Stacking for multivariate time series classification

The multivariate time series (MTS) classification is an important classification problem in which data has the temporal attribute. Because relationships between many variables of the MTS are complex and time-varying, existing methods perform not well in MTS classification with many attribute variables. Thus, in this paper, we propose a novel model-based classification method, called Kullback-Leibler Divergence-based Gaussian Model Classification (KLD-GMC), which converts the original MTS data into two important parameters of the multivariate Gaussian model: the mean vector and the inverse covariance matrix. The inverse covariance is the most important parameter, which can obtain the information between the variables. So that the more variables, the more information could be obtained by the inverse covariance, KLD-GMC can deal with the relationship between variables well in the MTS. Then the sparse inverse covariance of each subsequence is solved by Graphical Lasso. Furthermore, the Kullback-Leibler divergence is used as the similarity measurement to implement the classification of unlabeled subsequences, because it can effectively measure the similarity between different distributions. Experimental results on classical MTS datasets demonstrate that our method can improve the performance of multivariate time series classification and outperform the state-of-the-art methods.

Early classification of time series has been receiving a lot of attention as of late, particularly in the context of gene expression. In the biomédical realm, early classification can be of tremendous help, by identifying the onset of a disease before it has time to fully take hold, or determining that a treatment has done its job and can be discontinued. In this paper we present a state-of-the-art model, which we call the Early Classification Model (ECM), that allows for early, accurate, and patient-specific classification of multivariate time series. The model is comprised of an integration of the widely-used HMM and SVM models, which, while not a new technique per se, has not been used for early classification of multivariate time series classification until now. It attained very promising results on the datasets we tested it on: in our experiments based on a published dataset of response to drug therapy in Multiple Sclerosis patients, ECM used only an average of 40% of a time series and was able to outperform some of the baseline models, which needed the full time series for classification.

Classification of time series is an essential requirement of various applications that demand continuous monitoring of dynamical systems such as industrial process and health care monitoring. Feature extraction plays a vital role in deciding performance of the time series models. In recent years deep learning techniques have shown an excellent performance to extract highly discriminating features for the classification of the time series. A Convolutional Neural Network (CNN) is a unified framework that performs the feature learning and classification tasks simultaneously. Using the CNN to perform the classification of the multivariate time series is still a challenging task. In this paper, we propose an attention-based multivariate convolutional neural network (AT-MVCNN) that consists of the attention feature-based input tensor scheme to encode informations across the multiple time stamps. The method is capable of learning the temporal characteristics of the multivariate time series. The efficacy of the proposed method is tested on Human Activity Recognition (HAR) and Occupancy Detection datasets. The experiments and results show the proposed method outperforms the other deep learning and traditional machine learning models.

Time series classification algorithms have been mainly dominated by non-deep learning models. Deep learning for Multivariate Time Series Classification (MTSC) has gained huge interest in recent years. Most state of the art deep learning methods are convolutional-based where 1-dimensional (1D) convolutions are used to extract features from the 2-dimensional time series. This study shows that factorization of 1D convolution filters into disjoint temporal and spatial components yields significant accuracy improvements with almost no additional computational cost. Based on our study on disjoint temporal-spatial filters, we have designed a novel filter block called "1+1D", which emphasizes the interaction between dimensions to improve the model performance of the convolution based on deep learning MTSC models. We also proposed a new and effective MTSC method called Disjoint-CNN using our proposed 1+1D filter blocks and through our extensive experiments show that our model (called Disjoint-CNN) outperforms the state-of-the-art MTSC models on 26 datasets in the UEA Multivariate time series archive, achieving the highest average rank among 9 MTSC benchmark models.

Multivariate time series data often have a very high dimensionality. Classifying such high dimensional data poses a challenge because a vast number of features can be extracted. Furthermore, the meaning of the normally intuitive term similar needs to be precisely defined. Representing the time series data effectively is an essential task for decision-making activities such as prediction, clustering and classification. In this paper we propose a feature-based classification approach to classify real-world multivariate time series generated by drilling rig sensors in the oil and gas industry. Our approach encompasses two main phases: representation and classification. For the representation phase, we propose a novel representation of time series which combines trend-based and value-based approximations (we abbreviate it as TVA). It produces a compact representation of the time series which consists of symbolic strings that represent the trends and the values of each variable in the series. The TVA representation improves both the accuracy and the running time of the classification process by extracting a set of informative features suitable for common classifiers. For the classification phase, we propose a memory-based classifier which takes into account the antecedent results of the classification process. The inputs of the proposed classifier are the TVA features computed from the current segment, as well as the predicted class of the previous segment. Our experimental results on real-world multivariate time series show that our approach enables highly accurate and fast classification of multivariate time series.

ST-Tree with interpretability for multivariate time series classification

Due to high dimensionality and multiple variables, unsupervised classification of multivariate time series (MTS) involves more challenging problems than those of univariate ones. Unlike the vectorization of a feature matrix in traditional clustering algorithms, an unsupervised pattern recognition scheme based on matrix data is proposed for MTS samples in this paper. To reduce the computational load and time consumption, a novel variable-based principal component analysis (VPCA) is first devised for the dimensionality reduction of MTS samples. Afterward, a spatial weighted matrix distance-based fuzzy clustering (SWMDFC) algorithm is proposed to directly group MTS samples into clusters as well as preserve the structure of the data matrix. The spatial weighted matrix distance (SWMD) integrates the spatial dimensionality difference of elements of data into the distance of MST pairs. In terms of the SWMD, the MTS samples are clustered without vectorization in the dimensionality-reduced feature matrix space. Finally, three open-access datasets are utilized for the validation of the proposed unsupervised classification scheme. The results show that the VPCA can capture more features of MTS data than principal component analysis (PCA) and 2-D PCA. Furthermore, the clustering performance of SWMDFC is superior to that of fuzzy c -means clustering algorithms based on the Euclidean distance or image Euclidean distance.

Offshore oil drilling is a complex process that requires careful coordination of hardware and control systems. Fault monitoring systems play an important role in such systems for safe and profitable operations. Thus, predictive maintenance and monitoring operating conditions of drilling systems are critical to the overall production cycle. In this paper, we are addressing the topic of condition monitoring of a critical part in the process of oil drilling, the Internal Blowout Preventer (IBOP) system in the top drive assembly in offshore oil drilling. In our work, we aim to design an intelligent system for monitoring the health of IBOP system using discrete event systems (DES) based control method in combination with multivariate time series classification deep learning method. The proposed system comprises two stages: 1) produce IBOP system logical behaviour analysis using Hierarchical Colored Petri Nets (HCPN) approach; 2) develop an activity detection or a classifier module using reservoir computing framework for classification of multivariate time series for activity monitoring and fault detection for the top drive assembly.
 The combination of these methods would enable automation of monitoring and early detection of incidents during drilling operations. We present the preliminary results of a model in Petri Nets used to simulate a monitoring system for IBOP valve in top drive assembly and activity classification of activities relevant to IBOP condition monitoring. The effects of failure rate and repair time of each component on system performance are to be researched at a later stage.

Multivariate time series classification (MTSC) is a fundamental and essential research problem in the domain of time series data mining. Recently deep neural networks emerged as an end-to-end solution for MTSC and achieve state-of-the-art results on several public datasets. It is favored by its hierarchical feature extraction ability and most of the researches focus on designing a network architecture to ensure its performance on MTSC. Despite this, there are seldom investigations on the attention mechanism in MTSC, which has been demonstrated as an effective module to extract features in other domains. In this paper, we propose a residual channel and temporal attention (CT_CAM) module, which aims to refine the feature extracted from the convolutional neural network and thus improve the classification performance. Extensive experiments on 15 public MTSC datasets show that the proposed CT_CAM module achieves competitive performance compared with nine baseline methods and three other attention modules.

While machine learning has been increasingly incorporated into structural damage detection, most existing methods still rely on hand-crafted damage features. For a given structure, the performance of detection is heavily impacted by the quality of features, and choosing the optimal features may be difficult and time-consuming. Various time series classification algorithms studied in machine learning are able to classify structural responses into damage conditions without feature engineering; however, most of them only deal with univariate time series classification and are either inapplicable or ineffective on multivariate (i.e. multi-dimensional) data, thus unable to fully utilize all sensors available on real bridges. To address these limitations, we propose a global bridge damage detection method based on multivariate time series classification with optimized functional echo state networks. In this method, data from multiple sensors are directly used as inputs without feature extraction. Training of the functional echo state network is simple and straightforward, and by leveraging the nonlinear mapping capacity and dynamic memory of functional echo state network, the separability of different classes, that is, classifying accuracy is enhanced compared to conventional classification algorithms. Furthermore, hyperparameters of the functional echo state network are automatically optimized with particle swarm optimization algorithm, which further improves the accuracy while saving the cost of manual tuning. Experimental results on two classical data sets show that functional echo state network achieves high and stable accuracy, which indicate that our method can detect global bridge structural damage efficiently by analyzing multiple sensor data, and is prospected to be applied in real bridge structural health monitoring systems.

TV-Net: Temporal-Variable feature harmonizing Network for multivariate time series classification and interpretation

Sensor-based methods for human gait analysis often utilize electromyography capturing rich time-series data. Then, for transparent and explainable analysis interpretable methods are of prime importance. This paper presents analytical approaches in a framework for interpretable anomaly detection and classification of multivariate time series for human gait analysis. We exemplify the application utilizing a real-world medical dataset in the biomechanical orthopedics domain.

Multivariate Time Series Classification (MTSC) is a challenging task in real-world applications. Current approaches emphasize modeling multiscale relationships over time. However, the Multivariate Time Series (MTS) also exhibits multiscale cross-channel relationships. Furthermore, the long-term temporal relationships in time series are difficult to capture. In this paper, we introduce MD-Former, a Multiscale Dual-Branch Attention network leveraging the Transformer architecture to capture multiscale relationships across time and channels for MTSC. In MD-Former, MTS is embedded into 2D vectors using Channel-Patching (CP) to retain channel information. Following this, we develop two branches: the Interlaced Attention Branch (IAB) and the Channel-Independent Attention Branch (CIAB). The IAB facilitates the fusion of information across channels and time, while the CIAB prevents the loss of information resulting from excessive fusion. Both the IAB and CIAB consist of multiple layers, each representing a distinct time scale. Finally, we utilize features from each layer of both IAB and CIAB as inputs to the Multiscale Classification Head (MCH) for feature fusion and classification. Experimental results show that MD-Former achieves performance levels that are comparable to SOTA methods in MTSC.

Contrastive learning (CL), a self-supervised paradigm, has become increasingly effective for Multivariate Time-Series (MTS) classification by aligning representations from different augmented views of unlabeled data. While prior CL methods have primarily emphasized temporal consistency—using temporal augmentations and contrasting to preserve sequence patterns under perturbations—they tend to neglect spatial consistency, which involves maintaining stable sensor readings and their interdependencies. Given that MTS data are commonly derived from multiple sensors, spatial consistency plays a vital role in enhancing the overall performance of CL approaches. To overcome this limitation, we propose Graph-Aware Contrasting (TS-GAC), a framework designed to promote spatial consistency in MTS data. TS-GAC introduces graph augmentations, including node and edge perturbations, to ensure robustness in both sensor values and inter-sensor relations. Furthermore, it employs graph contrasting—comprising both node-level and graph-level mechanisms—to learn resilient sensor-wise and global-wise features. To complement spatial modeling, we also integrate a multi-window temporal contrasting strategy to enforce temporal robustness within individual sensors. Experimental results across diverse MTS classification datasets confirm that TS-GAC achieves state-of-the-art performance.

Time series classification with their image representation