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- Title
Global Optimization in Least-Squares Multidimensional Scaling by Distance Smoothing.
- Authors
Groenen, P. J. F.; Heiser, W. J.; Meulman, J. J.
- Abstract
Abstract: Least-squares multidimensional scaling is known to have a serious problem of local minima, especially if one dimension is chosen, or if city-block distances are involved. One particular strategy, the smoothing strategy proposed by Pliner (1986, 1996), turns out to be quite successful in these cases. Here, we propose a slightly different approach, called distance smoothing. We extend distance smoothing for any Minkowski distance. In addition, we extend the majorization approach to multidimensional scaling to have a one-step update for Minkowski parameters larger than 2 and use the results for distance smoothing. We present simple ideas for finding quadratic majorizing functions. The performance of distance smoothing is investigated in several examples, including two simulation studies.
- Subjects
MULTIDIMENSIONAL scaling; STATISTICAL smoothing; MINKOWSKI geometry
- Publication
Journal of Classification, 1999, Vol 16, Issue 2, p225
- ISSN
0176-4268
- Publication type
Article
- DOI
10.1007/s003579900055