Weighted Euclidean biplots
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- dc.contributor.author Greenacre, Michaelca
- dc.contributor.author Groenen, Patrick J. F.ca
- dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
- dc.date.accessioned 2017-07-26T10:50:33Z
- dc.date.available 2017-07-26T10:50:33Z
- dc.date.issued 2013-07-01
- dc.date.modified 2017-07-23T02:19:48Z
- dc.description.abstract We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.
- dc.format.mimetype application/pdfca
- dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=1380
- dc.identifier.citation Journal of Classification, 2016, 33, 442-459
- dc.identifier.uri http://hdl.handle.net/10230/20976
- dc.language.iso eng
- dc.relation.ispartofseries Economics and Business Working Papers Series; 1380
- 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.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
- dc.subject.keyword biplot
- dc.subject.keyword correspondence analysis
- dc.subject.keyword distance
- dc.subject.keyword majorization
- dc.subject.keyword multidimensional scaling
- dc.subject.keyword singular-value decomposition
- dc.subject.keyword weighted least squares
- dc.subject.keyword Statistics, Econometrics and Quantitative Methods
- dc.title Weighted Euclidean biplotsca
- dc.title.alternative
- dc.type info:eu-repo/semantics/workingPaper