HO-OTSVD: A Novel Tensor Decomposition and Its Incremental Decomposition for Cyber–Physical–Social Networks (CPSN)

The development of social networks and ubiquitous sensing promotes the network space into a new stage, which integrates the cyber network, physical network, and social network into cyber-physical-social networks (CPSN). In this paper, we propose a CPSN-based service framework. The framework firstly represents CPSN as an adjacency tensor. Then, a novel tensor decomposition method named high-order orthogonal tensor singular value decomposition (HO-OTSVD) is proposed for knowledge discovery. To cope with the dynamic CPSN, an incremental HO-OTSVD (IHO-OTSVD) is developed to update the orthogonal tensor basis and the core tensor. Furthermore, we propose high-order bidiagonal Lanczos algorithm to cope with the orthogonalization of HO-OTSVD, wherein the complexity reduces from cubic execution time to quadratic execution time. Finally, we use a recommendation system as a case study to evaluate the effectiveness and efficiency of the proposed CPSN-based framework. The results show that HO-OTSVD method outperforms the existing methods.