Sparse CP Factorization For Higher-order Tensor

With the rapid development of modern computer technology,especially in the field of machine learning and artificial intelligence research more and more extensive and in-depth.People are more and more strict in the establishment of the basic theory of high-dimensional data,especially in the study of data decomposition of high-order tensors.How to decompose data in data processing directly affects the performance of the algorithm.For example,in face data,some processsing methods use ordinary singular value decomposition or directly arrange the data into a one-dimensional vector.This method cannot guarantee the retention of important information of the data and also destroys the spatial structure of the image,resulting in the instability of the data.Therefore,how to decompose data so as to maintain the important information of data to the greatest extent has become an important research topic.Tensor decomposition is an important technique in data decomposition,and more and more scholars begin to pay attention to it.At present,the classical decomposition methods are: CP decomposition,Tucker decomposition,HOSVD decomposition and so on.These decomposition can well process data and save its main information.However,due to the development of modern fields,the requirements for tensor decomposition are becoming more and morestringent,and new decomposition methods are urgently needed to meet different requirements.Traditional tensor decomposition algorithm cannot very good features the characteristics after decomposition,which will not be able to effectively solve the problem of sparse.Aiming at these problems,based on the work in front of the thin soft threshold truncation operation algorithm is proposed,and combined with classic tensor decomposition construct new truncated thin soft threshold algorithm.The main research work is as follows:Firstly,for the classical tensor CP decomposition algorithm,the soft threshold and truncation operations are embedded.In this paper,a combination of soft threshold and truncation operations is embedded on the basis of the tensor CP decomposition algorithm.In particular,combining can do sparse decomposition composition operation Genevera i.Allen's soft threshold and Misha e.Kilmer truncation operating advantages of the two technologies will be embedded into the tensor CP decomposition algorithm,to avoid the effect exists for special data under a single operation performance is not ideal,even in the normal data is too sparse would happen.Secondly,Soft threshold and truncation operations can also be performed for Tucker decomposition of tensors.because itself has a strong link with CP decomposition Tucker decomposition,when Tucker decomposition of nuclear tensor,dimensions and it is the same super diagonal tensor,it becomes a tensor of CP decomposition.At the same time of tensor Tucker decomposition is high order SVD decomposition form of promotion,the algorithm for HOOI decomposition algorithm.This algorithm is the use of the truncation operations to achieve sparse effect.Shortcomings are not same with sparse effect,soft threshold operation,introduced here,Tucker soth-tru algorithm,which constitutes the new algorithm tensor,retains the advantages of HOOI algorithm and USES soft threshold to solve the problem of too sparse and poor sparse effect on special data.Finally,a new tensor decomposition algorithm t-svd is proposed for tensor SVD decomposition.T-SVD algorithm is based on the map to the Fourier Ye Yu do singular value decomposition of tensor slice.This algorithm also does not have to do sparse decomposition factor operation,our soft threshold and truncation applies this algorithm operation.Specific,in the mapped to fu Ye Yu and do SVD decomposition factors we do soft threshold and cutting operation,by learning to the appropriate parameters to ensure that the algorithm is sparse and tensor maximum retention of information.For the purpose of this article put forward based on tensor decomposition is thin softthreshold and truncation algorithm operation,not only from the theory to prove the convergence of the algorithm.It also USES the mixed gaussian distribution to generate random data and distribution of experimental comparison and analysis of the generated data.Through the experiment proves that the proposed sparse soft threshold and truncation algorithm which can keep tensor as much as possible the main information and make it thin.In the high-dimensional data processing using this method can improve the performance of the algorithm.So it is of important practical application value.