A Distributed HOSVD Method With Its Incremental Computation for Big Data in Cyber-Physical-Social Systems
Abstract:
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.
Existing System:
In this section, the state-of-the-art on the SVD/HOSVD computation is briefly reviewed. SVD, an often-used efficient tool for redundancy reduction, denoising, and dimensionality reduction, can be realized by two types of methods: QR-based method and the Jacobi-based method. As mentioned earlier, the QR-based method, also called Golub–Kahan SVD computational method, has two main processes—the bidiagonal process and the process of diagonalizing the bidiagonal form [11], [25], [26].
Proposed System:
A tensor is utilized for data representation. HOSVD, as an extension of SVD in high-order space, is widely utilized in many application domains after tensor representation. A multilinear generalization of SVD, and how tensor symmetries affect the decomposition, was investigated and discussed in [10]. Furthermore, HOSVD is widely used by academia and industry in many areas, such as image data processing [9], noise reduction [6], latent semantic analysis [17], and human motion recognition [9]. However, the distributed HOSVD method with its incremental computation is an important research advance in terms of improved communication and computation complexities and reduced execution times.
Conclusion:
Dimensionality reduction and high-quality extraction of Big Data using the distributed and incremental methods for decision makers and service providers in CPSS are implemented. First, the DHOSVD algorithms are presented, including the inner-block and inter-block algorithms. Second, according to the computation requirement for streaming data in CPSS, we proposed and analyzed the distributed and incremental computational approaches, respectively. Third, a series of experiments and simulations are carried out to demonstrate the effectiveness of our proposed algorithms.
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