Bayesian High-Order Tensor Completion Model With Its Applications in Social Intelligence

Tensor completion is a powerful tool for social intelligence, finding widespread application in recommendation systems, social content mining, and social data recovery. However, existing methods based on tensor-singular value decomposition (t-SVD) are limited to 3rd-order data. Although the traditional CANDECOMP/PARAFAC (CP) and Tucker models can directly complete high-order data, they encounter trouble in rank estimation. While the Bayesian tensor completion model within a probabilistic framework can improve performance and facilitate rank estimation, they face significant efficiency challenges when handling large-scale high-order data. To mitigate these shortcomings, a Bayesian high-order tensor completion (BHOTC) model is proposed in this article. The proposed model is founded upon high-order t-SVD, enabling the direct completion of high-order data without dimensionality reduction. Moreover, within a fully Bayesian framework and benefiting from the hierarchical sparsity priors, the model automatically extracts the potential low-rank structure from high-order data, which significantly enhances the accuracy and robustness. For model learning, a faster variational inference approach is developed in the frequency domain to estimate the posterior parameters, which greatly reduces the time overhead. The advantages of our model are that it considers the high-order tensor completion tasks within the Bayesian framework and develops a faster posterior inference approach. Extensive experiments validate the effectiveness of BHOTC, demonstrating its ability to deliver high-accuracy predictions on sparsely observed tensors—such as courier location distribution in social intelligence systems—as well as high-quality reconstruction on dense tensors, including visual data such as facial images.