AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

Multivariate Time Series Anomaly Detection Based on Spatial-Temporal Network and Transformer in Industrial Internet of Things

In the Industrial Internet of Things(IIoT),sensors generate time series data to reflect the working state.When the systems are attacked,timely identification of outliers in time series is critical to ensure security.Although many anomaly detection methods have been proposed,the temporal correlation of the time series over the same sensor and the state(spatial)correlation between different sensors are rarely considered simultaneously in these methods.Owing to the superior capability of Transformer in learning time series features.This paper proposes a time series anomaly detection method based on a spatial-temporal network and an improved Transformer.Additionally,the methods based on graph neural networks typically include a graph structure learning module and an anomaly detection module,which are interdependent.However,in the initial phase of training,since neither of the modules has reached an optimal state,their performance may influence each other.This scenario makes the end-to-end training approach hard to effectively direct the learning trajectory of each module.This interdependence between the modules,coupled with the initial instability,may cause the model to find it hard to find the optimal solution during the training process,resulting in unsatisfactory results.We introduce an adaptive graph structure learning method to obtain the optimal model parameters and graph structure.Experiments on two publicly available datasets demonstrate that the proposed method attains higher anomaly detection results than other methods.

Fine-Grained Multivariate Time Series Anomaly Detection in IoT

Sensors produce a large amount of multivariate time series data to record the states of Internet of Things(IoT)systems.Multivariate time series timestamp anomaly detection(TSAD)can identify timestamps of attacks and malfunctions.However,it is necessary to determine which sensor or indicator is abnormal to facilitate a more detailed diagnosis,a process referred to as fine-grained anomaly detection(FGAD).Although further FGAD can be extended based on TSAD methods,existing works do not provide a quantitative evaluation,and the performance is unknown.Therefore,to tackle the FGAD problem,this paper first verifies that the TSAD methods achieve low performance when applied to the FGAD task directly because of the excessive fusion of features and the ignoring of the relationship’s dynamic changes between indicators.Accordingly,this paper proposes a mul-tivariate time series fine-grained anomaly detection(MFGAD)framework.To avoid excessive fusion of features,MFGAD constructs two sub-models to independently identify the abnormal timestamp and abnormal indicator instead of a single model and then combines the two kinds of abnormal results to detect the fine-grained anomaly.Based on this framework,an algorithm based on Graph Attention Neural Network(GAT)and Attention Convolutional Long-Short Term Memory(A-ConvLSTM)is proposed,in which GAT learns temporal features of multiple indicators to detect abnormal timestamps and A-ConvLSTM captures the dynamic relationship between indicators to identify abnormal indicators.Extensive simulations on a real-world dataset demonstrate that the proposed algorithm can achieve a higher F1 score and hit rate than the extension of existing TSAD methods with the benefit of two independent sub-models for timestamp and indicator detection.

A Memory-Guided Anomaly Detection Model with Contrastive Learning for Multivariate Time Series

Some reconstruction-based anomaly detection models in multivariate time series have brought impressive performance advancements but suffer from weak generalization ability and a lack of anomaly identification.These limitations can result in the misjudgment of models,leading to a degradation in overall detection performance.This paper proposes a novel transformer-like anomaly detection model adopting a contrastive learning module and a memory block(CLME)to overcome the above limitations.The contrastive learning module tailored for time series data can learn the contextual relationships to generate temporal fine-grained representations.The memory block can record normal patterns of these representations through the utilization of attention-based addressing and reintegration mechanisms.These two modules together effectively alleviate the problem of generalization.Furthermore,this paper introduces a fusion anomaly detection strategy that comprehensively takes into account the residual and feature spaces.Such a strategy can enlarge the discrepancies between normal and abnormal data,which is more conducive to anomaly identification.The proposed CLME model not only efficiently enhances the generalization performance but also improves the ability of anomaly detection.To validate the efficacy of the proposed approach,extensive experiments are conducted on well-established benchmark datasets,including SWaT,PSM,WADI,and MSL.The results demonstrate outstanding performance,with F1 scores of 90.58%,94.83%,91.58%,and 91.75%,respectively.These findings affirm the superiority of the CLME model over existing stateof-the-art anomaly detection methodologies in terms of its ability to detect anomalies within complex datasets accurately.

A prediction comparison between univariate and multivariate chaotic time series

The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.

Generating Adversarial Samples on Multivariate Time Series using Variational Autoencoders

Classification models for multivariate time series have drawn the interest of many researchers to the field with the objective of developing accurate and efficient models.However,limited research has been conducted on generating adversarial samples for multivariate time series classification models.Adversarial samples could become a security concern in systems with complex sets of sensors.This study proposes extending the existing gradient adversarial transformation network(GATN)in combination with adversarial autoencoders to attack multivariate time series classification models.The proposed model attacks classification models by utilizing a distilled model to imitate the output of the multivariate time series classification model.In addition,the adversarial generator function is replaced with a variational autoencoder to enhance the adversarial samples.The developed methodology is tested on two multivariate time series classification models:1-nearest neighbor dynamic time warping(1-NN DTW)and a fully convolutional network(FCN).This study utilizes 30 multivariate time series benchmarks provided by the University of East Anglia(UEA)and University of California Riverside(UCR).The use of adversarial autoencoders shows an increase in the fraction of successful adversaries generated on multivariate time series.To the best of our knowledge,this is the first study to explore adversarial attacks on multivariate time series.Additionally,we recommend future research utilizing the generated latent space from the variational autoencoders.

Multivariate time series prediction based on AR_CLSTM

Time series is a kind of data widely used in various fields such as electricity forecasting,exchange rate forecasting,and solar power generation forecasting,and therefore time series prediction is of great significance.Recently,the encoder-decoder model combined with long short-term memory(LSTM)is widely used for multivariate time series prediction.However,the encoder can only encode information into fixed-length vectors,hence the performance of the model decreases rapidly as the length of the input sequence or output sequence increases.To solve this problem,we propose a combination model named AR_CLSTM based on the encoder_decoder structure and linear autoregression.The model uses a time step-based attention mechanism to enable the decoder to adaptively select past hidden states and extract useful information,and then uses convolution structure to learn the internal relationship between different dimensions of multivariate time series.In addition,AR_CLSTM combines the traditional linear autoregressive method to learn the linear relationship of the time series,so as to further reduce the error of time series prediction in the encoder_decoder structure and improve the multivariate time series Predictive effect.Experiments show that the AR_CLSTM model performs well in different time series predictions,and its root mean square error,mean square error,and average absolute error all decrease significantly.

Generic reconstruction technology based on RST for multivariate time series of complex process industries

In order to effectively analyse the multivariate time series data of complex process,a generic reconstruction technology based on reduction theory of rough sets was proposed,Firstly,the phase space of multivariate time series was originally reconstructed by a classical reconstruction technology.Then,the original decision-table of rough set theory was set up according to the embedding dimensions and time-delays of the original reconstruction phase space,and the rough set reduction was used to delete the redundant dimensions and irrelevant variables and to reconstruct the generic phase space,Finally,the input vectors for the prediction of multivariate time series were extracted according to generic reconstruction results to identify the parameters of prediction model.Verification results show that the developed reconstruction method leads to better generalization ability for the prediction model and it is feasible and worthwhile for application.

Production performance forecasting method based on multivariate time series and vector autoregressive machine learning model for waterflooding reservoirs

A forecasting method of oil well production based on multivariate time series(MTS)and vector autoregressive(VAR)machine learning model for waterflooding reservoir is proposed,and an example application is carried out.This method first uses MTS analysis to optimize injection and production data on the basis of well pattern analysis.The oil production of different production wells and water injection of injection wells in the well group are regarded as mutually related time series.Then a VAR model is established to mine the linear relationship from MTS data and forecast the oil well production by model fitting.The analysis of history production data of waterflooding reservoirs shows that,compared with history matching results of numerical reservoir simulation,the production forecasting results from the machine learning model are more accurate,and uncertainty analysis can improve the safety of forecasting results.Furthermore,impulse response analysis can evaluate the oil production contribution of the injection well,which can provide theoretical guidance for adjustment of waterflooding development plan.

A Novel Graph Structure Learning Based Semi-Supervised Framework for Anomaly Identification in Fluctuating IoT Environment

With the rapid development of Internet of Things(IoT)technology,IoT systems have been widely applied in health-care,transportation,home,and other fields.However,with the continuous expansion of the scale and increasing complexity of IoT systems,the stability and security issues of IoT systems have become increasingly prominent.Thus,it is crucial to detect anomalies in the collected IoT time series from various sensors.Recently,deep learning models have been leveraged for IoT anomaly detection.However,owing to the challenges associated with data labeling,most IoT anomaly detection methods resort to unsupervised learning techniques.Nevertheless,the absence of accurate abnormal information in unsupervised learning methods limits their performance.To address these problems,we propose AS-GCN-MTM,an adaptive structural Graph Convolutional Networks(GCN)-based framework using a mean-teacher mechanism(AS-GCN-MTM)for anomaly identification.It performs better than unsupervised methods using only a small amount of labeled data.Mean Teachers is an effective semi-supervised learning method that utilizes unlabeled data for training to improve the generalization ability and performance of the model.However,the dependencies between data are often unknown in time series data.To solve this problem,we designed a graph structure adaptive learning layer based on neural networks,which can automatically learn the graph structure from time series data.It not only better captures the relationships between nodes but also enhances the model’s performance by augmenting key data.Experiments have demonstrated that our method improves the baseline model with the highest F1 value by 10.4%,36.1%,and 5.6%,respectively,on three real datasets with a 10%data labeling rate.

STDNet: A Spatio-Temporal Decomposition Neural Network for Multivariate Time Series Forecasting

Long-term multivariate time series forecasting is an important task in engineering applications. It helps grasp the future development trend of data in real-time, which is of great significance for a wide variety of fields. Due to the non-linear and unstable characteristics of multivariate time series, the existing methods encounter difficulties in analyzing complex high-dimensional data and capturing latent relationships between multivariates in time series, thus affecting the performance of long-term prediction. In this paper, we propose a novel time series forecasting model based on multilayer perceptron that combines spatio-temporal decomposition and doubly residual stacking, namely Spatio-Temporal Decomposition Neural Network (STDNet). We decompose the originally complex and unstable time series into two parts, temporal term and spatial term. We design temporal module based on auto-correlation mechanism to discover temporal dependencies at the sub-series level, and spatial module based on convolutional neural network and self-attention mechanism to integrate multivariate information from two dimensions, global and local, respectively. Then we integrate the results obtained from the different modules to get the final forecast. Extensive experiments on four real-world datasets show that STDNet significantly outperforms other state-of-the-art methods, which provides an effective solution for long-term time series forecasting.

MULTIVARIATE ABSOLUTE DEGREE OF GREY INCIDENCE BASED ON DISTRIBUTION CHARACTERISTICS OF POINTS

The analysis result of absolute degree of grey incidence for multivariate time series is often inconsistent with the qualitative analysis. To overcome this shortage, a multivariate absolute degree of grey incidence based on distribution characteristics of points is proposed. Based on the geometric description of multivariate time se- ries, the neighborhood extrema are extracted in the different regions, and a characteristic point set is constructed. Then according to the distribution of the characteristic point set, a characteristic point sequence reflecting the ge- ometric features of multivariate time series is obtained. The incidence analysis between multivariate time series is transformed into the relational analysis between characteristic point sequences, and a grey incidence model is established. The model possesses the properties of translational invariance, transpose and rank transform invari- ance, and satisfies the grey incidence analysis axioms. Finally, two cases are studied and the results prove the ef- fectiveness of the model.

A multivariate grey incidence model for different scale data based on spatial pyramid pooling

In order to solve the problem that existing multivariate grey incidence models cannot be applied to time series on different scales, a new model is proposed based on spatial pyramid pooling.Firstly, local features of multivariate time series on different scales are pooled and aggregated by spatial pyramid pooling to construct n levels feature pooling matrices on the same scale. Secondly,Deng's multivariate grey incidence model is introduced to measure the degree of incidence between feature pooling matrices at each level. Thirdly, grey incidence degrees at each level are integrated into a global incidence degree. Finally, the performance of the proposed model is verified on two data sets compared with a variety of algorithms. The results illustrate that the proposed model is more effective and efficient than other similarity measure algorithms.

Identifying,exploring,and interpreting time series shapes in multivariate time intervals

We introduce a concept of episode referring to a time interval in the development of a dynamic phenomenon that is characterized by multiple time-variant attributes.A data structure representing a single episode is a multivariate time series.To analyse collections of episodes,we propose an approach that is based on recognition of particular patterns in the temporal variation of the variables within episodes.Each episode is thus represented by a combination of patterns.Using this representation,we apply visual analytics techniques to fulfil a set of analysis tasks,such as investigation of the temporal distribution of the patterns,frequencies of transitions between the patterns in episode sequences,and co-occurrences of patterns of different variables within same episodes.We demonstrate our approach on two examples using real-world data,namely,dynamics of human mobility indicators during the COVID-19 pandemic and characteristics of football team movements during episodes of ball turnover.

A Total Variation Based Method for Multivariate Time Series Segmentation

Multivariate time series segmentation is an important problem in data mining and it has arisen in more and more practical applications in recent years.The task of time series segmentation is to partition a time series into segments by detecting the abrupt changes or anomalies in the time series.Multivariate time series segmentation can provide meaningful information for further data analysis,prediction and policy decision.A time series can be considered as a piecewise continuous function,it is natural to take its total variation norm as a prior information of this time series.In this paper,by minimizing the negative log-likelihood function of a time series,we propose a total variation based model for multivariate time series segmentation.An iterative process is applied to solve the proposed model and a search combined the dynamic programming method is designed to determine the breakpoints.The experimental results show that the proposed method is efficient for multivariate time series segmentation and it is competitive to the existing methods for multivariate time series segmentation.

Multivariate Time Series Forecasting with Transfer Entropy Graph

Multivariate Time Series(MTS)forecasting is an essential problem in many fields.Accurate forecasting results can effectively help in making decisions.To date,many MTS forecasting methods have been proposed and widely applied.However,these methods assume that the predicted value of a single variable is affected by all other variables,ignoring the causal relationship among variables.To address the above issue,we propose a novel end-to-end deep learning model,termed graph neural network with neural Granger causality,namely CauGNN,in this paper.To characterize the causal information among variables,we introduce the neural Granger causality graph in our model.Each variable is regarded as a graph node,and each edge represents the casual relationship between variables.In addition,convolutional neural network filters with different perception scales are used for time series feature extraction,to generate the feature of each node.Finally,the graph neural network is adopted to tackle the forecasting problem of the graph structure generated by the MTS.Three benchmark datasets from the real world are used to evaluate the proposed CauGNN,and comprehensive experiments show that the proposed method achieves state-of-the-art results in the MTS forecasting task.

Exploring and visualizing temporal relations in multivariate time series

This paper introduces an approach to analyzing multivariate time series(MVTS)data through progressive temporal abstraction of the data into patterns characterizing the behavior of the studied dynamic phenomenon.The paper focuses on two core challenges:identifying basic behavior patterns of individual attributes and examining the temporal relations between these patterns across the range of attributes to derive higher-level abstractions of multi-attribute behavior.The proposed approach combines existing methods for univariate pattern extraction,computation of temporal relations according to the Allen’s time interval algebra,visual displays of the temporal relations,and interactive query operations into a cohesive visual analytics workflow.The paper describes the application of the approach to real-world examples of population mobility data during the COVID-19 pandemic and characteristics of episodes in a football match,illustrating its versatility and effectiveness in understanding composite patterns of interrelated attribute behaviors in MVTS data.

Rolling Iterative Prediction for Correlated Multivariate Time Series

Correlated multivariate time series prediction is an effective tool for discovering the chang rules of temporal data,but it is challenging tofind these rules.Recently,deep learning methods have made it possible to predict high-dimensional and complex multivariate time series data.However,these methods cannot capture or predict potential mutation signals of time series,leading to a lag in data prediction trends and large errors.Moreover,it is difficult to capture dependencies of the data,especially when the data is sparse and the time intervals are large.In this paper,we proposed a prediction approach that leverages both propagation dynamics and deep learning,called Rolling Iterative Prediction(RIP).In RIP method,the Time-Delay Moving Average(TDMA)is used to carry out maximum likelihood reduction on the raw data,and the propagation dynamics model is applied to obtain the potential propagation parameters data,and dynamic properties of the correlated multivariate time series are clearly established.Long Short-Term Memory(LSTM)is applied to capture the time dependencies of data,and the medium and long-term Rolling Iterative Prediction method is established by alternately estimating parameters and predicting time series.Experiments are performed on the data of the Corona Virus Disease 2019(COVID-19)in China,France,and South Korea.Experimental results show that the real distribution of the epidemic data is well restored,the prediction accuracy is better than baseline methods.

Multivariate time series imputation for energy data using neural networks

Multivariate time series with missing values are common in a wide range of applications,including energy data.Existing imputation methods often fail to focus on the temporal dynamics and the cross-dimensional correlation simultaneously.In this paper we propose a two-step method based on an attention model to impute missing values in multivariate energy time series.First,the underlying distribution of the missing values in the data is learned.This information is then further used to train an attention based imputation model.By learning the distribution prior to the imputation process,the model can respond flexibly to the specific characteristics of the underlying data.The developed model is applied to European energy data,obtained from the European Network of Transmission System Operators for Electricity.Using different evaluation metrics and benchmarks,the conducted experiments show that the proposed model is preferable to the benchmarks and is able to accurately impute missing values.

High-performance formaldehyde prediction for indoor air quality assessment using time series deep learning

Indoor air pollution resulting from volatile organic compounds(VOCs),especially formaldehyde,is a significant health concern needed to predict indoor formaldehyde concentration(Cf)in green intelligent building design.This study develops a thermal and wet coupling calculation model of porous fabric to account for the migration of formaldehyde molecules in indoor air and cotton,silk,and polyester fabric with heat flux in Harbin,Beijing,Xi’an,Shanghai,Guangzhou,and Kunming,China.The time-by-time indoor dry-bulb temperature(T),relative humidity(RH),and Cf,obtained from verified simulations,were collated and used as input data for the long short-term memory(LSTM)of the deep learning model that predicts indoor multivariate time series Cf from the secondary source effects of indoor fabrics(adsorption and release of formaldehyde).The trained LSTM model can be used to predict multivariate time series Cf at other emission times and locations.The LSTM-based model also predicted Cf with mean absolute percentage error(MAPE),symmetric mean absolute percentage error(SMAPE),mean absolute error(MAE),mean square error(MSE),and root mean square error(RMSE)that fell within 10%,10%,0.5,0.5,and 0.8,respectively.In addition,the characteristics of the input dataset,model parameters,the prediction accuracy of different indoor fabrics,and the uncertainty of the data set are analyzed.The results show that the prediction accuracy of single data set input is higher than that of temperature and humidity input,and the prediction accuracy of LSTM is better than recurrent neural network(RNN).The method’s feasibility was established,and the study provides theoretical support for guiding indoor air pollution control measures and ensuring human health and safety.