Privacy Preserving High-Order Bi-Lanczos in Cloud–Fog Computing for Industrial Applications

Industrial cyber-physical-social systems (CPSSs), a prominent data-driven paradigm, tightly couple and coordinat social space into cyber-physical systems (CPSs) within industrial environments. With the proliferation of cloud-fog computing, cloud-fog computing becomes the most prominent computing paradigm used to implement industrial data analysis. However, the open environment of cloud-fog computing and the limited control of industrial CPSSs users make industrial data analysis without compromising users' privacy one great research challenge in practical cloud-fog-based industrial applications. High-order Bi-Lanczos (HOBI-Lanczos) approach has shown remarkable success in heterogeneous data analysis in industrial applications. In this paper, a novel privacy preserving HOBILanczos approach using tensor train in cloud-fog computing is proposed for industrial data applications. Specifically, a privacy preserving industrial data analysis model using cloud-fog computing and tensor train is firstly proposed. The proposed model enables fogs and clouds to securely carry out industrial data analysis for large-scale tensors given in a tensor train format. In addition, by using this model, a privacy preserving HOBILanczos approach is provided. Last but not least, by using a brain-controlled robot system case study, the proposed approach is theoretically and empirically analyzed. Our proposed approach is proven to be secure. A series of experiments corroborate the superiority of the proposed approach in cloud-fog computing for industrial applications.