A model and algorithm for multidimensional scaling with external constraints on the distances
dc.contributor.author | Borg, Ingwer | en_US |
dc.contributor.author | Lingoes, James C. | en_US |
dc.date.accessioned | 2006-09-11T16:24:42Z | |
dc.date.available | 2006-09-11T16:24:42Z | |
dc.date.issued | 1980-03 | en_US |
dc.identifier.citation | Borg, Ingwer; Lingoes, James C.; (1980). "A model and algorithm for multidimensional scaling with external constraints on the distances." Psychometrika 45(1): 25-38. <http://hdl.handle.net/2027.42/45739> | en_US |
dc.identifier.issn | 1860-0980 | en_US |
dc.identifier.issn | 0033-3123 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/45739 | |
dc.description.abstract | A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The approach defines an objective function which is a linear composite of the loss function of the point configuration X relative to the proximity data P and the loss of X relative to a pseudo-data matrix R . The matrix R is set up such that the side constraints to be imposed on X 's distances are expressed by the relations among R 's numerical elements. One then uses a double-phase procedure with relative penalties on the loss components to generate a constrained solution X . Various possibilities for constructing actual MDS algorithms are conceivable: the major classes are defined by the specification of metric or nonmetric loss for data and/or constraints, and by the various possibilities for partitioning the matrices P and R . Further generalizations are introduced by substituting R by a set of R matrices, R i , i =1, ... r , which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time. | en_US |
dc.format.extent | 971752 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag; The Psychometric Society | en_US |
dc.subject.other | Psychometrics | en_US |
dc.subject.other | Geometric Models | en_US |
dc.subject.other | Constrained Multidimensional Scaling | en_US |
dc.subject.other | Psychology | en_US |
dc.subject.other | Statistical Theory and Methods | en_US |
dc.subject.other | Assessment, Testing and Evaluation | en_US |
dc.subject.other | Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law | en_US |
dc.subject.other | Hypothesis Testing | en_US |
dc.subject.other | Nonlinear Optimization | en_US |
dc.title | A model and algorithm for multidimensional scaling with external constraints on the distances | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Psychology | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | The University of Michigan, 1005 North University Building, 48109, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationother | Rheinisch-Westfälische Technische Hochschule, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/45739/1/11336_2005_Article_BF02293597.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF02293597 | en_US |
dc.identifier.source | Psychometrika | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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