| In recent years,with the development of computer science,there are more and more multidimensional data appearing in our life,such as video stream,RGB image and so on.Traditional method usually have to rearrange multidimensional data into two-dimensional matrix forms to analysis,which can miss the correlation and destroy the structure of the original data.Tensor is a multidimensional array,which is the high-order generalization of vectors and matrices.Tensor is a powerful tool for multidimensional data analysis due to it can keep the structure from damage,which has be the focus on research and widely be applied to machine learning,data mining,signal processing and elsewhere.This paper considers modified versions of the alternating least-squares(ALS)and the regularized alternating least-squares(RALS)algorithms for tensor decomposition.We propose two hybrid alternating methods by combining the extra-gradient method with Newton’s method,where at each subproblem,the correction step of the extra-gradient is replaced by a Newton step.Theoretically,the step-size of the correction step can be possibly chosen in a wide range.Under certain assumptions,we analyze the global convergence of our algorithm.Preliminary numerical experiments show the effectiveness of the proposed methods,compared to the standard ALS and RALS algorithms. |
