Representation Of Time Series Research Articles

Improved global 250 m 8-day NDVI and EVI products from 2000–2021 using the LSTM model

Satellite vegetation index (VI) products, such as normalized difference vegetation index (NDVI) and enhanced vegetation index (EVI), have been widely used. However, they are severely contaminated by clouds and other factors and provide false signals of the surface vegetation conditions. In this study, the new global seamless 250 m, eight-day NDVI and EVI products from 2000–2021 were developed from Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance data using a long short-term memory (LSTM) neural network method. High-quality globally representative time series VI samples were constructed to train the model using a combination of the Savitzky-Golay filter (SG), Global LAnd Surface Satellite (GLASS) leaf area index (LAI) fitting and upper envelope methods. To evaluate the proposed method and the 250 m VI products, the MODIS VI product (MOD13Q1) was used for the inter-comparisons using four widely used VI reconstruction methods. Assuming that the MODIS VI data of high quality represents the true values, the root mean square error (RMSE) for NDVI and EVI generated by the LSTM model are 0.0734 and 0.0509, respectively.

TS-TWC: A time series representation learning framework based on Time-Wavelet contrasting

Nowadays, labeling time series datasets requires specialized knowledge and is time-consuming. Moreover, transfer learning faces a gap between the source and target domains. Therefore, we propose a Time Series representation learning framework based on Time-Wavelet Contrasting (TS-TWC) in this paper. It is pre-trained on unlabeled samples and fine-tuned on a small amount of labeled data. The features in the wavelet domain are used as a complement and are called wavelet series. First, the time series and its wavelet series are augmented by an attention-based augmentation structure. Then, a Time-Wavelet contrasting module contrasts the time series with its augmented data, as well as the time series views with their corresponding wavelet series views. In addition, a triple-view contrasting module uses the Daubechies and Haar wavelet bases to increase the number of views for contrastive learning. The aim is to reduce the pre-training batch size and improve the learning effect. In the fine-tuning and inference stages, this module also includes a tri-view fusion structure to assist in learning or extracting discriminative representations. Finally, our model is tested on five pairs of datasets using transfer learning. Experiments show that the proposed framework is effective in learning transferable representations in pre-training and obtaining discriminative representations in fine-tuning. It outperforms the state-of-the-art models on most of the metrics.

A new network representation for time series analysis from the perspective of combinatorial property of ordinal patterns

Revealing system behavior from observed time series is a fundamental problem worthy of in-depth study and exploration, and has attracted extensive attention in a wide range of fields due to its wide application values. In this paper, we propose a novel network construction method for time series analysis, which is different from the existing ordinal network method concerning the transition probability of ordinal patterns in transition networks. The proposed network representation is based on the combinatorial property concerning the inversion number of ordinal patterns from the ordinal partitions of time series. For the proposed network construction method, the network nodes are represented by each ordinal partition of time series and the edge weight between network nodes is determined by a novel proximity relationship of ordinal patterns which is a newly defined metric based on the inversion number of ordinal patterns. Using random signals and chaotic signals as examples, we demonstrate the potential of the proposed network construction method for the network representation of time series. We also employ the proposed network construction method in quantitative EEG for the identification of three different physiological and pathological brain states. According to the results of AUC values, one can observe that the discriminating power of the AND of the proposed network construction method is slightly stronger than that of the available ordinal network. The experimental results illustrate that our proposed network construction method opens up a new pathway for network representation of time series, which is capable of quantifying time series for feature extraction and pattern learning for time series analysis.

A Shapelet-Based Framework for Unsupervised Multivariate Time Series Representation Learning

Recent studies have shown great promise in unsupervised representation learning (URL) for multivariate time series, because URL has the capability in learning generalizable representation for many downstream tasks without using inaccessible labels. However, existing approaches usually adopt the models originally designed for other domains (e.g., computer vision) to encode the time series data and rely on strong assumptions to design learning objectives, which limits their ability to perform well. To deal with these problems, we propose a novel URL framework for multivariate time series by learning time-series-specific shapelet-based representation through a popular contrasting learning paradigm. To the best of our knowledge, this is the first work that explores the shapelet-based embedding in the unsupervised general-purpose representation learning. A unified shapelet-based encoder and a novel learning objective with multi-grained contrasting and multi-scale alignment are particularly designed to achieve our goal, and a data augmentation library is employed to improve the generalization. We conduct extensive experiments using tens of real-world datasets to assess the representation quality on many downstream tasks, including classification, clustering, and anomaly detection. The results demonstrate the superiority of our method against not only URL competitors, but also techniques specially designed for downstream tasks. Our code has been made publicly available at https://github.com/real2fish/CSL.

Deep Temporal State Perception Toward Artificial Cyber–Physical Systems

Cyber-Physical systems, as the cornerstone of smart city, has been attracting great interest from academia and industry. It aims to monitor/ control physical components via communication and computation, while ensuring effectiveness, intelligence, and security. The related research has pointed that the state perception on physical device is the prerequisite for boosting overall CPS performance. Towards this end, we present an effective deep temporal perception networks to achieve classification based state detection. Namely, we first design a multi-feature encoding network for multi-view time series representation. Concretely, on the one hand, we utilize two piecewise aggregate representation strategies to obtain the key temporal trends; on the other hand, we adopt a temporal symbolic representation strategy to capture the necessary contextual semantic correlations. Thereafter, we develop a comprehensive representation enhancement module to improve feature comprehension capability, and thus boosting the overall performance and interpretability. Corresponding comparison experiments, ablation studies, and data visualization analyses on benchmark datasets have verified the effectiveness of our model.

Dimensionality reduction and features visual representation based on conditional probabilities applied to activity classification

A large part of the information emitted by contemporary technological devices comes in the form of time series. The massive commercialization of these kinds of devices has made the study of time series feature extraction techniques acquire a vital relevance in last years. Two main things are essential when applying feature extraction techniques to time series: to reduce the dimensionality so it occupies the least amount of storage memory possible, and to make features that contain the relevant information regarding the nature of the data set and the goals to be achieved. For this purpose, we propose in this work a brand new technique called the State Changes Representation for Time Series (SCRTS), which relies on the relevant data associated with the conditional probabilities of the time series (also known in the literature as Markov model’s features), and the distribution of its values. This method is length-independent, which means that we can apply it to time series of different dimensions obtaining the same number of features for each one. Also, it provides a visual representation of the input data, so it is possible to interpret what makes a certain time series different from the other. After explaining how it works, we apply it to 3 different wearable accelerometer data sets. This algorithm reduces the original dimension of the time series considerably (in the best case from 5499 values to 31), having a good performance in the classification results (in the best chance with an accuracy of 98%).

On the use of matrix profiles and optimal transport theory for multivariate time series anomaly detection within structural health monitoring

In order for a practical application of structural health monitoring to be considered successful, not only is the detection of anomalies important but so is the tracking of various other behaviors, which may be induced by changing operational conditions or environmental variations. Rather than being problems of anomaly detection, these are known as problems of changing contexts or changing semantics. In this paper, we propose a novel, and efficient method which is able to perform both tasks: anomaly detection, and semantic analysis, simultaneously, and which is also able to scale to a multi-sensor network array. The proposed methodology works to combine a recent development from the field of time series data mining known as matrix profiling, as well as ideas from a popular area of mathematics known as optimal transport theory. In particular, matrix profiles will be used to generate curves of semantic segmentation, over multivariate time series data. From here, it will be demonstrated that by finding the unbalanced optimal transport barycenter one can successfully pool together information from a sensor array network in such a way that the presence of false positive transition points is reduced significantly when compared to the baseline mean. Moreover, this will be demonstrated to occur in a hierarchical fashion by employing a variational mode decomposition across each sensor in the network array. Overall, the proposed methodology: (i) Can work in the small data context without requiring a large amount of data for model training and validation, (ii) Applies readily to unsupervised and semi-supervised learning settings, (iii) Can extend to the online learning setting, (iv) Is adaptable and robust for sensor array network problems, (v) Does not require specifying any threshold, and (vi) Is highly interpretable. Finally, the proposed methodology will be validated on three different levels of investigation: (i) A numerical dataset of an aerospace model based on a two-dimensional plate model, (ii) An experimental dataset of a building from Los Alamos National Laboratories, and finally, (iii) A field investigation on a cable-stayed bridge located in Sydney, Australia.

PARSE: A personalized clinical time-series representation learning framework via abnormal offsets analysis

Background and objective:Clinical risk prediction of patients is an important research issue in the field of healthcare, which is of great significance for the diagnosis, treatment and prevention of diseases. In recent years, a large number of deep learning-based methods have been proposed for clinical prediction by mining relevant features of patients' health condition from historical Electronic Health Records (EHRs) data. However, most of these existing methods only focus on discovering the time series characteristics of physiological indexes such as laboratory tests and physical examinations, and fail to comprehensively consider the deviation degree of these physiological indexes from the normal range and their stability, thus greatly limiting the prediction performance.Methods:We propose a personalized clinical time-series representation learning framework via abnormal offsets analysis named PARSE for clinical risk prediction. In PARSE, while extracting relevant temporal features from the original EHR data, we further capture relevant features of abnormal condition as complementary information from the absolute offset of each physiological index's observed values from its normal value and the relative offset between each physiological index's observed values in two adjacent time steps. Finally, an adaptive fusion module is introduced to effectively integrate the above features to obtain the personalized patient's representations for clinical risk prediction.Results:We conduct an in-hospital mortality prediction task on two public real-world datasets. PARSE achieves the highest F1 scores of 48.1% and 40.3%, outperforming the state-of-the-art methods with a boost of 2.4% and 6.2% on two datasets respectively. Furthermore, the results of ablation experiments demonstrate that the two abnormal offsets and the proposed adaptive fusion method are contributing.Conclusions:PARSE can better extract the risk-related information from the EHRs data and improve the personalization of the patients' representations. Each part of PARSE improves the final prediction performance independently.

A hybrid VMD based contextual feature representation approach for wind speed forecasting

Accurate wind speed prediction is critical for efficient power system operation, regulation, security analysis, and energy trading. However, the stochastic nature of the wind makes wind speed forecasting (WSF) difficult. Thus, a novel hybrid WSF approach termed VMD-Ts2Vec-SVR comprising variational mode decomposition (VMD), contextual time series representation (Ts2Vec) model, and support vector regression (SVR) is proposed. In the proposed approach, VMD is used to decompose the raw input wind speed for denoising, and extracting the main features of the original series, Ts2Vec model is used to learn the sequential contextual representations in all semantic levels from the denoised series, and SVR is used to predict the future wind speed from the contextual representation. Two experiments are performed for testing the proposed approach using wind speed dataset collected from Leicester, and Portland wind farms. For validation of the proposed approach for different time intervals, it is tested for 5-min, 10-min, 15-min, 30-min, 1-h, and 2-h ahead WSF. The performance of the proposed approach is compared with seven individual models, seven hybrid VMD based models for better validation. Two experiments demonstrated both the proposed approach’s superior performance across all time horizons and its viability for the WSF.

Weathergami

Abstract Adapted from the sports concept of scorigami, the weathergami chart is introduced. Weathergami charts depict the frequency of occurrence of the full range of daily maximum and minimum temperature combinations observed at a location. These charts highlight essential features of climate not evident in traditional representations. A variation of the weathergami chart displays transition frequencies, which describe the likelihood of particular day-to-day changes in maximum and minimum temperatures. Likewise, weathergami anomaly charts reveal characteristics of changing climate not evident in standard time series representations. Several examples are provided, with comparisons to climate descriptions found in popular textbooks.

Sensing in the swarm: Spectro-temporal variation may facilitate self-recognition of echoes for bats flying in dense groups

Most biosonar models predict that bats rely on the correct assignment of an echo from a broadcast signal to successfully perceive their environment, which should be difficult for bats in dense groups. Brazilian free-tailed bats (Tadarida brasiliensis) form some of the largest aggregations on the planet and have flexible characteristics of their echolocation signals. We hypothesize they use subtle variations in spectro-temporal characteristics to facilitate echolocation in dense groups. To record from inside the swarm, we used both a stationary microphone that opportunistically captured the passing bat swarm, and a custom video and acoustic recorder carried by a trained hawk that flew through the swarm. We computed spectrograms from the acoustic recordings and extracted “time-frequency ridges.” These ridges were fit to low-order polynomials to generate model frequency modulation functions, which in turn uniquely determine continuous time-series representations of modeled emission waveforms. Standard signal detection methods (cross correlation and background normalization) enabled quantitative estimation of detection performance, including rejection of interfering emissions and echoes. Our results demonstrate that subtle but specific variation in spectro-temporal shape can constitute the basis of call differentiation, which may be an adaptive strategy used to reject acoustic signals from conspecifics when echolocating in dense swarms.

RIFT: Pretraining and Applications for Representations of Interrelated Financial Time Series

RIFT: Pretraining and Applications for Representations of Interrelated Financial Time Series

Enhancement of Electromagnetic Scattering Computation Acceleration Using LSTM Neural Networks

This paper presents the electromagnetic long short-term memory neural network (EM-LSTMNN) approach to accelerate radar cross-section (RCS) calculations in optimizing low RCS for electrically large targets. The proposed method converts the conventional electromagnetic numerical calculation into an efficient numerical calculation using the LSTM neural network, resulting in a significant improvement in RCS computation speed. To assess the effectiveness of this approach, a downscaled model of a large-sized ship is employed as the target for low RCS optimization. Each modification made to the target’s mesh data during the optimization process is stored in the dataset as a new element. As the ship scaling model undergoes modifications during the optimization process, the new mesh data are recorded, thus adding a new element to the dataset at each time step. This forms a time series representation of the mesh model. By utilizing the dataset collected throughout the optimization process, the proposed EM-LSTMNN model is trained using data-driven approaches, with a training time of approximately 106 s. It is worth noting that this training time is significantly smaller compared to existing methods that employ fully connected neural networks. The performance of the proposed approach is demonstrated by comparing the RCS calculation results obtained through this method with those obtained through traditional electromagnetic simulations.

An adaptive embedding procedure for time series forecasting with deep neural networks

Nowadays, solving time series prediction problems is an open and challenging task. Many solutions are based on the implementation of deep neural architectures, which are able to analyze the structure of the time series and to carry out the prediction. In this work, we present a novel deep learning scheme based on an adaptive embedding mechanism. The latter is exploited to extract a compressed representation of the input time series that is used for the subsequent forecasting. The proposed model is based on a two-layer bidirectional Long Short-Term Memory network, where the first layer performs the adaptive embedding and the second layer acts as a predictor. The performances of the proposed forecasting scheme are compared with several models in two different scenarios, considering both well-known time series and real-life application cases. The experimental results show the accuracy and the flexibility of the proposed approach, which can be used as a prediction tool for any actual application.

Contextual Explanations for Decision Support in Predictive Maintenance

Explainable artificial intelligence (XAI) methods aim to explain to the user on what basis the model makes decisions. Unfortunately, general-purpose approaches that are independent of the types of data, model used and the level of sophistication of the user are not always able to make model decisions more comprehensible. An example of such a problem, which is considered in this paper, is a predictive maintenance task where a model identifying outliers in time series is applied. Typical explanations of the model’s decisions, which present the importance of the attributes, are not sufficient to support the user for such a task. Within the framework of this work, a visualisation and analysis of the context of local explanations presenting attribute importance are proposed. Two types of context for explanations are considered: local and global. They extend the information provided by typical explanations and offer the user greater insight into the validity of the alarms triggered by the model. Evaluation of the proposed context was performed on two time series representations: basic and extended. For the extended representation, an aggregation of explanations was used to make them more intuitive for the user. The results show the usefulness of the proposed context, particularly for the basic data representation. However, for the extended representation, the aggregation of explanations used is sometimes insufficient to provide a clear explanatory context. Therefore, the explanation using simplification with a surrogate model on basic data representation was proposed as a solution. The obtained results can be valuable for developers of decision support systems for predictive maintenance.

Bidirectional piecewise linear representation of time series with application to collective anomaly detection

Directly mining high-dimensional time series presents several challenges, such as time and space costs. This study proposes a new approach for representing time series data and evaluates its effectiveness in detecting collective anomalies. The proposed method, called bidirectional piecewise linear representation (BPLR), represents the original time series using a set of linear fitting functions, which allows for dimensionality reduction while maintaining its dynamic characteristics. Similarity measurement is then performed using the piecewise integration (PI) approach, which achieves good detection performance with low computational overhead. Experimental results on synthetic and real-world data sets confirm the effectiveness and advantages of the proposed approach. The ability of the proposed method to capture more dynamic details of time series leads to consistently superior performance compared to other existing methods.

Spatial and Temporal Deep Learning in Air-Coupled Ultrasonic Testing for Enabling NDE 4.0

Air-coupled ultrasonic (ACU) testing has been used for several years to detect defects in plate-like structures. Especially, for automated testing procedures, ACU testing is advantageous in comparison to conventional testing. However, the evaluation of the measurement data is usually done in a manual manner, which is an obstruction to the application of ACU testing. The goal of this study is to automate and improve defect characterization and NDE 4.0 accordingly with deep learning. In conventional ACU testing the measurement data contains temporal (A-scans) and spatial (C-scans) information. Both data types are investigated in this study. For the A-scans, which represent time series data, neural network architectures tailored to such data types are applied. In addition, it is evaluated if further adaptions of the training procedure increase the performance. The C-scans are segmented by applying different U-net similar architectures and training strategies. In order to use spatial and temporal information, a further approach is taken. The prediction of the time series models is segmented with image models. The performance of all trained models and training strategies is compared with the F1-score and benchmarked against the conventional evaluation, which is thresholding of the C-scans. As specimens, artificial defects in acrylic and carbon fiber-reinforced polymer plates are investigated.

Predicting Financial Time Series for Value Investment

Value investment is an attractive paradigm for individual investors. It involves different steps including evaluating past performance that could be challenging. We propose a representation for financial time series in a form appropriate for both human interpretation and automatic processing. We design a model for predicting sequence of values as opposed to point values. Combined with application of encoder-decoder type of neural network model architecture this allows interpretation of model parameters and intermediate activations by domain experts. We show that predictions better than the trivial last observed value are possible. Therefore, informed investment decisions can be supported by neural network models and the proposed representation and model interpretation.

Predicting Online Item-Choice Behavior: A Shape-Restricted Regression Approach

This paper examines the relationship between user pageview (PV) histories and their itemchoice behavior on an e-commerce website. We focus on PV sequences, which represent time series of the number of PVs for each user–item pair. We propose a shape-restricted optimization model that accurately estimates item-choice probabilities for all possible PV sequences. This model imposes monotonicity constraints on item-choice probabilities by exploiting partial orders for PV sequences, according to the recency and frequency of a user’s previous PVs. To improve the computational efficiency of our optimization model, we devise efficient algorithms for eliminating all redundant constraints according to the transitivity of the partial orders. Experimental results using real-world clickstream data demonstrate that our method achieves higher prediction performance than that of a state-of-the-art optimization model and common machine learning methods.

Adaptive error bounded piecewise linear approximation for time-series representation

Error-bounded piecewise linear approximation (l∞-PLA) has been proven effective in addressing challenges in data management and analytics. It works by approximating the original time series with linear segments such that the approximation error on each data point does not exceed a pre-defined threshold. To achieve this goal, most prior works on l∞-PLA use a fixed error threshold during the entire approximation process, assuming a stable time series. However, in many real-world applications, the distribution of values on the time series undergoes substantial changes in different temporal stages. This introduces a need to adaptively tune the error threshold based on the properties of the time series while considering the trade-off between representation error and storage resources. In this work, we propose a general framework for constructing l∞-PLA with adaptive error bounds (AEPLA). It works by dividing the original time series into a set of intervals and assigns adaptive error bounds to these sub-sequences based on their fluctuation levels. Next, these sub-sequences are approximated using a user-defined l∞-PLA method. We implement this framework by employing three different types of l∞-PLA methods and evaluate the performance of our approach on an extensive set of real-world time-series datasets from industrial and scientific domains. Our experiments show that constructing l∞-PLA using the AEPLA framework can provide better a trade-off between representation error and storage resources and achieves lower time and space costs than applying the original l∞-PLA methods.