Weighted metric multidimensional scaling

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Greenacre, Michael J.. Weighted metric multidimensional scaling. 2004
To cite or link this document: http://hdl.handle.net/10230/765
dc.contributor.author Greenacre, Michael J.
dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
dc.date.issued 2004-09-01
dc.identifier.uri http://hdl.handle.net/10230/765
dc.description.abstract This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.
dc.language.iso eng
dc.relation.ispartofseries Economics and Business Working Papers Series; 777
dc.rights L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.title Weighted metric multidimensional scaling
dc.type info:eu-repo/semantics/workingPaper
dc.date.modified 2014-06-03T07:14:11Z
dc.subject.keyword Statistics, Econometrics and Quantitative Methods
dc.subject.keyword biplot
dc.subject.keyword correspondence analysis
dc.subject.keyword distance
dc.subject.keyword multidimensional scaling
dc.subject.keyword singular-value decomposition
dc.rights.accessRights info:eu-repo/semantics/openAccess

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