Treffer: The multimode Procrustes problem
Title:
The multimode Procrustes problem
Authors:
Source:
Linear algebra and its applications. 349:245-264
Publisher Information:
New York, NY: Elsevier Science, 2002.
Publication Year:
2002
Physical Description:
print, 23 ref
Original Material:
CRAN
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Sciences appliquees, Applied sciences, Recherche operationnelle. Gestion, Operational research. Management science, Recherche opérationnelle et modèles formalisés de gestion, Operational research and scientific management, Optimisation. Problèmes de recherche, Optimization. Search problems, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Automatique théorique. Systèmes, Control theory. Systems, Divers, Miscellaneous, Analyse composante principale, Principal component analysis, Análisis componente principal, Analyse donnée, Data analysis, Análisis datos, Analyse n dimensionnelle, Multidimensional analysis, Análisis n dimensional, Condition optimalité, Optimality condition, Condición optimalidad, Equation différentielle, Differential equation, Ecuación diferencial, Equation matricielle, Matrix equation, Ecuación matricial, Géométrie différentielle, Differential geometry, Geometría diferencíal, Minimisation, Minimization, Minimización, Modèle géométrique, Geometrical model, Modelo geométrico, Méthode moindre carré, Least squares method, Método cuadrado menor, Optimisation sous contrainte, Constrained optimization, Optimización con restricción, Procrustes problem, Riemannian connection, multimode
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mechanical Engineering, Strathclyde University, Glasgow G1 1XJ, Scotland, United Kingdom
Applied Mathematics and Numerical Methods Department, Sandia National Laboratories, Albuquerque, NM 87185, United States
Applied Mathematics and Numerical Methods Department, Sandia National Laboratories, Albuquerque, NM 87185, United States
ISSN:
0024-3795
Rights:
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Mathematics
Operational research. Management
Mathematics
Operational research. Management
Accession Number:
edscal.14285023
Database:
PASCAL Archive
Weitere Informationen
In this paper, we consider a generalization of the well-known Procrustes problem relevant to principal component analysis of multidimensional data arrays. This multimode Procrustes problem is a complex constrained minimization problem which involves the simultaneous least-squares fitting of several matrices. We propose two solutions of the problem: the projected gradient approach which leads to solving ordinary differential equations on matrix manifolds, and differential-geometric approach for optimization on products of matrix manifolds. A numerical example concerning the three-mode Procrustes illustrates the developed algorithms.