Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis

Patrick J.F. Groenen*, Bart Jan Van Os, Jacqueline J. Meulman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)

Abstract

An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution.

Original languageEnglish
Pages (from-to)511-524
Number of pages14
JournalPsychometrika
Volume65
Issue number4
DOIs
Publication statusPublished - Dec 2000

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