An Algorithm Of Tensor Train Decomposition Based On Block Coordinate Descent

With the development of modern society,data is becoming larger and larger.There is an increasing demand for tools that can effectively process data,such as data com-pression to reduce data storage space.The Tensor Train decomposition is undoubtedly a powerful data compression tool.It not only proves the feasibility of this method to efficiently process high-dimensional datas in theory,but also provides an exact and fea-sible algorithm to calculate it.At same time,its shortcomings are also obvious.The calculation cost of TT decomposition increases exponentially with the order of the ten-sor.This article mainly build a new TT decomposition algorithm,hoping to provide a new way to do the TT decomposition,which can reduce some calculation costs.This article mainly completes two tasks: one is to construct a new algorithm of tensor train decomposition based on the block coordinate descent method,which is es-sentially different from the traditional TT-SVD method.The convergence of the al-gorithm is theoretically proved,and the numerical results show that the algorithm is asymptotic convergence.The second is to use the SRFT random projection matrix to perform low-rank approximation on the tensor.SRFT is a structural random matrix composed of three parts.This construction method can speed up the process of pro-jection and maintain the geometric characteristics of the data.Numerical experiments show that the algorithm has a good performance on high-order tensor.