Cyber-physical-social systems (CPSS), integrating cyber, physical, and social spaces together, bring both conveniences and challenges to humans. For practical applications and user convenience, it is essential that the Big Data produced in CPSS be processed in real time. Therefore, Big Data computation should avoid redundant computations on historical data when dealing with periodic incoming data. In this paper, we propose a columnwise high-order singular value decomposition (HOSVD) algorithm to realize dimensionality reduction, extraction, and noise reduction for tensor-represented Big Data. First, the distributed HOSVD (DHOSVD) is proposed using the columnwise Jacobi-based approach to realize the distributed computation of HOSVD. Second, big streaming data are continuously produced and the intermediate results could be recorded for the next computational step. Third, we propose a similar columnwise incremental HOSVD (IHOSVD) scheme to support online computation on temporally incremental data streaming. The performance of the two HOSVD-based schemes will illustrate the scalability of our efficient real-time Big Data processing methods.
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