Time Warping Distance Research Articles

Asymmetric Gait Analysis Using a DTW Algorithm with Combined Gyroscope and Pressure Sensor.

Walking is one of the most basic human activities. Various diseases may be caused by abnormal walking, and abnormal walking is mostly caused by disease. There are various characteristics of abnormal walking, but in general, it can be judged as asymmetric walking. Generally, spatiotemporal parameters can be used to determine asymmetric walking. The spatiotemporal parameter has the disadvantage that it does not consider the influence of the diversity of patterns and the walking speed. Therefore, in this paper, we propose a method to analyze asymmetric walking using Dynamic Time Warping (DTW) distance, a time series analysis method. The DTW distance was obtained by combining gyroscope data and pressure data. The experiment was carried out by performing symmetrical walking and asymmetrical walking, and asymmetric walking was performed as a simulation of hemiplegic walking by fixing one ankle using an auxiliary device. The proposed method was compared with the existing asymmetric gait analysis method. As a result of the experiment, a p-value lower than 0.05 was obtained, which proved that there was a statistically significant difference.

Improved spectral clustering approach — A new tool for unsupervised seismic facies analysis of variable window length

The traditional constant time window-based waveform classification method is a robust tool for seismic facies analysis. However, when the interval thickness is seismically variable, the fixed time window is not able to contain the complete geologic information of interest. Therefore, the constant time window-based waveform classification method is inapplicable to conduct seismic facies analysis. To expand the application scope of seismic waveform classification in the strata with varying thickness, we have proposed a novel scheme for unsupervised seismic facies analysis of variable window length. The input of the top and bottom horizons can guarantee the comprehensive geologic information of the target interval. Throughout the whole workflow, we use the dynamic time warping (DTW) distance to measure the similarities between seismic waveforms of different lengths. First, we improve the traditional spectral clustering algorithm by replacing the Euclidean distance with the DTW distance. Therefore, it can be applicable in the interval of variable thickness. Second, to solve the problem of large computation when applying the improved spectral clustering approach, we adopt the method of seismic data thinning based on the technology of the superpixel. We combine these two algorithms and perform the integrated workflow of improved spectral clustering. The experiments on synthetic data show that the proposed workflow outperforms the traditional fixed time window-based clustering algorithm in recognizing the boundaries of different lithologies and lithologic associations with varying thickness. The practical application shows great promise for reservoir characterization of interval with varying thickness. The plane map of waveform classification provides convincing reference to delineate reservoir distribution of the data set.

Clustering Provinces in Indonesia Based on Daily Covid-19 Cases

The latest form of coronavirus is Coronavirus Disease 2019 (Covid-19). It was discovered in Wuhan, Hubei Province, China. The Covid-19 virus is growing very rapidly. Starting from Wuhan which then spread to the surrounding provinces to all provinces in China, and even spread to other countries such as Indonesia. Until August 17, 2020, an update from the KEMENKES RI that the development of Covid-19 in 34 Indonesian Provinces was positive ( 141,370), recovered (94,458), and died (6,207). This means that the case fatality rate in Indonesia is 4.39%. As a disease that is currently becoming a pandemic has a major impact in all sectors, it is very important to explore data and carry out clustering that is useful for policy making for the government such as decision making on WFH, PSBB, New Normal, or lockdown. The clustering provinces based on those similarities (homogeneity) data to find out which provinces have Covid-19 cases with similar characteristics and between clusters have different characteristics. Clusterization is expected to inform areas of high, medium, and low risk and their characteristic characteristics. Based on Covid-19 data, we used the hierarchical clustering method shows there are 4 clusters: cluster 1 (Jakarta and East Java), cluster 2 (Central Java, West Java, and South Sulawesi), cluster 3 (South Kalimantan, North Sumatra, South Sumatra, Papua, Bali, and East Kalimantan), and the provinces others in cluster 4. Validation of clustering shows Dynamic Time Warping (DTW) distance for hierarchical clustering (average linkage) is a good classification with an average silhouette value of 0.70.

Fault Recognition of Indicator Diagrams Based on the Dynamic Time Warping Distance of Differential Curves

Oil recovery with pumping units is widely used in oilfield development at present. The management level of pumping units is related to the overall economic benefit of oilfield. In order to effectively control the production management of pumping wells, it is necessary to take all the production data to formulate a reasonable working system and make continuous analyses about the daily management level of pumping wells. The analysis and interpretation of the indicator diagram is a direct understanding way about the situation of deep well pumps in petroleum engineering. However, the complicated practical oilfield conditions often lead to the distortion of regular indicator diagrams, resulting in the low efficiency of fault-type diagnosis and wrong recognition. A new method of identifying the fault type of indicator diagrams is proposed by using the dynamic time warping (DTW) distance, through which a two-dimensional indicator diagram is transformed into a one-dimensional differential curve. The experimental results of real indicator diagrams show that the method is effective for the type diagnosis of indicator diagrams with high accuracy and fast speed.

Dynamic Time Warping-Based Features With Class-Specific Joint Importance Maps for Action Recognition Using Kinect Depth Sensor

This paper proposes a novel 3D action recognition technique that uses time-series information extracted from depth image sequences for use in systems of human daily activity monitoring. To this end, each action is represented as a multi-dimensional time series, where each dimension represents the position variation of one skeleton joint over time. The time series is then mapped onto a vector space using Dynamic Time Warping (DTW) distance. Furthermore, to employ the correlation-distinctiveness relationship of the sequences in recognition, this vector space is remapped onto a discriminative space using the regularized Fisher method, where final decisions about the actions are made. Unlike other available methods, the time-warping used in the mapping strategy makes the feature space robust to temporal variations of the motion sequences. Moreover, our method eliminates the need for a complicated design method for extracting the static and dynamic information of a motion sequence. Furthermore, most existing methods treat all skeletal joints identically for different actions, while some joints are more discriminative to distinguish a specific action. Thanks to the nature of the proposed features, we propose to use a separate set of discriminative joints, called joint importance map for each class of action. Evaluation results on four well-known datasets, TST, UTKinect, UCFKinect, and NTU RGB+D show competitive performance with the state-of-the-art methods in human action recognition.

On-air English Capital Alphabet (ECA) recognition using depth information

On-air writing can be considered as a time-dependent event where hand gesture is produced in a natural environment through index finger movement. A sequence of such movements containing several time steps in 3D space can be utilized to construct an English Capital Alphabet (ECA). While Previous researches investigated 2D features, we believe that depth information may play a significant role along with other features in recognition of these dynamic gestures. We have captured hand finger motion information using a depth camera and represented them as depth images for each ECA. The hand finger trajectory data were extracted from the depth image, and a combination of depth-based features and non-depth features were generated; depth variation was performed in the depth-based features, and then, all the feature values were converted into time-series data. Dynamic Time Warping distances were determined between a template ECA and a test ECA for each ECA collected from 15 participants. These distance-based features were then fed into a multi-class SVM for training and testing and got the recognition accuracy of $$80.77\%$$ without depth and $$88.21\%$$ with depth-based features. To cope with the over-fitting problem, we applied the resampling technique and got the highest recognition accuracy of 96.85%, and at last, we applied some feature selection techniques to analyze the recognition results.

Identification Method of Electrical Load for Electrical Appliances Based on K-Means ++ and GCN

Most cluster identification studies regarding consumer electricity load is faced with problems of erroneous clustering method similarity, low clustering quality and poor identification accuracy. To solve these problems, this paper utilizes the elbow method, k- Means ++, entropy weight method and a graph convolutional neural network to provide a means for cluster identification based on electrical appliance power data collected via smart sockets. In this article, elbow and entropy weight methods were used to achieve the adaptive clustering algorithm. To obtain the electrical appliance load curves, Euclidean and dynamic time warping (DTW) distances were integrated and the similarity measurement method was used to improve the k-means ++ algorithm, which was then applied to data collected via smart socket clustering. Next, clustering results were input into the graph convolutional neural network (GCN) for identification purposes and appliance type information was obtained. Finally, experiments were conducted using electrical load data from 20 commercial users. The method used was a combination of the k-means algorithm and long short-term memory network (LSTM). The results show that under optimal K value conditions (as determined by the elbow score), the methods used in this paper have improved clustering quality and recognition accuracy, when compared to LSTM.

Using wavelet transform and dynamic time warping to identify the limitations of the CNN model as an air quality forecasting system

Abstract. As the deep learning algorithm has become a popular data analysis technique, atmospheric scientists should have a balanced perception of its strengths and limitations so that they can provide a powerful analysis of complex data with well-established procedures. Despite the enormous success of the algorithm in numerous applications, certain issues related to its applications in air quality forecasting (AQF) require further analysis and discussion. This study addresses significant limitations of an advanced deep learning algorithm, the convolutional neural network (CNN), in two common applications: (i) a real-time AQF model and (ii) a post-processing tool in a dynamical AQF model, the Community Multi-scale Air Quality Model (CMAQ). In both cases, the CNN model shows promising accuracy for ozone prediction 24 h in advance in both the United States of America and South Korea (with an overall index of agreement exceeding 0.8). For the first case, we use the wavelet transform to determine the reasons behind the poor performance of CNN during the nighttime, cold months, and high-ozone episodes. We find that when fine wavelet modes (hourly and daily) are relatively weak or when coarse wavelet modes (weekly) are strong, the CNN model produces less accurate forecasts. For the second case, we use the dynamic time warping (DTW) distance analysis to compare post-processed results with their CMAQ counterparts (as a base model). For CMAQ results that show a consistent DTW distance from the observation, the post-processing approach properly addresses the modeling bias with predicted indexes of agreement exceeding 0.85. When the DTW distance of CMAQ versus observation is irregular, the post-processing approach is unlikely to perform satisfactorily. Awareness of the limitations in CNN models will enable scientists to develop more accurate regional or local air quality forecasting systems by identifying the affecting factors in high-concentration episodes.

COMPARING EFFICIENCY BETWEEN TWO MEASURES OF EUCLID AND DTW USED IN DISCOVERY MOTIF IN TIME SERIES

The study on time series databases which is based on efficient retrieval of unknown patterns and frequently encountered in time series, called motif, has attracted much attention from many researchers recently. These motifs are very useful for the exploration of data and provide solutions to many problems in various fields of applications. In this paper, we try to study and evaluate the efficiency of the use of both Euclidean and Dynamic Time Warping (DTW) distance meassures, utilizing Bruteforce and Mueen – Keogh algorithms (MK), of which MK algorithm has performed efficiently in terms of CPU time and the accuracy of the problem of discovery the motif patterns. The efficiency of this method has been proven through experiment on real databases.

FastDTW is Approximate and Generally Slower Than the Algorithm it Approximates

Many time series data mining problems can be solved with repeated use of distance measure. Examples of such tasks include similarity search, clustering, classification, anomaly detection and segmentation. For over two decades it has been known that the Dynamic Time Warping (DTW) distance measure is the best measure to use for most tasks, in most domains. Because the classic DTW algorithm has quadratic time complexity, many ideas have been introduced to reduce its amortized time, or to quickly approximate it. One of the most cited approximate approaches is FastDTW. The FastDTW algorithm has well over a thousand citations and has been explicitly used in several hundred research efforts. In this work, we make a surprising claim. In any realistic data mining application, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">approximate</i> FastDTW is much slower than the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exact</i> DTW. This fact clearly has implications for the community that uses this algorithm: allowing it to address much larger datasets, get exact results, and do so in less time.

Mapping Paddy Rice Using Weakly Supervised Long Short-Term Memory Network with Time Series Sentinel Optical and SAR Images

Rice is one of the most important staple food sources worldwide. Effective and cheap monitoring of rice planting areas is demanded by many developing countries. This study proposed a weakly supervised paddy rice mapping approach based on long short-term memory (LSTM) network and dynamic time warping (DTW) distance. First, standard temporal synthetic aperture radar (SAR) backscatter profiles for each land cover type were constructed on the basis of a small number of field samples. Weak samples were then labeled on the basis of their DTW distances to the standard temporal profiles. A time series feature set was then created that combined multi-spectral Sentinel-2 bands and Sentinel-1 SAR vertical received (VV) band. With different combinations of training and testing datasets, we trained a specifically designed LSTM classifier and validated the performance of weakly supervised learning. Experiments showed that weakly supervised learning outperformed supervised learning in paddy rice identification when field samples were insufficient. With only 10% of field samples, weakly supervised learning achieved better results in producer’s accuracy (0.981 to 0.904) and user’s accuracy (0.961 to 0.917) for paddy rice. Training with 50% of field samples also presented improvement with weakly supervised learning, although not as prominent. Finally, a paddy rice map was generated with the weakly supervised approach trained on field samples and DTW-labeled samples. The proposed data labeling approach based on DTW distance can reduce field sampling cost since it requires fewer field samples. Meanwhile, validation results indicated that the proposed LSTM classifier is suitable for paddy rice mapping where variance exists in planting and harvesting schedules.

Affine Shape Comparison using Different Distances

In this work, we propose to compare affine shape using Hausdorff distance (HD), Dynamic Time Warping (DTW), Frechet (DF), and Earth Mover distance (EMD). Where there is only a change in resolution shape distance are computed between shape coordinates because the distance is not invariant under rotation or affinity. In case of transformation, distances are calculated not between shape coordinates but between Arc length or Affine Arc length. Arc length is invariant under rotation while Affine Arc length is invariant under affinity. The main advantage is invariance under change of resolution, rotation, and affinity.

A deep neural network based correction scheme for improved air-tissue boundary prediction in real-time magnetic resonance imaging video

The real-time Magnetic Resonance Imaging (rtMRI) video captures the vocal tract movements in the mid-sagittal plane during speech. Air tissue boundaries (ATBs) are contours that trace the transition between the high-intensity tissue corresponding to the speech articulators and the low-intensity airway cavity in the rtMRI video. The ATB segmentation in an rtMRI video is a common preprocessing step which is used for many speech production and speech processing applications. However, ATB segmentation is very challenging due to the low resolution and low signal-to-noise ratio of the rtMRI images. Several works have been proposed in the literature for accurate ATB segmentation. However, every ATB segmentation technique, be it knowledge-based or data-driven, has its own limitations due to model assumption or data quality. The errors in the predicted ATBs from a typical ATB segmentation approach can be corrected in a data-driven manner as a post-processing step. In this work, we propose a deep neural network (DNN) based correction scheme for improving the ATB segmentation. In the DNN based correction approach, the correction of each point on a predicted ATB is done using a pattern of intensity variation in the direction of the normal to the predicted ATB at that point. For this, inputs and target outputs needed for DNN training are generated using a normal-grid based method. Experimental results show that the proposed DNN based correction yields more accurate ATBs in terms of Dynamic Time Warping (DTW) distance compared to the ATB segmentation approaches it is applied on. Thus, the DNN based correction could be used as a post-processing step to improve the accuracy of the predicted ATBs from any segmentation scheme.

Prediction of dissolved oxygen in pond culture water based on K-means clustering and gated recurrent unit neural network

Dissolved oxygen in water is an important ecological factor in ensuring the healthy growth of aquatic products, as hypoxic stress is known to restrict the growth of aquatic products. The accurate monitoring and prediction of dissolved oxygen is the key to precise regulation and control of pond aquaculture water quality. The current dissolved oxygen prediction model has some limitations, such as a short prediction period and inadequate prediction accuracy for actual production demands. Therefore, a prediction model of dissolved oxygen in pond culture was proposed based on K-means clustering and Gated Recurrent Unit (GRU) neural network. Firstly, the key factors affecting the changes in dissolved oxygen were selected by principal component analysis (PCA). The dissolved oxygen time series was then subjected to K-means clustering, and the dissolved oxygen prediction model was constructed using GRU. To improve the clustering effect, we enhanced the similarity calculation for the time series based on the variation of dissolved oxygen. This process combined the Euclidean distance with the dynamic time-warping distance. The proposed method can predict the dissolved oxygen content of aquaculture water over different time intervals according to the demands of real-world scenarios. The average absolute error of the 30-min interval model was 0.264, and the mean absolute percentage error was 3.5 %. Experimental results indicated that the proposed method achieves higher prediction accuracy and flexibility than the conventional approach.

Efficient segmentation-based methods for anomaly detection in static and streaming time series under dynamic time warping

The problem of time series anomaly detection has attracted a lot of attention due to its usefulness in various application domains. However, most of the methods proposed so far used Euclidean distance to deal with this problem. Dynamic Time Warping (DTW) distance is more suitable than Euclidean distance because of its capability in shape-based similarity checking in many practical fields, for example those with multimedia data. In this paper, we propose two efficient anomaly detection methods, EP-Leader-DTW and SEP-Leader-DTW, for static and streaming time series under DTW, respectively. Our methods are based on time series segmentation, subsequence clustering, and anomaly scoring. For segmentation, the major extrema method is used to obtain subsequences. For clustering, we apply Leader algorithm to cluster the subsequences along with a lower bounding technique to accelerate DTW distance computation. Experimental results on several benchmark time series datasets reveal that our method for anomaly detection in static time series under DTW can perform very fast and accurately on large time series datasets. For streaming time series, our method can meet the instantaneous requirement with high accuracy. As a result, our anomaly detection methods are applicable to both static and streaming time series in practice.

A DTW distance-based seismic waveform clustering method for layers of varying thickness

Seismic waveform clustering is a useful technique for lithologic identification and reservoir characterization. The current seismic waveform clustering algorithms are predominantly based on a fixed time window, which is applicable for layers of stable thickness. When a layer exhibits variable thickness in the seismic response, a fixed time window cannot provide comprehensive geologic information for the target interval. Therefore, we propose a novel approach for a waveform clustering workflow based on a variable time window to enable broader applications. The dynamic time warping (DTW) distance is first introduced to effectively measure the similarities between seismic waveforms with various lengths. We develop a DTW distance-based clustering algorithm to extract centroids, and we then determine the class of all seismic traces according to the DTW distances from centroids. To greatly reduce the computational complexity in seismic data application, we propose a superpixel-based seismic data thinning approach. We further propose an integrated workflow that can be applied to practical seismic data by incorporating the DTW distance-based clustering and seismic data thinning algorithms. We evaluated the performance by applying the proposed workflow to synthetic seismograms and seismic survey data. Compared with the the traditional waveform clustering method, the synthetic seismogram results demonstrate the enhanced capability of the proposed workflow to detect boundaries of different lithologies or lithologic associations with variable thickness. Results from a practical application show that the planar map of seismic waveform clustering obtained by the proposed workflow correlates well with the geological characteristics of wells in terms of reservoir thickness.

Fuzzy clustering based on feature weights for multivariate time series

As an important set of techniques for data mining, time series clustering methods had been studied by many researchers. Although most existing solutions largely focus on univariate time series clustering, there has been a surge in interest in the clustering of multivariate time series data. In this paper, a feature-weighted clustering method is proposed based on two distance measurement methods called dynamic time warping (DTW) and shape-based distance (SDB). There are four stages in the proposed clustering algorithm. First, we pick cluster centers by the pop clustering method called clustering by fast search and find of density peaks (DPC). Next, by considering the overall matching of multivariate time series, a fuzzy membership matrix is generated by performing DTW on all variables. We then reconsider the contribution of each independent dimension by utilizing SBD to measure distances within each dimension and construct multiple fuzzy membership matrices. Finally, we utilize a traditional fuzzy clustering algorithm called fuzzy c-means to cluster the fuzzy membership matrices and generate clustering results. Simultaneously, a feature weight calculation method and novel equation for constructing fuzzy membership matrices are applied during the clustering process. We compare the proposed method to other clustering methods and the results indicate that the proposed method can improve clustering accuracy for multivariate time series datasets.

Online signature verification using single-template matching with time-series averaging and gradient boosting

In keeping with recent developments in artificial intelligence in the era of big data, there is a demand for online signature verification systems that operate at high speeds, provide a high level of security, and allow high tolerances while achieving sufficient performance. In response to these needs, the present study proposes a novel, single-template strategy using a mean template set and weighted multiple dynamic time warping (DTW) distances for a function-based approach to online signature verification. Specifically, to obtain an effective mean template for each feature while reflecting intra-user variability between all the reference samples, we adopt a novel time-series averaging method based on Euclidean barycenter-based DTW barycenter averaging. Then, by using the mean template set, we calculate multiple DTW distances from multivariate time series based on dependent and independent warping. Finally, to boost the discriminative power, we apply a weighting scheme using a gradient boosting model to efficiently combine the multiple DTW distances. Experimental results using the common SVC2004 Task1/Task2 and MCYT-100 signature datasets confirm that the proposed method is effective for online signature verification.

Invariant subspace learning for time series data based on dynamic time warping distance

Low-dimensional and compact representation of time series data is of importance for mining and storage. In practice, time series data are vulnerable to various temporal transformations, such as shift and temporal scaling, however, which are unavoidable in the process of data collection. If a learning algorithm directly calculates the difference between such transformed data based on Euclidean distance, the measurement cannot faithfully reflect the similarity and hence could not learn the underlying discriminative features. In order to solve this problem, we develop a novel subspace learning algorithm based on dynamic time warping (DTW) distance which is an elastic distance defined in a DTW space. The algorithm aims to minimize the reconstruction error in the DTW space. However, since DTW space is a semi-pseudo metric space, it is difficult to generalize common subspace learning algorithms for such semi-pseudo metric spaces. In this work, we introduce warp operators with which DTW reconstruction error can be approximated by reconstruction error between transformed series and their reconstructions in a subspace. The warp operators align time series data with their linear representations in the DTW space, which is in particular important for misaligned time series, so that the subspace can be learned to obtain an intrinsic basis (dictionary) for the representation of the data. The warp operators and the subspace are optimized alternatively until reaching equilibrium. Experiments results show that the proposed algorithm outperforms traditional subspace learning algorithms and temporal transform-invariance based methods (including SIDL, Kernel PCA, and SPMC et. al), and obtains competitive results with the state-of-the-art algorithms, such as BOSS algorithm.

Sufficient conditions for the existence of a sample mean of time series under dynamic time warping

Time series averaging is an important subroutine for several time series data mining tasks. The most successful approaches formulate the problem of time series averaging as an optimization problem based on the dynamic time warping (DTW) distance. The existence of an optimal solution, called sample mean, is an open problem for more than four decades. Its existence is a necessary prerequisite to formulate exact algorithms, to derive complexity results, and to study statistical consistency. In this article, we propose sufficient conditions for the existence of a sample mean. A key result for deriving the proposed sufficient conditions is the Reduction Theorem that provides an upper bound for the minimum length of a sample mean.