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.
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Groenen, P., Heiser, W. & Meulman, J. Global Optimization in Least-Squares Multidimensional Scaling by Distance Smoothing. J. of Classification 16, 225–254 (1999). https://doi.org/10.1007/s003579900055
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DOI: https://doi.org/10.1007/s003579900055