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The Dynamical System Approach to Multivariate Data Analysis

Trendafilov, Nickolay T. (2006). The Dynamical System Approach to Multivariate Data Analysis. Journal of Computational and Graphical Statistics, 15(3) pp. 628–650.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1198/106186006X130828
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Abstract

In this survey a number of problems arising in multivariate data analysis (MDA) are listed and reformulated as matrix fitting (e. g. least-squares, maximum likelihood, etc) constrained optimization problems
(OPs). The goal is to demonstrate that consideration and solution of these diverse MDA problems can be unified by means of the dynamical system approach. The approach transforms theMDA problems into dynamical systems on a manifold defined by the constraints of the original OP.

Item Type: Journal Article
ISSN: 1537-2715
Keywords: Matrix fitting problems; Constrained optimization; Initial value problems for ODEs on matrix manifolds; Steepest descent/ascent matrix flows; Principal components; Factor analysis; Procrustes problems; Metric multidimensional scaling; Three-way data; MATLAB
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 3894
Depositing User: Nickolay Trendafilov
Date Deposited: 30 Mar 2007
Last Modified: 02 Dec 2010 19:50
URI: http://oro.open.ac.uk/id/eprint/3894
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