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Nonmetric Linear Biplots

Nonmetric Linear Biplots A methodology is developed for constructing linear biplots for a class of nonmetric multidimensional scaling methods for multivariate data. The nonlinear transformations of nonmetric scaling manifest themselves in irregularly spaced calibration markers. Two approaches are examined, one based on Procrustean embedding, the other on a modification of the popular regression method. The widespread use of an unmodified regression method in association with nonlinear transformations is questioned. An example is given. The methodology presented here could potentially be developed to give an optimal represention of a matrix in fewer geometric dimensions than its rank. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

Nonmetric Linear Biplots

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Publisher
Springer Journals
Copyright
Copyright © 1999 by Springer-Verlag New York Inc.
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal, Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/s003579900053
Publisher site
See Article on Publisher Site

Abstract

A methodology is developed for constructing linear biplots for a class of nonmetric multidimensional scaling methods for multivariate data. The nonlinear transformations of nonmetric scaling manifest themselves in irregularly spaced calibration markers. Two approaches are examined, one based on Procrustean embedding, the other on a modification of the popular regression method. The widespread use of an unmodified regression method in association with nonlinear transformations is questioned. An example is given. The methodology presented here could potentially be developed to give an optimal represention of a matrix in fewer geometric dimensions than its rank.

Journal

Journal of Classification – Springer Journals

Published: Feb 28, 2014

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