Research On Multi-source Tensor Completion Algorithm Based On Tensor Decomposition

With the rapid development of information technology,the scale and volume of data are also exploding.Tensors,as a high-order extension of vectors and matrices,can more intuitively represent and maintain the structure and intrinsic relation of the original data.Researches based on tensor low-rank completion have received extensive attention in many fields,such as data mining,numerical analysis,image processing,signal processing,and computer vision.The existing tensor completion methods mostly performed on individual tensors under the premise of low rank assumptions.When the structure of tensor data is very complex or the proportion of missing is very high,the accuracy of individual tensor completion will be greatly affected.Using auxiliary information to jointly decompose tensors from multiple data sources can improve the completion accuracy of missing values.When there is a coupling relationship between multi-source tensors in a certain mode,the traditional methods assume that they shared the same factor matrix in this mode,and then model based on shared factor matrix.However,many real-world data sets may have more complex sharing relationships or even no mode coupling between them,but they are highly correlated.In response to these situations,this article completed the following two tasks:Firstly,the coupled tensor decomposition in case of partially shared factors(CTF-PSF)method is proposed in this paper for the situation where the multi-source tensors data share part of the factor matrices in coupled mode.It optimizes the shared and unshared parts of the data independently,respectively.Shared and unshared parts are fitted alternately by joint decomposition and individual decomposition,respectively.Experiment results have illustrated that this method can achieve the goal of improving the accuracy of multi-source tensors completion and obtaining better tensor completion accuracy with a lower parameter space.Secondly,an accurate multi-source tensors completion model via soft constrained shared factors(AMTC-SCSF)is proposed in this paper to solve the problem that the multi-source tensors have other sharing relationship,such as approximate sharing.This model is also suitable for the situation where there is no mode coupling between multi-source data but there is a very high correlation between the data.In addition,compared with the traditional model,the problem of influencing the completion accuracy due to the unbalanced observations of multi-source data is solved in this paper by adding error weights,and extend the model through constraint transfer to adapt to the situation where multiple tensors share multiple factor matrices.Experimental results have illustrated the accuracy,feasibility and effectiveness of the model.