Unfolding a symmetric matrix
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- dc.contributor.author Gower, John C.ca
- dc.contributor.author Greenacre, Michaelca
- 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.date.modified 2017-07-23T02:02:23Z
- 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/pdfca
- 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.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.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
- 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.title Unfolding a symmetric matrixca
- dc.type info:eu-repo/semantics/workingPaper