Majorization as a tool for optimizing a class of matrix functions

DOI10.1007/BF02294758zbMath0733.62067OpenAlexW1995855984MaRDI QIDQ809513

Henk A. L. Kiers

Publication date: 1990

Published in: Psychometrika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02294758

zbMATH Keywords

optimization problemtrace functionmajorizing functionfitting statistical models by least squaresmonotonic minimizationmonotonically convergent algorithm

Mathematics Subject Classification ID

Multivariate analysis (62H99) Factor analysis and principal components; correspondence analysis (62H25) Applications of mathematical programming (90C90)

Related Items

Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems, A monotonically convergent algorithms for factals, Maximization of sums of quotients of quadratic forms and some generalizations, Weighted least squares fitting using ordinary least squares algorithms, Techniques for rotating two or more loading matrices to optimal agreement and simple structure: A comparison and some technical details, Principal component analysis constrained by layered simple structures, Effective algorithms for solving trace minimization problem in multivariate statistics, A comparison of various methods for multivariate regression with highly collinear variables, AN EFFICIENT METHOD FOR SOLVING A CLASS OF MATRIX TRACE FUNCTION MINIMIZATION PROBLEM IN MULTIVARIATE STATISTICAL, A monotonically convergent algorithm for orthogonal congruence rotation, Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables, Minimization of a class of matrix trace functions by means of refined majorization, Analyzing multiset data by the power STATIS-ACT method, Proximal Distance Algorithms: Theory and Examples, A simple general procedure for orthogonal rotation, Distance-based discriminant analysis method and its applications, Analysis of \(k\) sets of data, with differential emphasis on agreement between and within sets, An alternating least squares algorithm for PARAFAC2 and three-way DEDICOM, Joint Procrustes analysis for simultaneous nonsingular transformation of component score and loading matrices, Constructing Common Factors from Continuous and Categorical Data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Correspondence analysis with least absolute residuals
• Convergence of the majorization method for multidimensional scaling
• Principal component analysis of three-mode data by means of alternating least squares algorithms
• Solving implicit equations in psychometric data analysis
• Additive structure in qualitative data: An alternating least squares method with optimal scaling features
• Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features
• A direct approach to individual differences scaling using increasingly complex transformations
• A generalization of Takane's algorithm for DEDICOM
• Annotated bibliography of three-mode factor analysis