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.

中文翻译：

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HO-OTSVD：一种用于网络物理社交网络 (CPSN) 的新型张量分解及其增量分解

社交网络和泛在感知的发展将网络空间推向了一个新的阶段，将网络、物理网络和社交网络融合为网络-物理-社交网络（CPSN）。在本文中，我们提出了一个基于 CPSN 的服务框架。该框架首先将 CPSN 表示为邻接张量。然后，提出了一种新的张量分解方法，称为高阶正交张量奇异值分解（HO-OTSVD），用于知识发现。为了应对动态 CPSN，开发了增量 HO-OTSVD（IHO-OTSVD）来更新正交张量基和核心张量。此外，我们提出了高阶双对角 Lanczos 算法来处理 HO-OTSVD 的正交化，其中复杂性从三次执行时间减少到二次执行时间。最后，我们使用推荐系统作为案例研究来评估所提出的基于 CPSN 的框架的有效性和效率。结果表明，HO-OTSVD 方法优于现有方法。