The IoT-based Healthcare Industry 5.0 offers intelligent solutions that utilize numerous sensors, generating massive amounts of data. These healthcare data with composite properties can be represented by high-order tensors, which enables the application of tensor multi-way analytics to uncover the latent features in data. However, existing tensor decomposition techniques often face challenges of limited interpretability and weak robustness, which constrain their application in the healthcare industry. To mitigate these challenges, this paper introduces a novel Bayesian Tensor Interpolative Decomposition (BTID) model, which is an extension of the concept of matrix interpolative decomposition and is designed to efficiently and interpretably analyze multi-way tensors. The proposed model performs low-rank approximation using a subset of the original data and employs the Bayesian learning approach to infer the weight matrices, thereby ensuring theoretical interpretability. Additionally, a hierarchical prior is incorporated within this model to address the complexities of the data and enhance model robustness. Finally, a clustering-driven strategy is developed to construct the skeleton matrix, ensuring its physical interpretability while facilitating the CP rank estimation. The BTID model has been comprehensively evaluated on synthetic and healthcare datasets, where the experimental outcomes confirm its superior accuracy, robustness, and interpretability compared with traditional tensor decomposition methods.

Multi-modal Time Series (MTS) is a vital ingredient to Predictive Multi-modal Artificial Intelligence (PMAI). MTS systems capture varying temporal modalities and their inherent dependencies for their accurate analytics. However, efficiently exploring these cross-modalities relationships is a challenging research due to their complexity facets and information redundancies. MTS patterns' pairwise similarity measures precede PMAI. Multi-modal Dynamic Time Warping (MDTW) is frequently explored to quantify similar MTS. Yet, it's reliant on the orthogonal conditioned local similarity measures that ignore the contributions of MTS' underlying structural relationships in the warping process and, hence, susceptible to unrealistic matching. This paper addresses the setbacks by recommending a scalable MTS recognition model, named Tensor-Slices Distance (TSD)-based MDTW (TSD-MDTW), that's subsequently advanced to two more distinct models termed Weighted modality and TSD (WmTSD-MDTW) and TSD-Mahalanobis (TSDMaha-MDTW). To quantify an alignment's cost, TSD-MDTW incorporates intrinsic spatial dependencies between modalities' coordinates, while WmTSD-MDTW relaxes information redundancies through weighing modalities based on information richness, whereas TSDMaha-MDTW embodies modalities dependencies and their coordinates' innate spatial dependencies. Besides, it proposes a scalable Tensor-based DTW (TDTW) model that re-formulates MDTW into multiple dimensions that are found paralleling warping processes. Theoretical and empirical experimental results on MTS multi-modal datasets encompassing load patterns and meteorological modalities reveal TDTW's efficiency and proposals' superior performances in terms of cluster compactness and separation over MDTW employing the state-of-the-art local similarity measures.

Tensor decomposition is a powerful tool for data analysis and has been extensively employed in the field of hyperspectral-multispectral image fusion (HMF). Existing tensor decomposition-based fusion methods typically rely on disruptive data vectorization/reshaping or impose rigid constraints on the arrangement of factor tensors, hindering the preservation of spatial-spectral structures and the modeling of cross-dimensional correlations. Although recent advances utilizing the Fully-Connected Tensor Network (FCTN) decomposition have partially alleviated these limitations, the process of reorganizing data into higher-order tensors still disrupts the intrinsic spatial-spectral structure. Furthermore, these methods necessitate extensive manual parameter tuning and exhibit limited robustness against noise and spatial degradation. To alleviate these issues, we propose the Bayesian FCTN (BFCTN) method. Within this probabilistic framework, a hierarchical sparse prior that characterizing the sparsity of physical elements, establishes connections between the factor tensors. This framework explicitly models the intrinsic physical coupling among spatial structures, spectral signatures, and local scene homogeneity. For model learning, we develop a parameter estimation method based on Variational Bayesian inference (VB) and the Expectation-Maximization (EM) algorithm, which significantly reduces the need for regularization parameter tuning. Extensive experiments demonstrate that BFCTN not only achieves state-of-the-art fusion accuracy and strong robustness but also exhibits practical applicability in complex real-world scenarios. The source code is available at: https://github.com/LinsongShan/BFCTN.

Large language models in deep learning have numerous parameters, requiring significant storage space and computational resources. Compression techniques are highly effective in addressing these challenges. With the development of hardware like Graphics Processing Unit (GPU), Tensor Core can accelerate low-precision matrix multiplication but achieve acceleration for sparse matrices is challenging. Due to its sparsity, the utilization of Tensor Cores is relatively low. To address this, we propose the based onTensorCoreCompressedSparseRow format (TC-CSR), which facilitates data loading on GPUs and matrix operations on Tensor Cores. Based on this format, we designed block Sparse Matrix-Matrix Multiplication (SpMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM) kernels, which are common operations in deep learning. Utilizing these designs, we achieved a$\mathbf {1.41\times }$speedup on Sputnik in scenarios of moderate sparsity and a$\mathbf {1.38\times }$speedup with large-scale highly sparse matrices. Benefit from our design, we achieved a$\mathbf {1.75\times }$speedup in end-to-end inference with sparse Transformers and save memory.

Multimodal sentiment analysis (MSA) integrates multiple sources of sentiment information for processing and has demonstrated superior performance compared to single-modal sentiment analysis, making it widely applicable in domains such as human–computer interaction and public opinion supervision. However, current MSA models heavily rely on black-box deep learning (DL) methods, which lack interpretability. Additionally, effectively integrating multimodal data, reducing noise and redundancy, as well as bridging the semantic gap between heterogeneous data remain challenging issues in multimodal DL. To address these challenges, we propose an interpretable multimodal Tucker fusion model with information filtering (IMTFMIF). We are the first to utilize the multimodal Tucker fusion model for MSA tasks. This approach maps multimodal data into a unified tensor space for fusion, effectively reducing modal heterogeneity and eliminating redundant information while maintaining interpretability. Furthermore, mutual information is employed to filter out task-irrelevant information and explain the association between input and output from an information flow perspective. We propose a novel approach to enhance the comprehension of multimodal data and optimize model performance in MSA tasks. Finally, extensive experiments conducted on three public multimodal datasets demonstrate that our proposed IMTFMIF achieves competitive performance compared to state-of-the-art methods.

Healthcare social networks (HSNs) are pivotal in spreading healthcare knowledge, providing support to both potential patients and medical professionals, and enhancing healthcare services. However, identifying unseen data in HSN poses a significant challenge due to their intrinsic heterogeneity, dynamic characteristics, and the scarcity of labeled data. Employing semantic knowledge transfer for class-agnostic zero-shot recognition stands out as a promising and innovative solution to this problem, but the visual-semantic gap and domain shift problems considerably hinder advancements in zero-shot recognition capabilities. Previous zero-shot models often impose constraints between vision and semantics in the loss part without explicitly injecting intermodality guidance into the feature refinement process. This article yields a novel zero-shot recognition framework for HSN, named the dual tensor prototype graph network, devoted to improving the performance of recognizing unseen objects in HSN leveraging semantic knowledge. We have developed an iterative and interactive updating strategy for dual tensor prototype graphs, explicitly leveraging the distribution information from one modality to guide the prototype graph updates of another modality. We constrain the update process of the dual prototype graphs by several tailored loss functions and episodic training, alleviating the inconsistency between semantic and visual manifolds. Extensive comparative experiments conducted on two medical imaging datasets and five zero-shot benchmarks affirm the stronger generalization ability of our proposed method compared with other advanced approaches, showing the potential of addressing zero-shot problems in HSN.

Nonnegative CANDECOMP/PARAFAC (CP) factorization of incomplete tensors is a powerful technique for finding meaningful and physically interpretable latent factor matrices to achieve nonnegative tensor completion. However, most existing nonnegative CP models rely on manually predefined tensor ranks, which introduces uncertainty and leads the models to overfit or underfit. Although the presence of CP models within the probabilistic framework can estimate rank better, they lack the ability to learn nonnegative factors from incomplete data. In addition, existing approaches tend to focus on point estimation and ignore estimating uncertainty. To address these issues within a unified framework, we propose a fully Bayesian treatment of nonnegative tensor completion with automatic rank determination. Benefitting from the Bayesian framework and the hierarchical sparsity-inducing priors, the model can provide uncertainty estimates of nonnegative latent factors and effectively obtain low-rank structures from incomplete tensors. Additionally, the proposed model can mitigate problems of parameter selection and overfitting. For model learning, we develop two fully Bayesian inference methods for posterior estimation and propose a hybrid computing strategy that reduces the time overhead for large-scale data significantly. Extensive simulations on synthetic data demonstrate that our model can recover missing data with high precision and automatically estimate CP rank from incomplete tensors. Moreover, results from real-world applications demonstrate that our model is superior to state-of-the-art methods in image and video inpainting. The code is available at https://github.com/zecanyang/BNTC.

Accurate and reliable traffic speed data prediction is crucial for Transportation Cyber-Physical Systems (T-CPS), as it directly impacts real-time traffic management, safety control, and overall system efficiency. However, existing deep learning-based traffic speed data prediction methods often require extensive training data and lack interpretability in their predictions. Although matrix and tensor factorization-based approaches enhance interpretability, the performance of these approaches is challenged in scenarios with extremely sparse observed data. These challenges greatly undermine the reliability of predictions and compromise the safety control of T-CPS. To alleviate these shortcomings, this paper proposes a Collaborative Bayesian Tensor Factorization (CBTF) method and applies it to the cloud-edge collaborative traffic speed data prediction scenario. By utilizing a shared factor matrix for collaborative tensor factorization, the proposed method can effectively predict missing data even with extremely limited observed data. For model learning, a posterior estimation method based on Markov Chain Monte Carlo (MCMC) is developed within a Bayesian framework. This approach not only provides point estimates for traffic speed predictions but also offers interval estimates, greatly improving the reliability and interpretability of the results. Extensive simulations demonstrate that the proposed method outperforms several existing approaches. Moreover, collaborative learning experiments reveal the superiority of the proposed approach, particularly in scenarios with a large number of edge nodes in a collaborative learning framework, and each edge node’s data is extremely sparse. Finally, the evaluation of the prediction interval validates the reliability of the proposed method.

The distributed computing paradigm of edge computing effectively addresses the challenges of data transmission delay and data privacy security. With the increasing popularity of IoT devices and 5 G networks, edge computing has a broader range of applications. The advancement in AI technology enables the realization of edge intelligence, which conducts data processing and analysis on edge devices to avoid excessive data transmission to the cloud, enhance system response speed, and protect user data privacy. In various edge intelligent systems like smart homes and autonomous driving, multimodal data plays a crucial role. However, missing modalities in such systems may lead to model failure in real-world environments. To tackle this issue, we propose a tensor-empowered modality reconstruction network (TMRN) that utilizes an end-to-end variational autoencoder for reconstructing missing modal data. This approach effectively enhances model robustness while reducing model size and training complexity. Furthermore, we introduce a supervised method for feature reconstruction to better align with the true distribution of missing modal data by leveraging tensor feature fusion and label supervision techniques. Additionally, we design a task information disentanglement module to make multimodal representations more relevant to specific tasks by effectively separating task-relevant from task-irrelevant information. Extensive experiments demonstrate that TMRN achieves competitive performance compared to existing state-of-the-art methods.

Mobile crowdsourcing (MC) has emerged as an efficient data collection and processing technique with the growing use of mobile devices. Mobile devices typically have numerous sensors to capture a variety of data types, including location information, speech, picture, and video data. Due to the lack of storage capacity and processing power of mobile devices, conducting in-depth analysis and computation of the data is impossible. Cloud-based MC is a viable solution to the issue of limited resources in data outsourcing. How to effectively represent and process encrypted heterogeneous data is an enormous challenge. To alleviate this matter, a unified encrypted-tensor model is proposed to represent heterogeneous data consisting of unstructured, semistructured, and structured data, which represents data in different formats and from various sources. Due to the heterogeneity of data, we devise the encrypted query index and implement the query scheme for structured, semistructured, and unstructured data by transforming heterogeneous data into a graph. We evaluated the search performance of our proposed scheme on real-world data sets. This article analyzes the aspects of time search efficiency, memory occupation, and approximation accuracy. Theoretical analysis and experimental results show that the searchable encryption method based on heterogeneous data proposed in this article can effectively represent and mine big data.

Artificial Intelligence of Things (AIoT) is an emerging paradigm that integrates artificial intelligence (AI) and Internet of Things (IoT) technologies to provide intelligent IoT solutions. The AIoT system acquires data in real time through IoT sensors, performs intelligent data analysis tasks anywhere in the terminal–edge–cloud continuum, and provides accurate decision-making services based on data predictions. Cloud–edge collaboration can reduce security risks for AIoT data prediction by sharing data features instead of raw data. However, sensitive user data may still be inferred by attackers through model parameter analysis, causing irreparable harm and serious consequences. Therefore, data prediction based on cloud–edge collaboration while maintaining privacy constraints remains a significant challenge. In this article, a differentially private federated tensor completion method is proposed for cloud–edge collaborative AIoT data prediction. This method embeds differential privacy (DP) mechanisms with cloud–edge collaboration. Each edge is capable of processing and analyzing data, and collaborative learning with other edges by sharing privacy-preserving model parameters. For model security, objective perturbation is applied to ensure that the tensor completion method satisfies DP. To achieve higher accuracy, parallel tensor decomposition is introduced to avoid the update conflicts problem of federated tensor completion. Through theoretical analysis, our method can provide data protection for tensor completion with high-security promise. The experiments are performed on both synthetic and real-world data sets to demonstrate the superior performance of our method in preserving data privacy.

Intelligent Internet of Things (IoT), is an emerging paradigm that integrates lightweight intelligence algorithms to various IoT devices to provide convenient and intelligent services for modern life and production. For this purpose, data should be efficiently processed to explore the hidden information to elevate the intelligence of services. However, the IoT data are collected from a complex environment with high speed, and high noise, which inevitably brings problems about missing and imparting challenges to the progression of intelligent IoT services. To recover the missing data with higher precision and provide data cornerstones for intelligent IoT systems, a sparse Bayesian tensor completion (SBTC) method is proposed in this article. With the hierarchical sparse prior, the proposed tensor completion model can obtain the underlying low-rank structure from the incomplete tensor, thereby recovering missing data with high accuracy. For model learning, a variational Bayesian inference method is developed in the frequency domain, which improves the model’s efficiency. The model proposed is within a fully Bayesian framework, thereby endowing the model with commendable robustness. The superiority of our model is fully demonstrated by comparing other state-of-the-art methods on synthetic data, traffic data, logistics data, and visual data. In particular, on traffic data and video data, our method has improved by at least 2% and 10dB.