Scalable Tensor-Train-Based Tensor Computations for Cyber–Physical–Social Big Data

Tensor-based big data analysis approaches are effectively exploited to handle multisource and heterogeneous cyber-physical-social big data generated from diverse spaces. However, the curse of dimensionality seriously restricts their widespread exploitation, especially under edge/fog computing environments. To alleviate the dilemma, we attempt to present a set of tensor-train (TT)-based tensor operations with their scalable computations and then propose a novel TT-based big data processing framework under edge/fog computing environments. Specifically, in this article, we first summarize and present a set of TT-based tensor operations by converting the original high-order tensor operation to a series of low-order (second- or third-order) TTcore-based operations. Then, we propose a two-layer scalable TT-based computation architecture, including inter-TTcore and intra-TTcore scalable models. Afterward, according to various scalable models, a series of scalable TT-based tensor computations (STT-TCs) with their complexity analysis are proposed in detail. Finally, we propose a novel TT-based big data processing framework to adapt to edge/fog computing environments. We conduct extensive experiments based on both random data sets and real-world ubiquitous bus traffic data sets. Experimental results demonstrate that the proposed STT-TCs can significantly improve computation efficiency and are suitable for edge/fog computing environments.