Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors
暂无分享,去创建一个
[1] Lieven De Lathauwer,et al. A survey of tensor methods , 2009, 2009 IEEE International Symposium on Circuits and Systems.
[2] Joos Vandewalle,et al. Computation of the Canonical Decomposition by Means of a Simultaneous Generalized Schur Decomposition , 2005, SIAM J. Matrix Anal. Appl..
[3] Rasmus Bro,et al. Improving the speed of multi-way algorithms:: Part I. Tucker3 , 1998 .
[4] Berkant Savas,et al. Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors , 2009, SIAM J. Sci. Comput..
[5] Pierre-Antoine Absil,et al. A Modified Particle Swarm Optimization Algorithm for the Best Low Multilinear Rank Approximation of Higher-Order Tensors , 2010, ANTS Conference.
[6] Robert H. Halstead,et al. Matrix Computations , 2011, Encyclopedia of Parallel Computing.
[7] Berkant Savas,et al. Krylov Subspace Methods for Tensor Computations , 2009 .
[8] J. Leeuw,et al. Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms , 1987 .
[9] Seungjin Choi,et al. Independent Component Analysis , 2009, Handbook of Natural Computing.
[10] Antoine Souloumiac,et al. Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..
[11] J. Cardoso,et al. Blind beamforming for non-gaussian signals , 1993 .
[12] J. Chang,et al. Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .
[13] F. L. Hitchcock. The Expression of a Tensor or a Polyadic as a Sum of Products , 1927 .
[14] F. L. Hitchcock. Multiple Invariants and Generalized Rank of a P‐Way Matrix or Tensor , 1928 .
[15] Phillip A. Regalia,et al. Monotonic convergence of fixed-point algorithms for ICA , 2003, IEEE Trans. Neural Networks.
[16] Elijah Polak,et al. Computational methods in optimization , 1971 .
[17] L. Lathauwer,et al. Dimensionality reduction in higher-order signal processing and rank-(R1,R2,…,RN) reduction in multilinear algebra , 2004 .
[18] J. Leeuw,et al. Principal component analysis of three-mode data by means of alternating least squares algorithms , 1980 .
[19] P. McCullagh. Tensor Methods in Statistics , 1987 .
[20] Carla D. Moravitz Martin,et al. A Jacobi-Type Method for Computing Orthogonal Tensor Decompositions , 2008, SIAM J. Matrix Anal. Appl..
[21] C. L. Nikias,et al. Signal processing with higher-order spectra , 1993, IEEE Signal Processing Magazine.
[22] Berkant Savas,et al. A Newton-Grassmann Method for Computing the Best Multilinear Rank-(r1, r2, r3) Approximation of a Tensor , 2009, SIAM J. Matrix Anal. Appl..
[23] Joos Vandewalle,et al. On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors , 2000, SIAM J. Matrix Anal. Appl..
[24] L. Lathauwer,et al. On the best low multilinear rank approximation of higher-order tensors , 2010 .
[25] Sabine Van Huffel,et al. Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors , 2008, Numerical Algorithms.
[26] C. L. Nikias,et al. Higher-order spectra analysis : a nonlinear signal processing framework , 1993 .
[27] Ganesh R. Naik,et al. Introduction: Independent Component Analysis , 2012 .
[28] Yurii Nesterov,et al. Generalized Power Method for Sparse Principal Component Analysis , 2008, J. Mach. Learn. Res..
[29] L. Lathauwer. First-order perturbation analysis of the best rank-(R1, R2, R3) approximation in multilinear algebra , 2004 .
[30] P. Kroonenberg. Applied Multiway Data Analysis , 2008 .
[31] Berkant Savas,et al. Krylov-Type Methods for Tensor Computations , 2010, 1005.0683.
[32] Sabine Van Huffel,et al. Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme , 2011, SIAM J. Matrix Anal. Appl..
[33] Levent Tunçel,et al. Optimization algorithms on matrix manifolds , 2009, Math. Comput..
[34] L. Tucker,et al. Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.
[35] Phillip A. Regalia,et al. On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors , 2001, SIAM J. Matrix Anal. Appl..
[36] Phillip A. Regalia,et al. The higher-order power method revisited: convergence proofs and effective initialization , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).
[37] Pierre-Antoine Absil,et al. Accelerated Line-search and Trust-region Methods , 2009, SIAM J. Numer. Anal..
[38] Mohammed Bennani Dosse,et al. The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal , 2008, Psychometrika.
[39] P. Regalia. Monotonically convergent algorithms for symmetric tensor approximation , 2013 .
[40] Richard A. Harshman,et al. Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .
[41] E. Polak,et al. Computational methods in optimization : a unified approach , 1972 .
[42] Pierre Comon,et al. Independent component analysis, A new concept? , 1994, Signal Process..
[43] Tamara G. Kolda,et al. Tensor Decompositions and Applications , 2009, SIAM Rev..
[44] Sabine Van Huffel,et al. Tucker compression and local optima , 2011 .
[45] Tamara G. Kolda,et al. Shifted Power Method for Computing Tensor Eigenpairs , 2010, SIAM J. Matrix Anal. Appl..
[46] Gene H. Golub,et al. Symmetric Tensors and Symmetric Tensor Rank , 2008, SIAM J. Matrix Anal. Appl..
[47] Joos Vandewalle,et al. Independent component analysis and (simultaneous) third-order tensor diagonalization , 2001, IEEE Trans. Signal Process..
[48] S. Friedland. Best rank one approximation of real symmetric tensors can be chosen symmetric , 2011, 1110.5689.
[49] Lieven De Lathauwer,et al. Tensor-based techniques for the blind separation of DS-CDMA signals , 2007, Signal Process..
[50] Joos Vandewalle,et al. A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..