamic Time Warping (DTW) method was applied to check if changes in the exchange rates were related to the spread of COVID-19, and if they were, to what extent it was so. The use of the DTW allows the calculation of the distance between analysed time series. In this study, it made it possible to group the analysed currencies according to their change relative to the pandemic dynamics. The study is based on data from the Stooq and Our World in Data websites. Data on the 17 studied currencies denominated in the New Zealand dollar came from the period between 1 January 2019 and 10 November 2021, and the COVID-19 data from the period between 1 March 2020 and 10 November 2021. The results demonstrate that exchange rates evolved differently in all the three analysed periods: the pre-pandemic period and the first and the second phase of the pandemic. The outbreak of the pandemic led to the concentration of most currencies around the US dollar. However, when the economies unfroze, a polarisation of the currency market occurred, with the world’s major currencies clustering either around the US dollar or the euro.

High-Resolution Mapping of Winter Cereals in Europe by Time Series Landsat and Sentinel Images for 2016–2020

Winter cereals, including wheat, rye, barley, and triticale, are important food crops, and it is crucial to identify the distribution of winter cereals for monitoring crop growth and predicting yield. The production and plating area of winter cereals in Europe both contribute 12.57% to the total global cereal production and plating area in 2020. However, the distribution maps of winter cereals with high spatial resolution are scarce in Europe. Here, we first used synthetic aperture radar (SAR) data from Sentinel-1 A/B, in the Interferometric Wide (IW) swath mode, to distinguish rapeseed and winter cereals; we then used a time-weighted dynamic time warping (TWDTW) method to discriminate winter cereals from other crops by comparing the similarity of seasonal changes in the Normalized Difference Vegetation Index (NDVI) from Landsat and Sentinel-2 images. We generated winter cereal maps for 2016–2020 that cover 32 European countries with 30 m spatial resolution. Validation using field samples obtained from the Google Earth Engine (GEE) platform show that the producer’s and user’s accuracies are 91% ± 7.8% and 89% ± 10.3%, respectively, averaged over 32 countries in Europe. The winter cereal map agrees well with agricultural census data for planted winter cereal areas at municipal and country levels, with the averaged coefficient of determination R2 as 0.77 ± 0.15 for 2016–2019. In addition, our method can identify the distribution of winter cereals two months before harvest, with an overall accuracy of 88.4%, indicating that TWDTW is an effective method for timely crop growth monitoring and identification at the continent level. The winter cereal maps in Europe are available via an open-data repository.

Impact of River-Reservoir Hybrid System on Zooplankton Community and River Connectivity

Anthropogenic connectivity regulation in rivers, such as via weirs and dams, affects the plankton community. We hypothesized that the longitudinal similarity of the zooplankton community in a river could change in a river–reservoir hybrid system (RRHS). The impact of weir construction on zooplankton communities in terms of species diversity, abundance, and community structure was examined biweekly at six sites on the Nakdong River for 14 years (before construction: 2002–2008; after construction: 2012–2018). We checked time-series alignment using a dynamic time-warping method between longitudinal survey sites. After RRHS, the zooplankton community showed an increasing number of species. However, RRHS decreased the longitudinal similarity in terms of number of zooplankton species and population density. Our results demonstrate the negative effect of lateral infrastructures on zooplankton populations due to river fragmentation and habitat alteration.

Clustering-enhanced stock price prediction using deep learning

In recent years, artificial intelligence technologies have been successfully applied in time series prediction and analytic tasks. At the same time, a lot of attention has been paid to financial time series prediction, which targets the development of novel deep learning models or optimize the forecasting results. To optimize the accuracy of stock price prediction, in this paper, we propose a clustering-enhanced deep learning framework to predict stock prices with three matured deep learning forecasting models, such as Long Short-Term Memory (LSTM), Recurrent Neural Network (RNN) and Gated Recurrent Unit (GRU). The proposed framework considers the clustering as the forecasting pre-processing, which can improve the quality of the training models. To achieve the effective clustering, we propose a new similarity measure, called Logistic Weighted Dynamic Time Warping (LWDTW), by extending a Weighted Dynamic Time Warping (WDTW) method to capture the relative importance of return observations when calculating distance matrices. Especially, based on the empirical distributions of stock returns, the cost weight function of WDTW is modified with logistic probability density distribution function. In addition, we further implement the clustering-based forecasting framework with the above three deep learning models. Finally, extensive experiments on daily US stock price data sets show that our framework has achieved excellent forecasting performance with overall best results for the combination of Logistic WDTW clustering and LSTM model using 5 different evaluation metrics.

Instance selection-based dissimilar weldment design prediction for resistant spot welding

Resistance spot welding (RSW) is a critical joining method in sheet-metal industries. The machine-learning technique fueled by the historical experimental data of the existing materials has been used to build the data-driven model (DDM). The DDM is expected to be a promising tool to investigate a new material and its welding behavior because DDM can narrow the range of the test matrix and can thus reduce the number of necessary physical experiments and the cost. However, one of crucial data quality problems with machine learning is that training data sets’ lack of descriptability for test sets causes poor prediction. This research starts by indicating that such data quality problems that exist in the context of weldment design. To resolve this problem, the presented study introduces a novel approach named Similar Weldment Case Selection (SWCS), which predicts the key parameter, the nugget size, of spot welding results of a new material by selecting the most similar one among the existing welding cases and then constructing a prediction model to generate the results. In order to overcome the difficulties with defining the selection criteria only with the material properties and geometric features, this study has come up with another factor, nugget-size weld-current series (NWS), to consider; the NWS is a factor that describes the shape of the relation between weld-current and nugget size. The similarity between two NWSs of different materials is calculated (quantified) with the dynamic time warping (DTW) method. Initially, the twelve conventional algorithms are tested for varying degrees of descriptability between the two weldment designs for test and train datasets; the prediction accuracies are found to be proportional to the train set’s descriptability on the test set. The results are then compared with those from the SWCS. The SWCS yields superior accuracy than the twelve algorithms do when the two materials are similar or different. However, the superiority disappears when the two are the same.

Clustering based on dynamic time warping to extract typical daily patterns from long-term operation data of a ground source heat pump system

While clustering has been commonly used to profile the building electricity consumption data, its application to HVAC system data is relatively less. Based on the operation data of a residential ground source heat pump (GSHP) system, a pre-processing procedure was set up, including acquisition, cleaning, missing-data fill-in, and standardization. Then hierarchical clustering was used, based on the dynamic time warping (DTW) distance calculation method. A new index, the sum of squares of errors based on DTW, was used to determine the best cluster number. The patterns were extracted based on clustering results.The heat exchange on the user-side during one cooling season was processed as a case study. We obtained 5 valid clusters and extracted patterns from each. For the studied case, the result based on the DTW method yields a better homogeneity compared to the Euclidean method. The method is then applied to a five-year operation data, where 9 and 6 patterns were obtained for the cooling and heating seasons, respectively. They mainly differed in shape, and the cooling patterns fluctuate more. Overall, clustering and pattern extraction can reduce the data dimension, and provide a data-driven view of how the system supplies the cooling and heating.

Use of Dynamic Time Warping for Description of Combustion Process in a Biomass Boiler

Abstract The efficient biomass energy use is a key prerequisite for the implementation of renewable energy development strategies on a regional level. For the highly efficient energy use in the combustion process, it is necessary to properly regulate the process based on its precise description. The paper aim is to evaluate whether dynamic time warping (DTW) methods can be used for this description, as well as for the recognition of the specific operating state of a biomass boiler. For the DTW analysis, operating records of more than 10 hours of a laboratory biomass boiler (P = 25 kW) were used, including an emission analysis, for which the operating modes were intentionally alternated in order to identify the stable and transient states of boiler operation. Based on the results, it can be stated that the identical partial operating sections of the controlled variables can be reliably identified in the operating variables of boiler by means of the DTW method, since its manifestations of operating regulation showed compliance with the given operating state, and it is possible to identify a partial quantity for estimating the total operating boiler state.

Building a full-waveform inversion starting model from wells with dynamic time warping and convolutional neural networks

Seismic full-waveform inversion (FWI) needs a feasible starting model because otherwise it might converge to a local minimum and the inversion result might suffer from detrimental artifacts. We have built a feasible starting model from wells by applying dynamic time warping (DTW) localized rewarp and convolutional neural network (CNN) methods alternatively. We use the DTW localized rewarp method to extrapolate the velocities at well locations to the nonwell locations in the model space. Rewarping is conducted based on the local structural coherence, which is extracted from a migration image of an initial infeasible model. The extraction uses the DTW method. The purpose of velocity extrapolation is to provide sufficient training samples to train a CNN, which maps local spatial features on the migration image into the velocity quantities of each layer. Furthermore, we design an interactive workflow to reject inaccurate network predictions and to improve CNN prediction accuracy by incorporating the Monte Carlo dropout method. We have determined that our method is robust against kinematic incorrectness in the migration velocity model, and it is capable of producing a feasible FWI starting model.

Comparison of Winter Wheat Extraction Methods Based on Different Time Series of Vegetation Indices in the Northeastern Margin of the Qinghai–Tibet Plateau: A Case Study of Minhe, China

The northeastern margin of the Qinghai–Tibet Plateau (QTP) is an agricultural protection area in China’s new development plan, and the primary region of winter wheat growth within QTP. Winter wheat monitoring is critical for understanding grain self-sufficiency, climate change, and sustainable socioeconomic and ecological development in the region. However, due to the complex terrain and high altitude of the region, with discontinuous arable land and the relatively low level of agricultural development, there are no effective localization methodologies for extracting and monitoring the detailed planting distribution information of winter wheat. In this study, Sentinel-2A/B data from 2019 to 2020, obtained through the Google Earth Engine platform, were used to build time series reference curves of vegetation indices in Minhe. Planting distribution information of winter wheat was extracted based on the phenology time-weighted dynamic time warping (PT-DTW) method, and the effects of different vegetation indices’ time series and their corresponding threshold parameters were compared. The results showed that: (1) the three vegetation indices—normalized difference vegetation index (NDVI), normalized differential phenology index (NDPI), and normalized difference greenness index (NDGI)—maintained high mapping potential; (2) under the optimal threshold, >88% accuracy of index identification for winter wheat extraction was achieved; (3) due to improved extraction accuracy and resulting boundary range, NDPI and its corresponding optimal parameter (T = 0.05) performed the best. The process and results of this study have certain reference value for the study of winter wheat planting information change and the formulation of dynamic monitoring schemes in agricultural areas of QTP.

Damage quantification of aluminum plates using SC-DTW method based on Lamb waves

Lamb waves were utilized to quantify micro-crack damage in aluminum plates, and the scattering and mode conversion of Lamb waves passing through cracks were analyzed. The dynamic time warping (DTW) method was used to match and compare each Lamb wave time series that represented different damage degrees. The matching difference between the damaged plate and undamaged plate was taken as a marker to measure the damage degree of the workpiece. At the same time, due to the pathological alignment of traditional DTW methods, the shape context (SC) profile recognition method was introduced to optimize the algorithm for calculating the distance between sampling points in the DTW method and solve the pathological alignment problem. Finally, the SC-DTW method based on Lamb waves was verified by the finite element simulation model and bending test of aluminum plates. The results showed that the method was feasible for quantifying the damage degree of aluminum plates and had a great advantage in the analysis and processing of time series in low-sampling frequency and high-noise scenarios.

Dynamic Time Warping Features Extraction Design for Quranic Syllable-based Harakaat Assessment

The use of technological speech recognition systems with a variety of approaches and techniques has grown exponentially in varieties of human-machine interaction applications. The assessment for Qur'anic recitation errors based on syllables utterance is used to meet the Tajweed rules which generally consist of Harakaat (prolonging). The digital transformation of Quranic voice signals with identification of Tajweed-based recitation errors of Harakaat is the main research work in this paper. The study focused on speech processing implemented using the representation of Quranic Recitation Speech Signals (QRSS) in the best digital format based on Al-Quran syllables and feature extraction design to reveal similarities or differences in recitation (based on Al-Quran syllables) between experts and student. The method of Dynamic Time Warping (DTW) is used as Short Time Frequency Transform (STFT) of QRSS syllable feature for Harakaat measurement. Findings from this paper include an approach based on human-guidance threshold classification that is used specifically to evaluate Harakaat based on the syllables of the Qur'an. The threshold classification performance obtained for Harakaat is above 80% in the training and testing stages. The results of the analysis at the end of the experiment have concluded that the threshold classification method for Minimum Path Cost (MPC) feature parameters can be used as an important feature to evaluate the rules of Tajwid Harakaat embedded in syllables.

Novel Dynamic Segmentation for Human-Posture Learning System Using Hidden Logistic Regression

In this letter, we propose a novel automatic-segmentation technique for a dynamic human-posture learning system using skeletal-graph time-series. The focused problem is very challenging as no fixed segment-size is appropriate for capturing precise human postures. Our proposed novel dynamic-segmentation scheme will first estimate the number of segments and then the optimal segmentation can be determined using hidden logistic regression subject to the estimated number of segments. Experimental results from the realworld Kinect data are compared with the well-known dynamic-time-warping (DTW) segmentation method. Based on our experiments, our proposed new scheme greatly outperforms the DTW method in terms of miss-detection probability and miss-alignment percentage.

The Comparison of Audio Analysis Using Audio Forensic Technique and Mel Frequency Cepstral Coefficient Method (MFCC) as the Requirement of Digital Evidence

Audio forensics is the application of science and scientific methods in handling digital evidence in the form of audio. In this regard, the audio supports the disclosure of various criminal cases and reveals the necessary information needed in the trial process. So far, research related to audio forensics is more on human voices that are recorded directly, either by using a voice recorder or voice recordings on smartphones, which are available on Google Play services or iOS Store. This study compares the analysis of live voices (human voices) with artificial voices on Google Voice and other artificial voices. This study implements the audio forensic analysis, which involves pitch, formant, and spectrogram as the parameters. Besides, it also analyses the data by using feature extraction using the Mel Frequency Cepstral Coefficient (MFCC) method, the Dynamic Time Warping (DTW) method, and applying the K-Nearest Neighbor (KNN) algorithm. The previously made live voice recording and artificial voice are then cut into words. Then, it tests the chunk from the voice recording. The testing of audio forensic techniques with the Praat application obtained similar words between live and artificial voices and provided 40,74% accuracy of information. While the testing by using the MFCC, DTW, KNN methods with the built systems by using Matlab, obtained similar word information between live voice and artificial voice with an accuracy of 33.33%.

Comparison of changes in the labour markets of post-communist countries with other EU member states

strengthen their international competitiveness. This was linked to the implementation of institutional and economic reforms, significant technological changes and improvements in the quality of human capital, as well as fiscal stabilisation policies. These changes affected their situation in the labour market.
 Purpose of the article: The aim of the study is to assess changes in the situation in the labour market in the EU with particular emphasis on the post-communist countries in the period 2002? 2019.
 Methods: The situation of countries in the European labour market was estimated using the TOPSIS method. A similarity matrix of changes in the composite variable for each country was then constructed using the Dynamic Time Warping method. On its basis, homogeneous clusters of countries were determined using the Ward?s method.
 Findings & value added: Four homogenous clusters of countries were formed. The post-communist ones belonged to two groups. In one, there were two countries ? Croatia and Slovakia. The rest of the post-communist countries were in a large cluster, which also included Germany, Malta, Finland, Portugal, France and Belgium. Changes of the situation in the post-communist countries in this group improved very much during the analysed period (this was particularly evident for Czechia, Estonia and Poland). It is interesting to investigate whether the reaction of labour markets to changes in the global economic situation in post-communist countries is similar to that in the old EU countries. The similarity of changes can be measured using the DTW method. There is an empirical research gap in this respect. Therefore, the added value is the use of this method in assessing similarities of changes in the labour market situation in post-communist countries in comparison to the Western European ones.

A generalized trajectories-based evaluation approach for pedestrian evacuation models

The fundamental diagram and self-organized phenomena in crowds are widely used to test the applicability of evacuation models. These benchmarks are good indicators for the validity of a model, whereas they are insufficient descriptors for the realistic microscopic behaviors of pedestrians. In recent years, the rapid increase of the trajectory datasets which benefits from the development of recognition technologies open the door to new possibilities for an extensive quantitative validation of the models. In this work, a trajectories-based analysis approach which contains types of indexes is proposed. The indexes are a mix of macroscopic type (fundamental diagram index, speed choice index, and direction choice index) and microscopic type (trajectories pattern index), distribution type (route length distribution index, travel time distribution index) and time-series type (starting position distance time-series index, destination position distance time-series index. Moreover, the Kolmogorov-Smirnov (K-S) test as well as the dynamic time warping (DTW) method are introduced to quantify the similarities of results on different types of indexes. In brief, by comparing experimental and simulation trajectories, we can measure a set of performance scores in different perspectives. Here, the Social Force Model (SFM) and Heuristics Model (HM) are respectively introduced and evaluated. According to the proposed evaluation approach, we show that the HM performs better than the SFM. Our analysis approach is model agnostic and is defined in a general way, such that it can be applied for trajectory sets from different experiment settings. This work can help to improve the accuracy of simulation models, and the pedestrian safety in crowd activities and autonomous vehicle navigation will be benefited.