Design And Implementation Of Distributed Tensor Train Decomposition Algorithms

With the rapid development of multi-sensor technology and computer science,there are many data attributes in the real world.The multi-attribute data set is conducive to a comprehensive analysis of the relationship between the attributes of data.Therefore,it is easy to mine association information in multi-attribute data by fusing multi-attribute data with high-order tensors.However,the resources required for processing high-order tensor such as computer memory and number of calculations will increase with the order,causing some algorithms to fail to produce results in polynomial time.This problem is called curse of dimensionality.The tensor train decomposition algorithm is a novel tensor decomposition algorithm,which transforms high-order tensors into multiple third-order tensors,and changes exponential problems into cubic problems,which can well cope with the problem of curse of dimensionality.However,for large-scale tensors,the traditional serial tensor train decomposition algorithm is inefficient,time-consuming,and cannot even load a complete tensor due to the memory limitation of a single machine.Therefore,for the high-order multi-attribute fusion data generated in the real world,the implementation of distributed tensor column decomposition algorithm will be the focus of this paper.In this paper,based on data slicing,two distributed tensor train decomposition algorithms are proposed.The parallel processing of the tensor train decomposition algorithm is realized,and the tensor train decomposition of large-scale data that can not be accommodated in computer memory can be processed.Finally,an application example of the algorithm in signal processing is given.The main research of this paper can be summarized as follows.1.A distributed tensor train decomposition algorithm based on data parallelism is proposed and implemented.The tensor train decomposition algorithm is an iterative algorithm as a whole.The distributed tensor train decomposition algorithm based on data parallelism unfolds the tensor to matrix in each step of the iteration.Then,the matrix is blocked,the singular value decomposition is performed on the block matrix in parallel,and then the results are merged to obtain the singular value decomposition result of this step.The algorithm saves a lot of time compared with the serial tensor train decomposition algorithm and maintains high numerical precision.However,the distributed tensor train decomposition algorithm based on data parallel is still a serial algorithm as a whole,only the steps in the operation process realize distributed computing,and there is still much room for improvement.2.A distributed incremental tensor train decomposition algorithm based on algorithm parallelism is proposed and implemented.The law of the unfolding matrix of each step in the iterative process of the tensor train decomposition algorithm is studied,and the formula of the transformation of the unfolding matrix of each step is derived.The operation of the overall algorithm is changed from iteration to parallel,and the singular value decomposition of each step is solved in parallel.Based on the idea of tensor blocking,the singular value decomposition are solved in parallel for each sub-tensor in each step,and then merged.The algorithm has a significant improvement compared to the distributed tensor train decomposition algorithm based on data parallelism.At the same time,the algorithm also implements an incremental tensor train decomposition algorithm to avoid double counting of historical data when data is incremented.3.Two application examples of tensor train decomposition in signal processing are realized,which are used for object recognition and bearing fault detection respectively.Good recognition results are obtained,and the feasibility of tensor train decomposition algorithm in feature extraction is verified.