求张量稀疏Z-特征向量的一种投影算法
|
摘要
带稀疏约束的优化模型常用于主成分分析和压缩感知等领域.随着张量研究的推进,高阶主成分分析和高阶压缩感知也被提出并取得一些研究成果.本文提出一个带稀疏约束的张量Z-特征向量求解的数学问题,并设计算法进行求解.
Sparse constrained optimization models are commonly used in the fields of principal component analysis and compressed sensing. With the advance of tensor research, higher-order principal component analysis and higher-order compressed sensing have also been proposed and achieved some research results. In this paper, we design an algorithm to solve tensor Z-eigenvectors with sparse constraints.
Sparse constrained optimization models are commonly used in the fields of principal component analysis and compressed sensing. With the advance of tensor research, higher-order principal component analysis and higher-order compressed sensing have also been proposed and achieved some research results. In this paper, we design an algorithm to solve tensor Z-eigenvectors with sparse constraints.
引文
[1] E J Candes ,T Tao.Near optimal signal recovery from random projections :Universal encoding strategies[J].IEEE Trans.Info.Theory.2006,52(12):5406-5425.
[2] D L Donoho.Compressed sensing[J].IEEE Trans.on Information Theory.2006,52(4):1289-1306.
[3] I T Jolliffe.Principal Component Analysis(Second Edition)[M].NY:Springer,2002.
[4] L Qi.Eigenvalues of a real supersymmetric tensor[J].J.Symb.Comput.,2005,40(6):1302-1324.
[5] Kofidis E,Regalia P A.On the best rank-1 approximation of higher-order supersymmetric tensors[J].SIAM J.Matrix Anal.Appl.2002,23:863-884.
[6] Kolda TG,Mayo J R.Shifted power method for computing tensor eigenpairs[J].SIAM J.Matrix Anal.Appl.2011,32:1095-1124.
[7] L Han.An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors[J].Numer.Algebr.Control Optim.2013,3:583-599.
[8] Kolda T G,Mayo J R.An adaptive shifted power method for computing generalized tensor eigenpairs[J].SIAM J.Matrix Anal.Appl.2014,35:1563-1581.
[9] C Cui,Y Dai,J Nie.All real eigenvalues of symmetric tensors[J].SIAM J.Matrix Anal.Appl.2014,35:1582-1601.
[10] S Hu,Z Huang,L Qi.Finding the extreme Z-eigenvalues of tensors via a sequential SDPs method[J].Numer.Linear Algebr.Appl.,2013,20:972-984.
[11] C Hao,C Cui,Y Dai.A sequential subspace projection method for extreme Z-eigenvalues of supersymmetric tensors[J].Numer.Linear Algebr.Appl.2015,22:283-298.
[12] C Hao,C Cui,Y Dai.A feasible trust-region method for calculating extreme Z-eigenvalues of symmetric tensors[J].Pacific J.Optim.,2015,11:291-307.
[13] Z Luo,L Qi,N Xiu.The sparsest solutions to Z-tensor complementarity problems[J].Optim.Lett.,2017,11(3):471-482.
[14] G Yu,Z Yu,Y Xu,et al.An adaptive gradient method for computing generalized tensor eigenpairs[J].Comput.Optim.& Appl.,2016:1-17.
[15] W W Hager,D T Phan,J Zhu.Projection algorithms for nonconvex minimization with application to sparse principal component analysis[J].J.Glob.Opt.,2016,65(4):657-676.
[2] D L Donoho.Compressed sensing[J].IEEE Trans.on Information Theory.2006,52(4):1289-1306.
[3] I T Jolliffe.Principal Component Analysis(Second Edition)[M].NY:Springer,2002.
[4] L Qi.Eigenvalues of a real supersymmetric tensor[J].J.Symb.Comput.,2005,40(6):1302-1324.
[5] Kofidis E,Regalia P A.On the best rank-1 approximation of higher-order supersymmetric tensors[J].SIAM J.Matrix Anal.Appl.2002,23:863-884.
[6] Kolda TG,Mayo J R.Shifted power method for computing tensor eigenpairs[J].SIAM J.Matrix Anal.Appl.2011,32:1095-1124.
[7] L Han.An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors[J].Numer.Algebr.Control Optim.2013,3:583-599.
[8] Kolda T G,Mayo J R.An adaptive shifted power method for computing generalized tensor eigenpairs[J].SIAM J.Matrix Anal.Appl.2014,35:1563-1581.
[9] C Cui,Y Dai,J Nie.All real eigenvalues of symmetric tensors[J].SIAM J.Matrix Anal.Appl.2014,35:1582-1601.
[10] S Hu,Z Huang,L Qi.Finding the extreme Z-eigenvalues of tensors via a sequential SDPs method[J].Numer.Linear Algebr.Appl.,2013,20:972-984.
[11] C Hao,C Cui,Y Dai.A sequential subspace projection method for extreme Z-eigenvalues of supersymmetric tensors[J].Numer.Linear Algebr.Appl.2015,22:283-298.
[12] C Hao,C Cui,Y Dai.A feasible trust-region method for calculating extreme Z-eigenvalues of symmetric tensors[J].Pacific J.Optim.,2015,11:291-307.
[13] Z Luo,L Qi,N Xiu.The sparsest solutions to Z-tensor complementarity problems[J].Optim.Lett.,2017,11(3):471-482.
[14] G Yu,Z Yu,Y Xu,et al.An adaptive gradient method for computing generalized tensor eigenpairs[J].Comput.Optim.& Appl.,2016:1-17.
[15] W W Hager,D T Phan,J Zhu.Projection algorithms for nonconvex minimization with application to sparse principal component analysis[J].J.Glob.Opt.,2016,65(4):657-676.