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.

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.