메뉴 건너뛰기




Volumn 31, Issue 2, 2009, Pages 248-271

A newton-grassmann method for computing the best multilinear rank-(r 1,r2,r3) approximation of a tensor

Author keywords

Approximation; Grassmann manifold; Multilinear; Newton; Rank; Tensor

Indexed keywords

ALGEBRAIC MANIPULATIONS; APPROXIMATION; APPROXIMATION PROBLEMS; GRASSMANN MANIFOLD; NEWTON EQUATION; NEWTON METHODS; NEWTON'S METHODS; QUADRATIC CONVERGENCE; TENSOR PRODUCTS;

EID: 68149125583     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/070688316     Document Type: Article
Times cited : (124)

References (27)
  • 2
    • 33845525246 scopus 로고    scopus 로고
    • Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
    • B. BADER AND T. KOLDA, Algorithm 862: MATLAB tensor classes for fast algorithm prototyping, ACM Trans. Math. Software, 32 (2006), pp. 635-653.
    • (2006) ACM Trans. Math. Software , vol.32 , pp. 635-653
    • Bader, B.1    Kolda, T.2
  • 3
    • 49749096526 scopus 로고    scopus 로고
    • Efficient MATLAB computations with sparse and factored tensors
    • B. W. BADER AND T. G. KOLDA, Efficient MATLAB computations with sparse and factored tensors, SIAM J. Sci. Comput., 30 (2007), pp. 205-231.
    • (2007) SIAM J. Sci. Comput. , vol.30 , pp. 205-231
    • Bader, B.W.1    Kolda, T.G.2
  • 7
    • 55349142218 scopus 로고    scopus 로고
    • Tensor rank and the ill-posedness of the best low-rank approximation problem
    • V. DE SILVA AND L.-H. LIM, Tensor rank and the ill-posedness of the best low-rank approximation problem, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 1084-1127.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 1084-1127
    • De Silva, V.1    Lim, L.-H.2
  • 8
    • 0032216898 scopus 로고    scopus 로고
    • The geometry of algorithms with orthogonality constraints
    • A. EDELMAN, T. ARIAS, AND S. T. SMITH, The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 303-353.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 303-353
    • Edelman, A.1    Arias, T.2    Smith, S.T.3
  • 11
    • 0001299069 scopus 로고    scopus 로고
    • An index formalism that generalizes the capabilities of matrix notation and algebra to n-way arrays
    • R. A. HARSHMAN, An index formalism that generalizes the capabilities of matrix notation and algebra to n-way arrays, J. Chemometrics, 15 (2001), pp. 689-714.
    • (2001) J. Chemometrics , vol.15 , pp. 689-714
    • Harshman, R.A.1
  • 12
    • 85163188929 scopus 로고
    • Multiple invariants and generalized rank of a p-way matrix or tensor
    • F. L. HITCHCOCK, Multiple invariants and generalized rank of a p-way matrix or tensor, J. Math. Phys. Camb., 7 (1927), pp. 39-70.
    • (1927) J. Math. Phys. Camb. , vol.7 , pp. 39-70
    • Hitchcock, F.L.1
  • 14
    • 67651114913 scopus 로고    scopus 로고
    • Dimensionality reduction for higher-order tensors: Algorithms and applications
    • M. ISHTEVA, L. DE LATHAUWER, P.-A. ABSIL, AND S. VAN HUFFEL, Dimensionality reduction for higher-order tensors: Algorithms and applications, Int. J. Pure Appl. Math., 42 (2008), pp. 337-343.
    • (2008) Int. J. Pure Appl. Math. , vol.42 , pp. 337-343
    • Ishteva, M.1    De Lathauwer, L.2    Absil, P.-A.3    Van Huffel, S.4
  • 15
    • 0033646780 scopus 로고    scopus 로고
    • Towards a standardized notation and terminology in multiway analysis
    • H. A. L. KIERS, Towards a standardized notation and terminology in multiway analysis, J. Chemometrics, 14 (2000), pp. 106-125.
    • (2000) J. Chemometrics , vol.14 , pp. 106-125
    • Kiers, H.A.L.1
  • 17
    • 37849024658 scopus 로고    scopus 로고
    • Multilinear operators for higher-order decompositions
    • Sandia National Laboratories, Albuquerque, NM
    • T. G. KOLDA, Multilinear Operators for Higher-order Decompositions, Technical report SAND2006-2081, Sandia National Laboratories, Albuquerque, NM, 2006.
    • (2006) Technical Report SAND2006-2081
    • Kolda, T.G.1
  • 18
    • 0002332422 scopus 로고
    • Principal component analysis of three-mode data by means of alternating least squares algorithms
    • P. M. KROONENBERG, Principal component analysis of three-mode data by means of alternating least squares algorithms, Psychometrika, 45 (1980), pp. 69-97.
    • (1980) Psychometrika , vol.45 , pp. 69-97
    • Kroonenberg, P.M.1
  • 19
    • 0036018640 scopus 로고    scopus 로고
    • Adaptive eigenvalue computations using Newton's method on the Grassmann manifold
    • E. LUNDSTRÖM AND L. ELDÉN, Adaptive eigenvalue computations using Newton's method on the Grassmann manifold, SIAM J. Matrix Anal. Appl., 23 (2002), pp. 819-839.
    • (2002) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 819-839
    • Lundström, E.1    Eldén, L.2
  • 21
    • 0001258795 scopus 로고
    • On search directions for minimization algorithms
    • M. J. D. POWELL, On search directions for minimization algorithms, Math. Program., 4 (1973), pp. 193-201.
    • (1973) Math. Program. , vol.4 , pp. 193-201
    • Powell, M.J.D.1
  • 22
    • 0002832234 scopus 로고
    • Algorithms for separable nonlinear least squares problems
    • A. RUHE AND P.-A WEDIN, Algorithms for separable nonlinear least squares problems, SIAM Rev., 22 (1980), pp. 318-337.
    • (1980) SIAM Rev. , vol.22 , pp. 318-337
    • Ruhe, A.1    Wedin, P.-A.2
  • 24
    • 0000666371 scopus 로고
    • The extension of factor analysis to three-dimensional matrices
    • H. Gulliksen and N. Frederiksen, eds., Holt, Rinehart and Winston, New York
    • L. R. TUCKER, The extension of factor analysis to three-dimensional matrices, in Contributions to Mathematical Psychology, H. Gulliksen and N. Frederiksen, eds., Holt, Rinehart and Winston, New York, 1964, pp. 109-127.
    • (1964) Contributions to Mathematical Psychology , pp. 109-127
    • Tucker, L.R.1
  • 25
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • L. R. TUCKER, Some mathematical notes on three-mode factor analysis, Psychometrika, 31 (1966), pp. 279-311.
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1
  • 26
    • 84944415516 scopus 로고    scopus 로고
    • Multilinear analysis of image ensembles: Tensor- faces, in Proceedings of the 7th European Conference on Computer Vision (ECCV'02)
    • Springer, New York
    • M. A. O. VASILESCU AND D. TERZOPOULOS, Multilinear analysis of image ensembles: Tensor- faces, in Proceedings of the 7th European Conference on Computer Vision (ECCV'02), Lect. Notes Comput. Sci. 2350, Springer, New York, 2002, pp. 447-460.
    • (2002) Lect. Notes Comput. Sci. , vol.2350 , pp. 447-460
    • Vasilescu, M.A.O.1    Terzopoulos, D.2
  • 27
    • 0041941095 scopus 로고    scopus 로고
    • Multilinear subspace analysis of image ensembles, in IEEE Conference on Computer Vision and Pattern Recognition (CVPR'03)
    • M. A. O. VASILESCU AND D. TERZOPOULOS, Multilinear subspace analysis of image ensembles, in IEEE Conference on Computer Vision and Pattern Recognition (CVPR'03), Madison WI, 2003, pp. 93-99.
    • (2003) Madison WI , pp. 93-99
    • Vasilescu, M.A.O.1    Terzopoulos, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.