Dynamic Time Warping Barycenter Averaging Research Articles

K-means DTW Barycenter Averaging: a clustering analysis of COVID-19 cases and deaths on the Brazilian federal units

K-means DTW Barycenter Averaging: a clustering analysis of COVID-19 cases and deaths on the Brazilian federal units

Weighted Fuzzy Clustering for Time Series With Trend-Based Information Granulation.

The highly dimensional characteristic of time series brings many challenges on direct mining time series, such as high cost in time and space. Granular computing provides a potential strategy for representing and dealing with time series at a higher level of abstraction. In this study, we propose an information granulation-based weighted fuzzy C -means (wFCM) method to realize time-series clustering, which could avoid high dimensionality processing and provide a concise and visible granular prototype for each cluster. In this method, each time series is first transformed into a series of information granules with trend following the principle of justifiable granularity. The formed granular time series can well capture the main features lying in the original time series and help realize dimensionality reduction. Then, the wFCM method is developed to complete time-series clustering in the granular space. Here, the dynamic time warping (DTW) is extended to capture the similarity for trend-based granular time series. Furthermore, the weighted DTW barycenter averaging is introduced to derive prototypes presented in a granular format, capturing the level, the fluctuation, and the changing trend, which are meaningful and understandable clustering results. The experiments conducted on real-world datasets coming from the UCR time-series database and Chinese stocks are presented to illustrate the effectiveness and practicality of the designed time-series clustering model.

Multi-source variational mode transfer learning for enhanced PM2.5 concentration forecasting at data-limited monitoring stations

Hybrid methods combining data decomposition with deep learning have recently exhibited remarkable performance in PM2.5 concentration forecasting. However, these methods still encounter limitations when confronted with monitoring sites lacking adequate historical data. To overcome this challenge, this study proposes a novel methodological framework named as Multi-source Variational Mode Transfer Learning (MSVMTL) that integrates data decomposition, deep learning, and multi-source transfer learning strategies. The framework consists of four stages: source domain selection, data decomposition by Variational Mode Decomposition (VMD), mode sequence clustering, and multi-source mode transfer learning. The source domain selection stage utilizes EMS (Euclidean Distance and Maximum Mean Discrepancy Distance) to identify the most suitable source domain for knowledge transfer. The mode sequence clustering employs the LDDK algorithm (Largest Triangle Three Buckets, Dynamic Time Warping, Dynamic Time Warping Barycenter Averaging, and K-means) to cluster modes from VMD-derived domains. The multi-source mode transfer stage combines VMD with pre-training and fine-tuning, leveraging source domain knowledge for target domain prediction. To validate the proposed framework, a case study, including multiple sets of comparative experiments and ablation study, was conducted using data from 12 air quality monitoring sites in Beijing, China. The experimental results demonstrate that EMS, LDDK, and multi-source mode transfer learning strategy all achieved excellent performance, and the presented MSVMTL significantly enhances the prediction accuracy of PM2.5 concentrations at monitoring sites with limited historical data.

A novel shape-based averaging algorithm for time series

Time series averaging is one of the essential subroutines in time series analysis. DTW Barycenter Averaging (DBA) has proven to be an effective and popular DTW-based time series averaging algorithm. However, DBA lacks the ability to average time series in the time domain, making it sensitive to initialization. In this research, we propose a novel shape-based time series averaging algorithm, called Shape DTW Weighted Averaging (ShapeDWA), to address the shortcomings of DBA. The proposed ShapeDWA algorithm combines the advantages of the DBA and the Cubic-spline DTW (CDTW) averaging methods. The concepts of time index averaging and re-sampling in the CDTW algorithm are incorporated into the DBA algorithm, giving ShapeDWA the ability to average a set of time series in both the amplitude and time domains. Moreover, ShapeDWA utilizes a weighed average instead of the barycenter average in DBA, which effectively attenuate the effects of noise, outliers, and local amplitude differences between the time series. To qualitatively evaluate and compare the proposed time series averaging algorithm, two metrics have been developed: average discrepancy distance and average time distortion. Extensive experimental results on the UCR time series database illustrate the superior performance of ShapeDWA over DBA and SSG, with an average reduction of 23.42% and 24.89% for average discrepancy distance, and 18.76% and 19.81% for average time distortion. Furthermore, the template matching-based classification experiment shows that ShapeDWA combined with these two developed metrics improves the classification rate by 17.07% and 16.42% compared to DBA and SSG, respectively.

Abnormal Chamber Detection in the Etching Process Using Time-Series Data Augmentation and Soft Labeling

In the semiconductor manufacturing etching process, a considerable amount of good-quality data can be obtained by the measurement process. As the etching process has an impact on subsequent processes and to check and control the condition of the wafer, the measurement process should be performed as much as possible. However, with the rapid development of technology in manufacturing, the process recipe has undergone frequent changes. Accordingly, the amount of data available in the field is limited, and the effective utilization of measured data is needed to improve the model’s performance in abnormal chamber detection. In this article, we propose to augment time-series data that are collected from equipment sensors in the etching process to improve the model’s performance. To accomplish this task, we utilize dynamic time-warping barycenter averaging (DBA) and soft labeling. DBA is applied to calculate the average of the time series, and the new label is given in the form of a soft label. To verify the efficiency of the proposed method, we compared several regression models with the proposed method and with several benchmark methods. In addition, we compared the proposed method with soft labeling and hard labeling. The experimental results show that the model with the proposed method is superior to the model with its other benchmark methods.

A Novel Data Augmentation Method for Improving the Accuracy of Insulator Health Diagnosis.

Performing ultrasonic nondestructive testing experiments on insulators and then using machine learning algorithms to classify and identify the signals is an important way to achieve an intelligent diagnosis of insulators. However, in most cases, we can obtain only a limited number of data from the experiments, which is insufficient to meet the requirements for training an effective classification and recognition model. In this paper, we start with an existing data augmentation method called DBA (for dynamic time warping barycenter averaging) and propose a new data enhancement method called AWDBA (adaptive weighting DBA). We first validated the proposed method by synthesizing new data from insulator sample datasets. The results show that the AWDBA proposed in this study has significant advantages relative to DBA in terms of data enhancement. Then, we used AWDBA and two other data augmentation methods to synthetically generate new data on the original dataset of insulators. Moreover, we compared the performance of different machine learning algorithms for insulator health diagnosis on the dataset with and without data augmentation. In the SVM algorithm especially, we propose a new parameter optimization method based on GA (genetic algorithm). The final results show that the use of the data augmentation method can significantly improve the accuracy of insulator defect identification.

Brazilian governmental database linkage to correct the municipalities underreported cases in a time-dependent cluster analysis on COVID-19.

ObjectivesCovid-19 databases have detailed information about each affected person in Brazil, but it has flaws in counting the number of cases, which are underreported. We aimed to construct and correct the cases dataset by linking different sources of data observations to study the pandemic evolution in Brazilian municipalities.
 ApproachUsing the electronic Unified Health System (e-SUS), a public and governmental database, we calculated the pandemic curves of COVID-19 cases. We applied the following approaches to investigate data anomalies a) to perform a descriptive analysis and compare these results with  a non-governmental database using Dynamic Time Warping distance; b) to verify and correct municipalities data anomalies linking to other public governmental database namely National Council of Health Secretaries (CONASS) with e-SUS. c) To apply a K-means DTW Barycenter Averaging in clustering analysis to describe the general behaviors of pandemic in Brazilian Municipalities.
 ResultsAround 10% records of cases in the e-SUS public governmental database were underreported. After the linkage and the data updating procedure, the time-dependent clustering analysis presents no anomalies and more interpretable results. The clustering analysis provided eight different behaviors of COVID-19 curves of cases. The degree of intensity for prevalence and incidence rates were identified according to eight clusters from the lowest to highest.
 ConclusionsUsing the matching procedure based on Dynamic Time Warping distance to correct the municipalities unreported cases, we provided a richer dataset to support a clustering time dependent analysis to characterize the Pandemic evolution in Brazil. These results may be explored in future deprivation social studies.

A new shape-based clustering algorithm for time series

Time series clustering is a research hotspot in data mining. Most of the existing clustering algorithms combine with the classical distance measure which ignore the offset of sequence shape. As a result, shape-based clustering algorithms are becoming increasingly popular. On the majority of data sets, the most representative shape-based clustering algorithm, KShape, which defines a shape-based distance with shift invariance, has been shown to outperform other algorithms.In this paper, we propose a new shape-based clustering algorithm named Fractional Order Shape-based k-cluster(FrOKShape), which defines a multi-variable shape-based distance by normalized fractional order cross-correlation and uses the DTW Barycenter Averaging (DBA) as a center computation strategy. Our distance exhibits excellent shape shift deviating properties and good compatibility integrated with a variety of existing clustering center strategies so that it can provide more potential good results. Experiments show that combining our distance with a traditional clustering algorithm produces excellent clustering indicators. In a series of comparative experiments, FrOKShape also exhibits a comparable result to the existing better shape-based clustering algorithm KShape.

Dynamic Time Warping Under Product Quantization, With Applications to Time-Series Data Similarity Search

The similarity search on sensor data generated by a myriad of sensing devices is a frequently encountered problem in the era of the Internet of Things (IoT). This sensor data generally appear in the form of time series, a temporally ordered sequence of real numbers obtained regularly in time. It has been widely accepted that the dynamic time warping (DTW) currently is the most prevalent similarity measure in the time-series mining community, mainly due to its flexibility and broad applicability. However, calculating DTW between two time series has quadratic time complexity, leading to unsatisfactory efficiency when performing the similarity search over the large time-series data set. The main contribution of this article is to propose a method called product quantization (PQ)-based DTW (PQDTW) for fast time-series approximate similarity search under DTW. The PQ, a well-known approximate nearest neighbor search approach, is used in PQDTW. Nevertheless, the conventional PQ is developed with the Euclidean distance and is not designed for DTW. To solve this problem, the DTW barycenter averaging (DBA) technique is utilized to adapt the PQ for DTW before using it. We employ PQDTW along with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">filter-and-refine</i> framework to efficiently and accurately perform the time-series similarity search. Our method can reasonably reduce many DTW computations in the filtering phase; thus, the query process is accelerated. We compare PQDTW with related popular algorithms using public time-series data sets. Experimental results verify that the proposal achieves the best tradeoff between query efficiency and retrieval accuracy compared to the competitors.

Plantar pressure-based temporal analysis of gait disturbance in idiopathic normal pressure hydrocephalus: Indications from a pilot longitudinal study

Background and Objective: Idiopathic normal pressure hydrocephalus (iNPH) is a common yet potentially reversible neurodegenerative disease, and gait disturbance is a major symptom. Lots of methodological and clinical work has been conducted on gait disturbance analysis for differential diagnosis, presurgical test, and postsurgery assessment of iNPH. Nevertheless, the verification analysis was mostly lacking for surgery response, and the temporal characteristics of ground reaction force has been rarely investigated.Methods: In this work, we propose that plantar pressure features fundamentally signifies iNPH gait disturbance and improvement after cerebrospinal fluid (CSF) drainage by lumbar puncture tap test as well as surgical shunt implantation. The plantar pressure signals of six iNPH patients and eight healthy controls were collected, and an online database of sixteen healthy controls were used. For patients, data were collected in five periods, which are the baseline before the tap test, 8, 24, and 72 hours after the tap test, and one month after the shunt implantation surgery, respectively. Fast dynamic time warping (DTW) with an improved DTW barycenter averaging (DBA) method was proposed for temporal analysis with the measured and online plantar pressure data. An plantar-pressure variation index (PPVI) was formulated to characterize the temporal dynamic stability of walking.Results: The PPVI based on temporal analysis of plantar pressure well discriminated the impaired gait (baseline, 24 and 72 hours after tap test) with the improved gait (8 hours after tap test and follow up after surgery) of the patients. Further, the PPVI was close for the improved gait of the patients and the healthy gait measured in our study as well as in the online database.Conclusions: Plantar pressure-based temporal features are promisingly effective for clinical examination and treatment of iNPH.

Online Signature Verification Using Locally Weighted Dynamic Time Warping via Multiple Fusion Strategies

Online signature verification is the process of using a dynamic signature verification system to confirm the writer’s identity. It can be used as a security system to confirm entrance applications and password substitutes, as well as a forensic tool to assist an expert’s investigation. This study proposes a novel online signature verification system based on a single-template strategy to improve performance in real-world scenarios. It employs discriminative mean signature template sets as well as fusion strategies of multiple local weighting and warping schemes, for dynamic time warping (DTW). The first step is to generate a set of user-specific mean signature templates for each feature using a recent time-series averaging method, namely, Euclidean barycenter-based DTW barycenter averaging. Then, using multiple and direct matching points between the mean signature templates and references for dependent and independent DTW, we obtain a local weighting estimate considering local stability sequences. Furthermore, we develop fusion strategies for calculating locally weighted DTW sets and concatenating them as a feature vector for each warping, followed by the construction of a support vector machine (SVM) classifier. Finally, in the verification phase, we use the single-template technique to compute a discriminative fused score using SVMs between the mean signature template sets and a query sample. The effectiveness of the proposed method is demonstrated by extensive experimental results obtained using three public online signature datasets: SVC2004 Task1/Task2 and MCYT-100.

An Improved Self-Training Method for Positive Unlabeled Time Series Classification Using DTW Barycenter Averaging.

Traditional supervised time series classification (TSC) tasks assume that all training data are labeled. However, in practice, manually labelling all unlabeled data could be very time-consuming and often requires the participation of skilled domain experts. In this paper, we concern with the positive unlabeled time series classification problem (PUTSC), which refers to automatically labelling the large unlabeled set U based on a small positive labeled set PL. The self-training (ST) is the most widely used method for solving the PUTSC problem and has attracted increased attention due to its simplicity and effectiveness. The existing ST methods simply employ the one-nearest-neighbor (1NN) formula to determine which unlabeled time-series should be labeled. Nevertheless, we note that the 1NN formula might not be optimal for PUTSC tasks because it may be sensitive to the initial labeled data located near the boundary between the positive and negative classes. To overcome this issue, in this paper we propose an exploratory methodology called ST-average. Unlike conventional ST-based approaches, ST-average utilizes the average sequence calculated by DTW barycenter averaging technique to label the data. Compared with any individuals in PL set, the average sequence is more representative. Our proposal is insensitive to the initial labeled data and is more reliable than existing ST-based methods. Besides, we demonstrate that ST-average can naturally be implemented along with many existing techniques used in original ST. Experimental results on public datasets show that ST-average performs better than related popular methods.

Semi-supervised Intrusive Appliance Load Monitoring in Smart Energy Monitoring System

Intrusive Load Monitoring (ILM) is a method to measure and collect the energy consumption data of individual appliances via smart plugs or smart sockets. A major challenge of ILM is automatic appliance identification, in which the system is able to determine automatically a label of the active appliance connected to the smart device. Existing ILM techniques depend on labels input by end-users and are usually under the supervised learning scheme. However, in reality, end-users labeling is laboriously rendering insufficient training data to fit the supervised learning models. In this work, we propose a semi-supervised learning (SSL) method that leverages rich signals from the unlabeled dataset and jointly learns the classification loss for the labeled dataset and the consistency training loss for unlabeled dataset. The samples fit into consistency learning are generated by a transformation that is built upon weighted versions of DTW Barycenter Averaging algorithm. The work is inspired by two recent advanced works in SSL in computer vision and combines the advantages of the two. We evaluate our method on the dataset collected from our developed Internet-of-Things based energy monitoring system in a smart home environment. We also examine the method’s performances on 10 benchmark datasets. As a result, the proposed method outperforms other methods on our smart appliance datasets and most of the benchmarks datasets, while it shows competitive results on the rest datasets.

Dimensionality Reduction and Motion Clustering During Activities of Daily Living: Decoupling Hand Location and Orientation.

This article is the second in a two-part series analyzing human arm and hand motion during a wide range of unstructured tasks. In this work, we track the hand of healthy individuals as they perform a variety of activities of daily living (ADLs) in three ways decoupled from hand orientation: end-point locations of the hand trajectory, whole path trajectories of the hand, and straight-line paths generated using start and end points of the hand. These data are examined by a clustering procedure to reduce the wide range of hand use to a smaller representative set. Hand orientations are subsequently analyzed for the end-point location clustering results and subsets of orientations are identified in three reference frames: global, torso, and forearm. Data driven methods that are used include dynamic time warping (DTW), DTW barycenter averaging (DBA), and agglomerative hierarchical clustering with Ward's linkage. Analysis of the end-point locations, path trajectory, and straight-line path trajectory identified 5, 5, and 7 ADL task categories, respectively, while hand orientation analysis identified up to 4 subsets of orientations for each task location, discretized and classified to the facets of a rhombicuboctahedron. Together these provide insight into our hand usage in daily life and inform an implementation in prosthetic or robotic devices using sequential control.

Time-series averaging and local stability-weighted dynamic time warping for online signature verification

To meet the recent demands for automated security systems, this study proposes a novel single-template strategy that uses mean templates and local stability-weighted dynamic time warping (LS-DTW) to simultaneously improve the speed and accuracy of online signature verification. Specifically, we adopt a recent time-series averaging method, called Euclidean barycenter-based DTW barycenter averaging (EB-DBA), to obtain an effective mean template set for each feature while preserving intra-user variability among reference samples. We then estimate the local stability of the mean template set by using direct matching points that represent stable signature regions in the DTW warping paths between the mean template set and the references. Subsequently, we boost the discriminative power in the verification phase using the LS-DTW distance measure that incorporates the local stability sequence as the weights for the DTW cost function between the mean template set and a query signature. Finally, we use the public SVC2004 Task2/MCYT-100 online signature datasets and the recent 3DAirSig in-air signature dataset to conduct experiments, whose results confirm the effectiveness of the proposed method in both the random- and skilled-forgery scenarios.

Information Granulation-Based Fuzzy Clustering of Time Series.

In this article, we propose a two-stage time-series clustering approach to cluster time series with different shapes. The first step is to represent the time series by a suite of information granules following the principle of justifiable granularity to perform dimensionality reduction, while the second step is to realize the fuzzy clustering of the time series in the transformed representation space (viz., the space of information granules). In the dimensionality reduction process, the numerical data are granulated using a collection of information granules forming a new sequence that can well describe the original time series. Then, when clustering the time series, dynamic time warping (DTW) is employed to measure the similarity between time series and DTW barycenter averaging (DBA) is generalized to weighted DBA to be involved in the fuzzy C -means (FCMs) algorithm. Finally, the experiments are conducted on the datasets coming from UCR time-series database and Chinese stocks to demonstrate the effectiveness and advantages of the proposed fuzzy clustering approach.

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.

Evaluation of Pattern Recognition Methods for Head Gesture-Based Interface of a Virtual Reality Helmet Equipped with a Single IMU Sensor.

The motivation of this paper is to examine the effectiveness of state-of-the-art and newly proposed motion capture pattern recognition methods in the task of head gesture classifications. The head gestures are designed for a user interface that utilizes a virtual reality helmet equipped with an internal measurement unit (IMU) sensor that has 6-axis accelerometer and gyroscope. We will validate a classifier that uses Principal Components Analysis (PCA)-based features with various numbers of dimensions, a two-stage PCA-based method, a feedforward artificial neural network, and random forest. Moreover, we will also propose a Dynamic Time Warping (DTW) classifier trained with extension of DTW Barycenter Averaging (DBA) algorithm that utilizes quaternion averaging and a bagged variation of previous method (DTWb) that utilizes many DTW classifiers that perform voting. The evaluation has been performed on 975 head gesture recordings in seven classes acquired from 12 persons. The highest value of recognition rate in a leave-one-out test has been obtained for DTWb and it equals 0.975 (0.026 better than the best of state-of-the-art methods to which we have compared our approach). Among the most important applications of the proposed method is improving life quality for people who are disabled below the neck by supporting, for example, an assistive autonomous power chair with a head gesture interface or remote controlled interfaces in robotics.

Enhanced time-aware QoS prediction in multi-cloud: a hybrid k-medoids and lazy learning approach (QoPC)

Cloud service providers should be able to predict the future states of their infrastructure in order to avoid any violation of Service Level Agreement. This becomes more complex when vendors have to deal with services from various providers in multi-clouds. As a result, QoS prediction can significantly support service providers in a better understanding of their resources future states. Users should also be very well aware of their resource needs, as well as the Quality of Service relative values. This paper proposes a hybrid approach to the prediction of the future value of the QoS features. The hybrid approach uses a modified version of k-medoids algorithm for the clustering of large time-series datasets, as well as a proposed algorithm inspired from the lazy learning and lower bound Dynamic Time Warping (LB-Keogh) for pruned DTW computations. The proposed method in this manuscript is a shape-based QoS prediction with a novel pre-processing method, which fulfills the missing data with statistically semi-real data. In order to solve the cold start problem, we proposed new algorithm based on the DTW Barycenter Averaging (DBA) algorithm. The results showed that our predicted values are very close to real values and achieve only 0.35 of the normalized mean absolute error rate, on average, for the WSDream dataset and 0.07 for the Alibaba dataset.

Adaptive Global Time Sequence Averaging Method Using Dynamic Time Warping

Time sequence averaging under dynamic time warping (DTW) is a non-trivial problem, and its exact solution requires unrealistic computational complexity in practice. The DTW barycenter averaging (DBA) method is one of the most effective iterative approximation solutions to date. However, there are still a few drawbacks in the DBA method. First, the length of the resulting average sequence depends on the selected initial average sequence; second, the discrepancy distance between the resulting average sequence and target sequence set is highly sensitive to the initialization, as we have demonstrated through the experiments described here. In this study, we propose an adaptive DBA (ADBA) algorithm to address these drawbacks. We define a scaling coefficient based on the DTW alignments such that the temporal aberrations between the average sequence and target sequence set can be qualitatively captured. The algorithm is realized by an iterative process. For each iteration, the temporary average sequence and target sequence set are partitioned into several aligned subsequence sets according to the variation in the signs of the scaling coefficients. Then, these partitioned average subsequences are adaptively compressed or stretched such that the average discrepancy distance and overall temporal aberration can be locally minimized. The comparison experiments carried out on the standard datasets illustrate that the proposed algorithm achieves lower average discrepancy distance, overall temporal aberration, and higher robustness than the available methods. Additionally, the proposed algorithm is verified by an accelerometer-based hand gesture recognition system, where ADBA produces more effective gesture templates.