Implementation And Application Of Parallel And Incremental Tensor-train-based System

In the era of big data,tensor is introduced to achieve the data presentation.However,higher order tensor will take up enormous storage space,accordingly,the computational overhead and memory shall be largely increased,further resulting in the "curse of dimensionality" problem and the low computational efficiency.In order to alleviate the problem of curse of dimensionality,tensor-train decomposition method has been proposed.It is possible and suitable to achieve the distributed storage and parallel computation for tensor-train data by virtue of the idea of divide-and-conquer in tensor-train decomposition.Therefore,this paper designs and implements a parallel tensor-train-based system.And a hybrid parallel framework is proposed for different tensor operations to further improve the computational efficiency for high order tensors.Then an incremental decomposition method based on tensor-train is proposed to avoid repeated decomposition for the history tensor data and reduce the execution time.Afterwards,the multivariate Markov prediction method based on tensor-train is designed and implemented in the parallel tensor-train-based system to achieve higher computational efficiency for the short-term and long-term prediction.The proposed parallel tensor-train-based system can uniformly manage the tensor-train data and directly perform tensor operations in parallel based on tensor-train format.And the incremental method can be performed in parallel in this system to reduce the execution time.Furthermore,this parallel tensor-train based system can also be applied to the prediction algorithm of multivariate Markov chain model and achieve the higher computational efficiency.