An Incremental Tensor-Train Decomposition for Cyber-Physical-Social Big Data

Cyber-physical-social big data generated from ubiquitous devices and diverse spaces generally are multi-source, heterogeneous, and deeply intertwined. To efficiently analyze and handle the ubiquitous cyber-physical-social big data, tensor is considered as an effective tool, but the curse of dimensionality is still the main bottleneck of tensor-based big data analysis. Tensor networks can considerably alleviate or overcome it through the tensor approximate theory. Therefore, this paper focuses on developing an efficient big data processing framework based on tensor networks and providing an incremental tensor train decomposition approach for the streaming big data. Concretely, this paper first presents a hierarchical cyber-physical-social big data processing framework composed of three planes, namely, data representation and decomposition, data storage and processing, and data analysis and service. Then, tensor train (TT) and quantized TT decompositions are particularly introduced to remarkably overcome the curse of dimensionality. Furthermore, to efficiently handle the continuous streaming big data and avoid the repeated decomposition for the history data, an incremental tensor train decomposition (ITTD) approach is proposed and the complexities are further analyzed in detail. Experimental results demonstrate that ITTD demonstrably outperforms the nonincremental TT decomposition in execution time on the precise of guaranteeing the nearly equal approximation error.