Nonlinear Data Structure Research Articles

FinSafeNet: securing digital transactions using optimized deep learning and multi-kernel PCA(MKPCA) with Nyström approximation.

With the swift advancement of technology and growing popularity of internet in business and communication, cybersecurity posed a global threat. This research focuses new Deep Learning (DL) model referred as FinSafeNet to secure loose cash transactions over the digital banking channels. FinSafeNet is based on a Bi-Directional Long Short-Term Memory (Bi-LSTM), a Convolutional Neural Network (CNN) and an additional dual attention mechanism to study the transaction data and influence the observation of various security threats. One such aspect is, relying these databases in most of the cases imposes a great technical challenge towards effective real time transaction security. FinSafeNet draws attention to the attack and reproductive phases of Hierarchical Particle Swarm Optimization (HPSO) feature selection technique simulating it in a battle for extreme time performance called the Improved Snow-Lion optimization Algorithm (I-SLOA). Upon that, the model then applies the Multi-Kernel Principal Component Analysis (MKPCA) accompanied by Nyström Approximation for handling the MKPCA features. MKPCA seeks to analyze and understand a non-linear structure of data whereas, Nyström Approximation reduces the burden on computational power hence allows the model to work in situations where large sizes of datasets are available but with no loss of efficiency of the model. This causes FinSafeNet to work easily and still be able to make accurate forecasts. Besides tackling feature selection and dimensionality reduction, the model presents advanced correlation measures as well as Joint Mutual Information Maximization to enhance variable correlation analysis. These improvements further help the model to detect the relevant features in transaction data that may present a threat to the security of the system. When tested on commonly used database for testing banks performance, for instance the Paysim database, FinSafeNet significantly improves upon the previous and fundamental approaches, achieving accuracy of 97.8%.

Adaptive Weighted Multiview Kernel Matrix Factorization and Its Application in Alzheimer’s Disease Analysis

Recent technology and equipment advancements have provided us with opportunities to better analyze Alzheimer’s disease (AD), where we could collect and employ the data from different image and genetic modalities that may potentially enhance the predictive performance. To perform better clustering in AD analysis, in this paper, we propose a novel model to leverage data from all different modalities/views, which can learn the weights of each view adaptively. Different from previous vanilla Non-negative matrix factorization which assumes data is linearly separable, we propose a simple yet efficient method based on kernel matrix factorization, which is not only able to deal with non-linear data structure but also can achieve better prediction accuracy. Experimental results on the ADNI dataset demonstrate the effectiveness of our proposed method, which indicates promising prospects for kernel application in AD analysis.

Partitioning and aggregating cross-tissue and tissue-specific genetic effects to identify gene-trait associations

TWAS have shown great promise in extending GWAS loci to a functional understanding of disease mechanisms. In an effort to fully unleash the TWAS and GWAS information, we propose MTWAS, a statistical framework that partitions and aggregates cross-tissue and tissue-specific genetic effects in identifying gene-trait associations. We introduce a non-parametric imputation strategy to augment the inaccessible tissues, accommodating complex interactions and non-linear expression data structures across various tissues. We further classify eQTLs into cross-tissue eQTLs and tissue-specific eQTLs via a stepwise procedure based on the extended Bayesian information criterion, which is consistent under high-dimensional settings. We show that MTWAS significantly improves the prediction accuracy across all 47 tissues of the GTEx dataset, compared with other single-tissue and multi-tissue methods, such as PrediXcan, TIGAR, and UTMOST. Applying MTWAS to the DICE and OneK1K datasets with bulk and single-cell RNA sequencing data on immune cell types showcases consistent improvements in prediction accuracy. MTWAS also identifies more predictable genes, and the improvement can be replicated with independent studies. We apply MTWAS to 84 UK Biobank GWAS studies, which provides insights into disease etiology.

Privacy in manifolds: Combining k-anonymity with differential privacy on Fréchet means

While anonymization techniques have improved greatly in allowing data to be used again, it is still really hard to get useful information from anonymized data without risking people’s privacy. Conventional approaches such as k-Anonymity and Differential Privacy have limitations in preserving data utility and privacy simultaneously, particularly in high-dimensional spaces with manifold structures. We address this challenge by focusing on anonymizing data existing within high-dimensional spaces possessing manifold structures. To tackle these issues, we propose and implement a hybrid anonymization scheme termed as the (β, k, b)-anonymization method that combines elements of both differential privacy and k-anonymity. This approach aims to produce high-quality anonymized data that closely resembles real data in terms of knowledge extraction while safeguarding privacy. The Fréchet mean, an operation applicable in metric spaces and meaningful in the manifold setting, serves as a key aspect of our approach. It provides insight into the geometry of data points within high-dimensional spaces. Our goal is to anonymize this Fréchet mean using our proposed approach and minimize the distance between the original and anonymized Fréchet mean to achieve data privacy without significant loss of information. Additionally, we introduce a novel Fréchet mean clustering model designed to enhance the clustering process for high-dimensional spaces. Through theoretical analysis and practical experiments, we demonstrate that our approach outperforms traditional privacy models both in terms of preserving data utility and privacy. This research contributes to advancing privacy-preserving techniques for complex and non-linear data structures, ensuring a balance between data utility and privacy protection.

Explaining deep learning-based representations of resting state functional connectivity data: focusing on interpreting nonlinear patterns in autism spectrum disorder.

Resting state Functional Magnetic Resonance Imaging fMRI (rs-fMRI) has been used extensively to study brain function in psychiatric disorders, yielding insights into brain organization. However, the high dimensionality of the rs-fMRI data presents significant challenges for data analysis. Variational autoencoders (VAEs), a type of neural network, have been instrumental in extracting low-dimensional latent representations of resting state functional connectivity (rsFC) patterns, thereby addressing the complex nonlinear structure of rs-fMRI data. Despite these advances, interpreting these latent representations remains a challenge. This paper aims to address this gap by developing explainable VAE models and testing their utility using rs-fMRI data in autism spectrum disorder (ASD). One-thousand one hundred and fifty participants (601 healthy controls [HC] and 549 patients with ASD) were included in the analysis. RsFC correlation matrices were extracted from the preprocessed rs-fMRI data using the Power atlas, which includes 264 regions of interest (ROIs). Then VAEs were trained in an unsupervised manner. Lastly, we introduce our latent contribution scores to explain the relationship between estimated representations and the original rs-fMRI brain measures. We quantified the latent contribution scores for both the ASD and HC groups at the network level. We found that both ASD and HC groups share the top network connectivitives contributing to all estimated latent components. For example, latent 0 was driven by rsFC within ventral attention network (VAN) in both the ASD and HC. However, we found significant differences in the latent contribution scores between the ASD and HC groups within the VAN for latent 0 and the sensory/somatomotor network for latent 2. This study introduced latent contribution scores to interpret nonlinear patterns identified by VAEs. These scores effectively capture changes in each observed rsFC feature as the estimated latent representation changes, enabling an explainable deep learning model that better understands the underlying neural mechanisms of ASD.

Identifying Novel Subtypes of Functional Gastrointestinal Disorder by Analyzing Nonlinear Structure in Integrative Biopsychosocial Questionnaire Data.

Background/Objectives: Given the limited success in treating functional gastrointestinal disorders (FGIDs) through conventional methods, there is a pressing need for tailored treatments that account for the heterogeneity and biopsychosocial factors associated with FGIDs. Here, we considered the potential of novel subtypes of FGIDs based on biopsychosocial information. Methods: We collected data from 198 FGID patients utilizing an integrative approach that included the traditional Korean medicine diagnosis questionnaire for digestive symptoms (KM), as well as the 36-item Short Form Health Survey (SF-36), alongside the conventional Rome-criteria-based Korean Bowel Disease Questionnaire (K-BDQ). Multivariate analyses were conducted to assess whether KM or SF-36 provided additional information beyond the K-BDQ and its statistical relevance to symptom severity. Questions related to symptom severity were selected using an extremely randomized trees (ERT) regressor to develop an integrative questionnaire. For the identification of novel subtypes, Uniform Manifold Approximation and Projection and spectral clustering were used for nonlinear dimensionality reduction and clustering, respectively. The validity of the clusters was assessed using certain metrics, such as trustworthiness, silhouette coefficient, and accordance rate. An ERT classifier was employed to further validate the clustered result. Results: The multivariate analyses revealed that SF-36 and KM supplemented the psychosocial aspects lacking in K-BDQ. Through the application of nonlinear clustering using the integrative questionnaire data, four subtypes of FGID were identified: mild, severe, mind-symptom predominance, and body-symptom predominance. Conclusions: The identification of these subtypes offers a framework for personalized treatment strategies, thus potentially enhancing therapeutic outcomes by tailoring interventions to the unique biopsychosocial profiles of FGID patients.

Archetype analysis and the PHATE algorithm as methods to describe and visualize pregnant women's levels of physical activity knowledge.

The knowledge of physical activity (PA) recommended for pregnant women and practical application of it has positive impact on the outcome. Nevertheless, it is estimated that in high-income countries over 40% of pregnant women are insufficiently physically active. One of the reasons is insufficient knowledge pregnant women have about allowed effort during pregnancy and both recommended and not recommended physical activities. Description of knowledge about physical activity the women have and distinguishing patterns of their knowledge is becoming an increasingly important issue. A common approach to handle survey data that reflect knowledge involves clustering methods or Principal Component Analysis (PCA). Nevertheless, new procedures of data analysis are still being sought. Using survey data collected by the Institute of Mother and Child Archetypal analysis has been applied to detect levels of knowledge reflected by answers given in a questionnaire and to derive patterns of knowledge contained in the data. Next, PHATE (Potential of Heat-diffusion for Affinity-based Trajectory Embedding) algorithm has been used to visualize the results and to get a deeper insight into the data structure. The results were compared with picture derived from PCA. Three archetypes representing three patterns of knowledge have been distinguished and described. The presentation of complex data in a low dimension was obtained with help of PHATE. The formations revealed by PHATE have been successfully described in terms of knowledge levels reflected by the survey. Finally, comparison of PHATE with PCA has been shown. Archetype analysis combined with PHATE provides novel opportunities in examining nonlinear structure of survey data and allows for visualization that captures complex relations in the data. PHATE has made it possible to distinguish sets of objects that have common features but were captured neither by Archetypal analysis nor PCA. Moreover, for our data, PHATE provides an image of data structure which is more detailed than interpretation of PCA.

Generalized latent multi-view clustering with tensorized bipartite graph

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

Dual auto-weighted multi-view clustering via autoencoder-like nonnegative matrix factorization

Multi-view clustering (MVC) can exploit the complementary information among multi-view data to achieve the satisfactory performance, thus having extensive potentials for practical applications. Although Nonnegative Matrix Factorization (NMF) has emerged as an effective technique for MVC, the existing NMF-based methods still have two main limitations: 1) They solely focus on the reconstruction of original data, which can be regarded as the decoder of an autoencoder, while neglecting the low-dimensional representation learning. 2) They lack the ability to effectively capture both linear and nonlinear structures of data. To solve these problems, in this paper, we propose a Dual Auto-weighted multi-view clustering model based on Autoencoder-like NMF (DA2NMF), which enables a comprehensive exploration of both linear and nonlinear structures. Specifically, we establish an autoencoder-like NMF model that learns linear low-dimensional representations by integrating data reconstruction and representation learning within a unified framework. Moreover, the adaptive graph learning is introduced to explore the nonlinear structures in data. We further design a dual auto-weighted strategy to adaptively compute weights for different views and low-dimensional representations, thereby obtaining an enhanced consistent graph. An effective algorithm based on Multiplicative Update Rule (MUR) is developed to solve the DA2NMF with the theoretical convergence guarantee. Experimental results show that the proposed DA2NMF can effectively improve the clustering performance compared with the state-of-the-art MVC algorithms.

Harnessing artificial intelligence for data-driven energy predictive analytics: A systematic survey towards enhancing sustainability

The escalating trends in energy consumption and the associated emissions of pollutants in the past century have led to energy depletion and environmental pollution. Achieving comprehensive sustainability requires the optimization of energy efficiency and the implementation of efficient energy management strategies. Artificial intelligence (AI), a prominent machine learning paradigm, has gained significant traction in control applications and found extensive utility in various energy-related domains. The utilization of AI techniques for addressing energy-related challenges is favored due to their aptitude for handling complex and nonlinear data structures. Based on the preliminary inquiries, it has been observed that predictive analytics, prominently driven by artificial neural network (ANN) algorithms, assumes a crucial position in energy management across various sectors. This paper presents a comprehensive bibliometric analysis to gain deeper insights into the progression of AI in energy research from 2003 to 2023. AI models can be used to accurately predict energy consumption, load profiles, and resource planning, ensuring consistent performance and efficient resource utilization. This review article summarizes the existing literature on the implementation of AI in the development of energy management systems. Additionally, it explores the challenges and potential areas of research in applying ANN to energy system management. The study demonstrates that ANN can effectively address integration issues between energy and power systems, such as solar and wind forecasting, power system frequency analysis and control, and transient stability assessment. Based on the comprehensive state-of-the-art study, it can be inferred that the implementation of AI has consistently led to energy reductions exceeding 25%. Furthermore, this article discusses future research directions in this field.

Swin Transformer based fluid classification using Gram angle field-converted well logging data: A novel approach

Fluid prediction is important in exploration work, helping to determine the location of exploration targets and the reserve potential of the estimated area. Machine learning methods can better adapt to different data distributions and nonlinear relationships through model training, resulting in better learning of these complex relationships. We first use the Gram angle field (GAF) to convert one-dimensional logging data into two-dimensional images. GAF can better capture the nonlinear structure and patterns in time series data by using trigonometric transformation. After that, we used the Swin Transformer model to classify the converted images. It captures the locality and timing of the image by moving the window. Swin Transformer uses a staged attention mechanism that allows the model to efficiently capture feature information at different scales. This allows the model to capture both local and global information in the image, contributing to a better understanding of the image content. The multi-scale feature capture capability of the Swin Transformer enables it to effectively capture different scales and spatial relationships in fluid prediction tasks. Tested in real data from Tarim Oilfield, the GAF-Swin Transformer model has better performance than other machine learning models. This study provides a new perspective in the field of fluid prediction.

Classification of Congestive Heart Failure Using Artificial Neural Network Based on Higher-Order Moments Detrended Fluctuation Analysis of Heart Rate Variability

Coronary heart disease or cardiovascular disease is a kind of heart disease that affects the heart and all the blood vessels in the body caused by a build-up of plaque in a person's arteries and can result in a stroke or heart attack. According to the Indonesian Ministry of Health, (Depkes RI) coronary heart disease is the main and first cause of all deaths by heart disease, which account for 26.4% among all other causes. Considering the severity of the condition, it is necessary to detect this kind of heart disease to reduce the number of deaths from heart disease. Heart disease detection can be performed by checking the Heart Rate Variability (HRV) signal. HRV assessment is carried out by analyzing short-term and long-term Electrocardiogram (ECG) records. To analyze HRV signals, a Higher-Order Moments Detrended Fluctuation Analysis feature extraction method is proposed to see the non-linear structure of HRV data. The input for Higher-Order Moments Detrended Fluctuation Analysis is an ECG signal which has been converted into an HRV signal. The output of the feature extraction shows that the value of kurtosis-based fluctuation function has a statistical significance in order to differentiate the HRV of heart disease patients and that of normal subjects. These values are then used as the input for classification using an Artificial Neural Network. The output of the classification is the classification of patients with heart disease and normal subjects. The results of the Higher-Order Moments Detrended Fluctuation Analysis feature extraction classification yield the best accuracy of 71.43% with a ROC value of 0.774 which can be categorized as a pretty good classification.

A Novel Deterministic Probabilistic Forecasting Framework for Gold Price with a New Pandemic Index Based on Quantile Regression Deep Learning and Multi-Objective Optimization

The significance of precise gold price forecasting is accentuated by its financial attributes, mirroring global economic conditions, market uncertainties, and investor risk aversion. However, predicting the gold price is challenging due to its inherent volatility, influenced by multiple factors, such as COVID-19, financial crises, geopolitical issues, and fluctuations in other metals and energy prices. These complexities often lead to non-stationary time series, rendering traditional time series modeling methods inadequate. Our paper presents a multi-objective optimization algorithm that refines the interval prediction framework with quantile regression deep learning in response to this issue. This framework comprehensively responds to gold’s financial market dynamics and uncertainties with a screening process of various factors, including pandemic-related indices, geopolitical indices, the US dollar index, and prices of various commodities. The quantile regression deep-learning models optimized by multi-objective optimization algorithms deliver robust, interpretable, and highly accurate predictions for handling non-linear relationships and complex data structures and enhance the overall predictive performance. The results demonstrate that the QRBiLSTM model, optimized using the MOALO algorithm, delivers excellent forecasting performance. The composite indicator AIS reaches −15.6240 and −11.5581 at 90% and 95% confidence levels, respectively. This underscores the model’s high forecasting accuracy and its potential to provide valuable insights for assessing future trends in gold prices. The deterministic and probabilistic forecasting framework for gold prices captures the market dynamics with the new pandemic index and comprehensively sets a new benchmark for predictive modeling in volatile market commodities like gold.

Multiview Subspace Clustering With Multilevel Representations and Adversarial Regularization.

Multiview subspace clustering has turned into a promising technique due to its encouraging ability to discover the underlying subspace structure. In recent studies, a lot of subspace clustering methods have been developed to strengthen the clustering performance of multiview data, but these methods rarely consider simultaneously the nonlinear structure and multilevel representation (MLR) information in multiview data as well as the data distribution of latent representation. To address these problems, we develop a new Multiview Subspace Clustering with MLRs and Adversarial Regularization (MvSC-MRAR), where multiple deep auto-encoders are utilized to model nonlinear structure information of multiview data, multiple self-expressive layers are introduced into each deep auto-encoder to extract multilevel latent representations of each view data, and diversity regularizations are designed to preserve complementary information contained in different layers and different views. Furthermore, a universal discriminator based on adversarial training is developed to enforce the output of each encoder to obey a given prior distribution, so that the affinity matrix for spectral clustering (SPC) is more realistic. Comprehensive empirical evaluation with nine real-world multiview datasets indicates that our proposed MvSC-MRAR achieves significant improvements than several state-of-the-art methods in terms of clustering accuracy (ACC) and normalized mutual information (NMI).

Pure kernel graph fusion tensor subspace clustering under non-negative matrix factorization framework

Currently, graph-based multi-kernel subspace clustering methods have achieved rich research results in dealing with nonlinear data structures. However, most of the methods still have the following two limitations: (1) the model optimization goal is finding the optimal consensus kernel rather than the optimal affinity graph, which leads to kernel noise always interfering with the learning of the target affinity graph in the optimization process; (2) in the process of finding the optimal affinity graph, only the correlation between different kernel views is exploited, ignoring the higher-order correlation between multiple kernel views. In light of this, we propose a pure kernel graph fusion tensor (PKGT) subspace clustering under non-negative matrix factorization (NMF) framework. Specifically, we first use NMF to construct local affinity feature graphs with standard block diagonal structure for each base kernel matrix, and then achieve adaptive weight assignment by optimizing the inconsistencies among multiple local affinity feature graphs. Finally, we use tensor to capture the higher-order correlation between multiple local affinity feature graphs to provide more feature information for the learning of optimal target affinity graph, which enhances the model clustering performance. Extensive experiments on nine real datasets demonstrate that PKGT has superior clustering performance. The code is available at https://github.com/ZS0124/PKGT.

Nonlinear Feature Selection Neural Network via Structured Sparse Regularization.

Feature selection is an important and effective data preprocessing method, which can remove the noise and redundant features while retaining the relevant and discriminative features in high-dimensional data. In real-world applications, the relationships between data samples and their labels are usually nonlinear. However, most of the existing feature selection models focus on learning a linear transformation matrix, which cannot capture such a nonlinear structure in practice and will degrade the performance of downstream tasks. To address the issue, we propose a novel nonlinear feature selection method to select those most relevant and discriminative features in high-dimensional dataset. Specifically, our method learns the nonlinear structure of high-dimensional data by a neural network with cross entropy loss function, and then using the structured sparsity norm such as l2,p -norm to regularize the weights matrix connecting the input layer and the first hidden layer of the neural network model to learn weight of each feature. Therefore, a structural sparse weights matrix is obtained by conducting nonlinear learning based on a neural network with structured sparsity regularization. Then, we use the gradient descent method to achieve the optimal solution of the proposed model. Evaluating the experimental results on several synthetic datasets and real-world datasets shows the effectiveness and superiority of the proposed nonlinear feature selection model.

Statistical Embedding: Beyond Principal Components

There has been an intense recent activity in embedding of very high-dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part, we cover nonlinear methods such as principal curves, multidimensional scaling, local linear methods, ISOMAP, graph-based methods and diffusion mapping, kernel based methods and random projections. The second part is concerned with topological embedding methods, in particular mapping topological properties into persistence diagrams and the Mapper algorithm. Another type of data sets with a tremendous growth is very high-dimensional network data. The task considered in part three is how to embed such data in a vector space of moderate dimension to make the data amenable to traditional techniques such as cluster and classification techniques. Arguably, this is the part where the contrast between algorithmic machine learning methods and statistical modeling, represented by the so-called stochastic block model, is at its greatest. In the paper, we discuss the pros and cons for the two approaches. The final part of the survey deals with embedding in R2, that is, visualization. Three methods are presented: t-SNE, UMAP and LargeVis based on methods in parts one, two and three, respectively. The methods are illustrated and compared on two simulated data sets; one consisting of a triplet of noisy Ranunculoid curves, and one consisting of networks of increasing complexity generated with stochastic block models and with two types of nodes.

Precise crop classification of UAV hyperspectral imagery using kernel tensor slice sparse coding based classifier

Precise crop classification plays a significant role in the agriculture field. An appropriate data source for precise crop classification is high spatial resolutions hyperspectral imagery (H2 imagery) acquired by unmanned aerial vehicle (UAV). However, for imagery with many different classes of crops, crop classification of UAV H2 imagery is a huge challenge. The significant spectral diversity, spatial heterogeneity and nonlinear data structure of UAV H2 imagery results in poor spectral discriminability. To improve the discriminability, a kernel tensor slice sparse coding-based classifier (KTSSCC) is proposed for precise crop classification of UAV H2 imagery in this research. The kernel tensor representation mechanism in KTSSCC can reduce the nonlinear separation while well preserving the spectral characteristics and spatial constraints of land-covers, and thus the discriminability is greatly improved. Furthermore, this paper puts forward the kernel tensor slice sparse orthogonal matching pursuit (KTSSOMP) algorithm to optimize kernel tensor slice sparse coding in the spectral space, which greatly reduces the computation cost. Moreover, there are very few parameters to be tuned in our proposed model. We assess the performance of KTSSCC on two real UAV hyperspectral imagery datasets, and find that, based on visual and quantitative results, it provides satisfactory crop classification results and outperforms the state-of-the-art approaches.

Scalable incomplete multi-view clustering via tensor Schatten p-norm and tensorized bipartite graph

Graph-based incomplete multi-view clustering (IMVC) methods have drawn considerable attention due to their good performance in exploring the nonlinear structure of data. However, they still have the following shortcomings. First, graph construction and eigen decomposition of the Laplacian matrix included in the IMVC methods generally have high computational complexity. Second, most methods do not consider the impact of missing views and neglect the potential relationships between different views. Third, few algorithms consider both intra-view and inter-view information for clustering. Therefore, we innovatively propose a scalable incomplete multi-view clustering via the tensor Schatten p-norm and tensorized bipartite graph (SIMVC/TSTBG) method, which combines tensorized bipartite graph, graph completion, and tensor low-rank constraint into a joint framework. Concretely, we first construct bipartite graphs based on the selected m anchor points and the n data points, reducing the size of the graph from n×n to n×m(m<<n), which considerably reduces the computational complexity. Second, we adaptively complete the missing bipartite graph, which reduces the effect of missing view information on the clustering results. Third, to explore connections between missing views and mine high-order information between views, we splice the bipartite graphs into a tensor and impose a tensor low-rank constraint, i.e., the tensor Schatten p-norm, on it. At the same time, we also design an efficient algorithm to solve SIMVC/TSTBG. To our knowledge, we are the first successful practice to integrate the tensor technique with the scalable IMVC method. Compared with other IMVC methods, the results on seven datasets fully show the high efficiency and effectiveness of SIMVC/TSTBG.

Temperature-induced response reconstruction method based on DL-AR model and attention mechanism

Data loss is unavoidable for structural health monitoring (SHM) systems due to various potential factors, such as equipment aging, radio interference. Previous studies have revealed that it is more challenging to extract structural state information from incomplete data. Therefore, it is important to develop high-precision response reconstruction methods for missing data. In this study, a hybrid deep-learning and autoregressive model with attention mechanism (DL-AR-ATT) framework is proposed to accurately reconstruct structural responses considering data correlations. The proposed model consists of the deep-learning (DL) and autoregressive (AR) components, which can simultaneously model the linear and nonlinear structure of data. To adaptively weight the contribution of the two components to the final result instead of directly summing, the study introduces a custom weighting layer into DL-AR-ATT. Moreover, the attention mechanism is introduced to eliminate redundant information caused by the data from multiple sensors as input. To verify the validity and feasibility of the proposed method, long-term SHM data from a long-span steel box girder suspension bridge and a prestressed concrete continuous box girder bridge are used. The results show that the reconstruction performance of DL-AR-ATT is superior to that of the one-dimensional convolutional neural network (1D-CNN)-based and hybrid DL and AR (DL-AR) models. Finally, the weights of the modules of DL-AR and DL-AR-ATT are visualized to verify the ability of the model to capture data correlations, and to explain how the attention and custom weighting layers improve the performance of DL-AR-ATT.