Computer Science ›› 2021, Vol. 48 ›› Issue (8): 66-71.doi: 10.11896/jsjkx.200900055

• Database & Big Data & Data Science • Previous Articles     Next Articles

Tensor Completion Method Based on Coupled Random Projection

YANG Hong-xin, SONG Bao-yan, LIU Ting-ting, DU Yue-feng, LI Xiao-guang   

  1. School of Information,Liaoning University,Shenyang 110036,China
  • Received:2020-09-07 Revised:2020-11-17 Published:2021-08-10
  • About author:YANG Hong-xin,born in 1990,postgra-duate,Ph.D,lecturer,is a member of China Computer Federation.His main research interests include image processing and matrix analysis.( Xiao-guang,born in 1973,postgra-duate,Ph.D,professor,Ph.D supervisor,is a member of China Computer Federation.His main research interests include data mining,machine learning and graph data analysis.
  • Supported by:
    National Natural Science Foundation of China(U1811261).

Abstract: In modern signal processing,the date with large scale,high dimension and complex structure need to be stored and analyzed in more and more fields.Tensors,as a high-order extension of vectors and matrices,can more intuitively represent the structure of high-dimensional data while maintaining the inherent relationship of the original data.Tensor completion plays an important role in recovering the original tensor from the noisy or missing tensor,which can be considered as an important branch of tensor and has been widely used in collaborative filtering,image restoration,data mining and other fields.This paper focuses on the drawbacks of high time complexity in the current tensor completion technology,and proposes a new method based on coupled random projection.The essential point of the proposed method consists of two parts:coupled tensor decomposition (CPD) and random projection matrix (RPM).Through the RPM,the original high-dimensional tensor is projected into the low-dimensional space to generate alternative tensor,and the tensor completion is realized in the low-dimensional space,and thus the efficiency of our method can be improved.Then,the CPD is used to realize the reconstruction of the original tensor by mapping the completed low-dimensional tensor into the high-dimensional space.Finally,the experiments are used to analyze the effectiveness and efficiency of the proposed method.

Key words: Coupled random projection, Coupled tensor decomposition, Random projection matrix, Tensor completion, Tensors

CLC Number: 

  • TP311
[1]ZHANG Y.Improved Sample Image Inpainting Algorithm Based on Image Structure Tensor[J].Journal of Chongqing University of Technology(Natural Science),2020,34(3):145-151.
[2]XIE Q,ZHANG Y,MENG D Y.Survey on Tensor SparsityMeasure[J].Journal of Chongqing University of Posts and Tele-communications(Natural Science Edition),2019,31(3):340-347.
[3]RENNIE D M,SREBRO N.Fast Maximum Margin Matrix Factorization for Collaborative Prediction[C]//Proceedings of International Conference on Machine Learning.2005:713-719.
[4]CANRAL R S,TORRE F D,COSTCIRA J P,et al.MatrixCompletion for Multi-Lable Image Classification[C]//Procee-dings of Neural Information Processing Systems.2011:120-128.
[5]KOLDA T,BADER B.Tensor decompositions and applications[J].SIAM Review,2009,51 (3):455-500.
[6]CHEN D B,YANG X M.Block-coded Video Deblocking Based on Low-rank Tensor Recovery[J].Computer Science,2016,43(9):280-283.
[7]LIU J,YE J,et al.Tensor completion for estimating missing va-lues in visual data[C]// Proceedings of IEEE International Conference on Computer Vision.2009:2114-2121.
[8]LIU J,MUSIALSKI P,WONKA P,et al.Tensor completion for estimating missing values in visual data[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35 (1):208-220.
[9]GANDY S,RECHT B,YAMADA I.Tensor completion andlow-n-rank tensor recovery via convex optimization[J].Inverse Problems,2011,27(2):025010.
[10]ACAR E,DUNLAVY D M,KOLDA T G,et al.Scalable tensor factorizations for incomplete data[J].Chemometrics and Intelligent Laboratory Systems,2011,106(1):41-56.
[11]XU Y,HAO R,YIN W,et al.Parallel matrix factorization for low-rank tensor completion[J].Inverse Problems and Imaging,2015,9(2):601-624.
[12]SILVA C D,HERRMANN F J.Optimization on the Hierarchical Tucker manifold-Applications to tensor completion[J].Li-near Algebra and Its Applications,2015,481:131-173.
[13]BIGONI D,ENGSIG-KARUP A P,MARZOUK Y M.Spectral tensor-train decomposition[J].Mathematics,2014,38(4):2405-2439.
[14]XU Z,YAN F,QI Y.Bayesian Nonparametric Models for Multiway Data Analysis[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2015,37(2):475-487.
[15]FENG Y L,SUN W J.A Matrix Completion method based on Fast Random Projection[J].Computer Applications and Software,2019(9):106-110.
[16]ARRIAGA R I,RUTTER D,CAKMAK M,et al.Visual Categorization with Random Projection[J].Neural Computation,2015,27(10):2132-2147.
[17]YOST D.The Johnson-Lindenstrauss space[J].Extracta Mathe-maticae,2007,12(2):185-192.
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