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Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems

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  • Kiers, Henk A. L.

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  • Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    • Handle: RePEc:eee:csdana:v:41:y:2002:i:1:p:157-170
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    References listed on IDEAS

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    1. Henk Kiers, 1995. "Maximization of sums of quotients of quadratic forms and some generalizations," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 221-245, June.
    2. Norman Cliff, 1966. "Orthogonal rotation to congruence," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 33-42, March.
    3. Henk Kiers, 1990. "Majorization as a tool for optimizing a class of matrix functions," Psychometrika, Springer;The Psychometric Society, vol. 55(3), pages 417-428, September.
    4. Jos Berge & Klaas Nevels, 1977. "A general solution to Mosier's oblique procrustes problem," Psychometrika, Springer;The Psychometric Society, vol. 42(4), pages 593-600, December.
    5. Henk Kiers & Jos Berge, 1992. "Minimization of a class of matrix trace functions by means of refined majorization," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 371-382, September.
    6. Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 251-266, June.
    7. Jan Leeuw, 1988. "Convergence of the majorization method for multidimensional scaling," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 163-180, September.
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    Cited by:

    1. Heij, C. & Groenen, P.J.F. & van Dijk, D.J.C., 2006. "Time series forecasting by principal covariate regression," Econometric Institute Research Papers EI 2006-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Naoto Yamashita, 2023. "Principal component analysis constrained by layered simple structures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 347-367, June.
    3. Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 649-662.
    4. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    5. Groenen, P.J.F. & Winsberg, S. & Rodriguez, O. & Diday, E., 2005. "SymScal: symbolic multidimensional scaling of interval dissimilarities," Econometric Institute Research Papers EI 2005-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Qingna Li & Houduo Qi & Naihua Xiu, 2011. "Block relaxation and majorization methods for the nearest correlation matrix with factor structure," Computational Optimization and Applications, Springer, vol. 50(2), pages 327-349, October.
    7. Laura Vicente-Gonzalez & Jose Luis Vicente-Villardon, 2022. "Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation," Mathematics, MDPI, vol. 10(15), pages 1-23, July.
    8. Rosember Guerra-Urzola & Niek C. Schipper & Anya Tonne & Klaas Sijtsma & Juan C. Vera & Katrijn Deun, 2023. "Sparsifying the least-squares approach to PCA: comparison of lasso and cardinality constraint," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 269-286, March.
    9. Krijnen, Wim P., 2006. "Convergence of the sequence of parameters generated by alternating least squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 481-489, November.
    10. K. Van Deun & P. J. F. Groenen, 2005. "Majorization Algorithms for Inspecting Circles, Ellipses, Squares, Rectangles, and Rhombi," Operations Research, INFORMS, vol. 53(6), pages 957-967, December.
    11. Groenen, P.J.F. & Giaquinto, P. & Kiers, H.A.L., 2003. "Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models," Econometric Institute Research Papers EI 2003-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Antonio Calcagnì & Luigi Lombardi & Lorenzo Avanzi & Eduardo Pascali, 2020. "Multiple mediation analysis for interval-valued data," Statistical Papers, Springer, vol. 61(1), pages 347-369, February.
    13. Groenen, P.J.F. & Kaymak, U. & van Rosmalen, J.M., 2006. "Fuzzy clustering with Minkowski distance," Econometric Institute Research Papers EI 2006-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Ryan Browne & Paul McNicholas, 2014. "Estimating common principal components in high dimensions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 217-226, June.
    15. Markovsky, Ivan & Niranjan, Mahesan, 2010. "Approximate low-rank factorization with structured factors," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3411-3420, December.
    16. Kim, Nam-Hwui & Browne, Ryan P., 2021. "In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    17. Kuroda, Masahiro & Mori, Yuichi & Iizuka, Masaya & Sakakihara, Michio, 2011. "Acceleration of the alternating least squares algorithm for principal components analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 143-153, January.
    18. Salvatore D. Tomarchio & Luca Bagnato & Antonio Punzo, 2022. "Model-based clustering via new parsimonious mixtures of heavy-tailed distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 315-347, June.
    19. van Deun, K. & Groenen, P.J.F. & Delbeke, L., 2005. "VIPSCAL: A combined vector ideal point model for preference data," Econometric Institute Research Papers EI 2005-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Li, Guoqi & Tang, Pei & Meng, Ziyang & Wen, Changyun & Pei, Jing & Shi, Luping, 2018. "Optimization on matrix manifold based on gradient information and its applications in network control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 481-500.
    21. Groenen, P.J.F. & Bioch, J.C. & Nalbantov, G.I., 2006. "Nonlinear support vector machines through iterative majorization and I-splines," Econometric Institute Research Papers EI 2006-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    22. Groenen, P.J.F. & Winsberg, S. & Rodriguez, O. & Diday, E., 2006. "I-Scal: Multidimensional scaling of interval dissimilarities," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 360-378, November.
    23. Groenen, P.J.F. & Nalbantov, G.I. & Bioch, J.C., 2007. "SVM-Maj: a majorization approach to linear support vector machines with different hinge errors," Econometric Institute Research Papers EI 2007-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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