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dc.contributor.author Gower, John C.
dc.contributor.author Greenacre, Michael
dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
dc.date.accessioned 2017-07-26T12:07:55Z
dc.date.available 2017-07-26T12:07:55Z
dc.date.issued 1996-01-01
dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=154
dc.identifier.citation Journal of Classification, 13, (1996), pp. 81-105
dc.identifier.uri http://hdl.handle.net/10230/20872
dc.description.abstract Graphical displays which show inter--sample distances are important for the interpretation and presentation of multivariate data. Except when the displays are two--dimensional, however, they are often difficult to visualize as a whole. A device, based on multidimensional unfolding, is described for presenting some intrinsically high--dimensional displays in fewer, usually two, dimensions. This goal is achieved by representing each sample by a pair of points, say $R_i$ and $r_i$, so that a theoretical distance between the $i$-th and $j$-th samples is represented twice, once by the distance between $R_i$ and $r_j$ and once by the distance between $R_j$ and $r_i$. Self--distances between $R_i$ and $r_i$ need not be zero. The mathematical conditions for unfolding to exhibit symmetry are established. Algorithms for finding approximate fits, not constrained to be symmetric, are discussed and some examples are given.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.relation.ispartofseries Economics and Business Working Papers Series; 154
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 Unfolding a symmetric matrix
dc.type info:eu-repo/semantics/workingPaper
dc.date.modified 2017-07-23T02:02:23Z
dc.subject.keyword dimensionality reduction
dc.subject.keyword distances
dc.subject.keyword graphics
dc.subject.keyword multidimensional scaling
dc.subject.keyword symmetric matrices
dc.subject.keyword unfolding
dc.subject.keyword Statistics, Econometrics and Quantitative Methods
dc.rights.accessRights info:eu-repo/semantics/openAccess


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