Research On Representation Method And Application Of Large-scale Tensor

In recent years,with the development of information acquisition and storage technology,the signal processing field has shown a multi-dimensional and large-scale development trend.In the processing of large-scale tensor data,traditional tensor decomposition algorithms can no longer meet the needs of the era of big data,and signal processing algorithms must be required to have a faster speed and less memory.Therefore,research on large-scale tensor decomposition algorithms has become a research hotspot in the field of signal processing.At present,some processing methods based on parallelization and randomization have been proposed and achieved some important results.These algorithms generally have the advantages of simple mathematical structure and fast running speed.On the other hand,coupled tensor decomposition has gradually attracted the attention of researchers due to its huge potential in unique identification and decomposition accuracy.If these advantages can be effectively combined,it will play an important role in promoting the development and application of tensor signal processing.This paper will study the coupled random projection and coupled tensor decomposition algorithms,and propose a large-scale tensor decomposition algorithm.The main content of this article is summarized as follows:·A large-scale tensor decomposition algorithm based on coupled random projection and coupled tensor decomposition is proposed.The algorithm first proposed a tensor compression method for coupled random projection of large-scale tensors.By this method,a series of projection tensors whose size is much smaller than the original tensor are obtained,and the projection tensor is used to replace the original tensor for subsequent algorithm processing,thereby achieving data compression.In the projection process,through the coupling design of the projection matrix,the projection tensor can be coupled in a certain dimension.Then,we can decompose the projection tensor through the coupling decomposition algorithm to obtain the corresponding factor matrices.Because the coupling tensor decomposition has the advantage of rank-one structure alignment,we only need to normalize the amplitude illegibility of the factor matrices.Finally,we can recover the factor matrix of the original tensor by solving a linear system.In summary,our algorithm completes the decomposition of large-scale tensors with less running space and time.In order to verify the performance of the algorithm,we designed several sets of comparative experiments,and the experimental results show that the algorithm has a good calculation accuracy.·Based on the above-mentioned large-scale tensor decomposition algorithm,we further study the application of direction of arrival estimation in broadband large array communication systems.Assuming that the large array uses a uniform linear array,we implement tensor construction by Fourier transform and spatial sampling the received signal.We will prove by mathematical derivation that the tensor satisfies the large-scale CPD model.Based on this,we can use the large-scale tensor decomposition algorithm proposed in this paper to decompose it,and obtain the direction of arrival angle information of the signal from the factor matrices.Finally,the comparison experimental results show that: in response to the estimation of the direction of arrival of large-scale broadband signals,the large-scale tensor decomposition algorithm proposed in this paper has higher accuracy than the traditional ESPRIT algorithm.Although compared to the traditional tensor decomposition algorithm(Direct-CPD),there is a performance loss,but less space is occupied and faster operating efficiency is obtained.