Sensitivity analysis of the strain criterion for multidimensional scaling

Computational Statistics and Data Analysis

Volumn 50, Issue 1 SPEC. ISS., 2006, Pages 135-153

  Lewis, R M ^a   Trosset, M W ^a  

^a Dept of Economics and Thomas Jefferson Program in Public Policy at the College of William and Mary   (United States)

Author keywords

Classical multidimensional scaling; Distance geometry; Distance matrices; Perturbation analysis; Principal coordinate analysis; Spectral decomposition

Indexed keywords

COMPUTER SOFTWARE; DATA REDUCTION; MATRIX ALGEBRA; MOLECULAR STRUCTURE; OPTIMIZATION; PERTURBATION TECHNIQUES;

DISTANCE GEOMETRY; DISTANCE MATRICES; MULTIDIMENSIONAL SCALING (MDS); PERTURBATION ANALYSIS; PRINCIPAL COORDINATE ANALYSIS; SPECTRAL DECOMPOSITION;

SENSITIVITY ANALYSIS;

EID: 24644480609     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2004.07.011     Document Type: Article

References (26)

1. I. Borg, and P. Groenen Modern Multidimensional Scaling Theory and Applications 1997 Springer New York
2. T.F. Cox, and M.A.A. Cox Multidimensional Scaling 1994 Chapman & Hall London
3. F. Critchley On certain linear mappings between inner-product and squared-distance matrices Linear Algebra Appl. 105 1988 91 107
4. J. de Leeuw, and W. Heiser Theory of multidimensional scaling P.R. Krishnaiah I.N. Kanal Handbook of Statistics vol. 2 1982 North-Holland Amsterdam 285 316 (Chapter 13)
5. B.S. Everitt, and G. Dunn Applied Multivariate Data Analysis 1991 Edward Arnold London
6. B.S. Everitt, and S. Rabe-Hesketh The Analysis of Proximity Data 1997 Edward Arnold London
7. J.C. Gower Some distance properties of latent root and vector methods in multivariate analysis Biometrika 53 1966 315 328
8. J.C. Gower, and P.J.F. Groenen Applications of the modified Leverrier-Faddeev algorithm for the construction of explicit matrix spectral decompositions and inverses Utilitas Math. 40 1991 51 64
9. W.J. Krzanowski, and F.H.C. Marriott Multivariate Analysis Part 1 Distributions, Ordination and Inference 1994 Edward Arnold London
10. A.S. Lewis Derivatives of spectral functions Math. Oper. Res. 21 1996 576 588
11. A.S. Lewis, and H.S. Sendov Twice differentiable spectral functions SIAM J. Matrix Anal. Appl. 23 2001 368 386
12. K.V. Mardia, J.T. Kent, and J.M. Bibby Multivariate Analysis 1979 Academic Press Orlando
13. J.J. Moré, and C.-H. Lin Newton's method for large bound-constrained optimization problems SIAM J. Optim. 9 1999 1100 1127
14. J.J. Moré, and G. Toraldo On the solution of large quadratic programming problems with bound constraints SIAM J. Optim. 1 1991 93 113
15. S.G. Nash, and J. Nocedal A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization SIAM J. Optim. 1 1991 358 372
16. Parks, T.A., 1985. Reducible nonlinear programming problems. Technical Report 85-8, Department of Mathematical Sciences, Rice University, Houston, TX, USA.
17. G.A.F. Seber Multivariate Observations 1984 Wiley New York
18. R. Sibson Studies in the robustness of multidimensional scaling perturbational analysis of classical scaling J. Roy. Statist. Soc. Ser. B 41 1979 217 229
19. W.S. Torgerson Multidimensional scaling I Theory and method. Psychometrika 17 1952 401 419
20. Trosset, M.W., 1997a. Computing distances between convex sets and subsets of the positive semidefinite matrices. Technical Report 97-3, Department of Computational & Applied Mathematics, Rice University, Houston, TX, USA.
21. M.W. Trosset Numerical algorithms for multidimensional scaling R. Klar P. Opitz Classification and Knowledge Organization 1997 Springer Berlin 80 92
22. M.W. Trosset Applications of multidimensional scaling to molecular conformation Comput. Sci. Statist. 29 1998 148 152
23. M.W. Trosset A new formulation of the nonmetric STRAIN problem in multidimensional scaling J. Classification 15 1998 15 35
24. M.W. Trosset Distance matrix completion by numerical optimization Comput. Optim. Appl. 17 2000 11 22
25. M.W. Trosset Extensions of classical multidimensional scaling via variable reduction Comput. Statist. 17 2002 147 163
26. J.H. Wilkinson The Algebraic Eigenvalue Problem 1965 Clarendon Press Oxford, England