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.

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.

Due to the particularity of the marginal environment, edge-based autonomous systems face significant risks associated with security operations. Traffic anomaly detection in edge-based autonomous systems has become increasingly crucial for ensuring the security of these systems. Existing works lack consideration of the relationship between traffic attributes and anomaly types. In particular, existing solutions struggle with detecting anomalies that primarily manifest statistical signs in only a few attributes. To address this, we propose a nonnegative factorization-based attribute residual summary and a nonparametric statistic framework for adaptive security monitoring in edge-based autonomous systems. Specifically, the nonnegative factorization, which depends on the multiplicative update rules, is introduced to extract attribute features. Using the tensor linear representation, the attribute residual summary is built, which depicts the statistic discrepancy well even if only a few of traffic attributes are affected, to implement adaptive security monitoring for various attacks in edge-based autonomous systems. Then, a nonparametric statistic framework is developed, which achieves the real-time detection by accumulating and comparing each statistic evidence. Extensive experiments with real-world traffic trace datasets validate the adaptivity, accuracy, real-time performance, and superiority of our method, particularly in dealing with anomalies that exhibit statistical signs in only a few traffic attributes.

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.

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.