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 ...
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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 scalablecomputations 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 tensorcomputations (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.
By leveraging neoteric analytical techniques associated with big data, numerous new data-focused computation and service models have flourished in service computing systems. Accurate future predictions based on tensor...
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By leveraging neoteric analytical techniques associated with big data, numerous new data-focused computation and service models have flourished in service computing systems. Accurate future predictions based on tensor-based multivariate Markov models can vigorously support enterprise decisions. However, the computation efficiency and quick response of tensor-based multimodal prediction approach are seriously restricted by the curse of dimensionality arising from high-order tensor. Therefore, to alleviate the problem, this paper focuses on proposing a tensor-train (TT)-based computation approach with its scalable implementation for high-order dominant eigen decomposition (HODED) in multivariate Markov models. First, we present a TT-based Einstein product directly based on decomposed TT cores and guarantee that the result remains TT format. Then, we put forward a scalable implementation for TT-based Einstein product in a distributed or parallel manner. Afterwards, we propose a scalable TT-based HODED (TT-HODED) algorithm and a multimodal accurate prediction algorithm. Furthermore, a TT-based big data processing and services framework is presented to provide accurate proactive services. Experimental results based on real-world GPS trajectory dataset demonstrate that TT-HODED algorithm can significantly improve the computation efficiency and reduce the running memory on the premise of guaranteeing the almost consistent prediction accuracy compared to the original HODED algorithm.
Accurate multi-modal predictions can vigorously support people's wise decisions. Predicting the future by leveraging eigentensor based multivariate Markov model or Z-eigenvector based multi-order Markov model has ...
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Accurate multi-modal predictions can vigorously support people's wise decisions. Predicting the future by leveraging eigentensor based multivariate Markov model or Z-eigenvector based multi-order Markov model has flourished in recent years. However, there is no integrated solution by combining multivariate Markov model, and multi-order Markov model with tensor-based calculation approach. Besides, the computation efficiency, and quick response of tensor-based calculation approach are seriously restricted by the curse of dimensionality arising from higher-order tensor. Therefore, this paper focuses on proposing a scalabletensor train (TT) based higher order dominant Z-eigen decomposition (HODZED) for multivariate multi-order Markov models under cloud/edge computing environments to provide quick accurate prediction. First, we propose a multivariate multi-order Markov model, and extend dominant Z-eigen decomposition to HODZED for calculating the dominant Z-eigentensor. Then, we propose two scalable TT-based HODZED (TT-HODZED), and improved TT-based HODZED (ITT-HODZED) algorithms to improve the computation efficiency. Afterwards, we present a multi-modal prediction algorithm based on the dominant Z-eigentensor. Experimental results based on the random dataset, and real-world GPS trajectory dataset demonstrate that TT-HODZED, and ITT-HODZED algorithms can significantly improve the computation efficiency, and reduce the running memory on the premise of guaranteeing the almost consistent prediction accuracy compared to the original HODZED algorithm.
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