Bayesian Tensor Interpolative Decomposition for IoT-Based Healthcare Data Multiway Analytics

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.