Global optimization in least-squares multidimensional scaling by distance smoothing

Least-squares multidimensional scaling is known to have a serious problem o f local minima, especially if one dimension is chosen, or if city-block dis tances are involved. One particular strategy, the smoothing strategy propos ed 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 e xtend the majorization approach to multidimensional scaling to have a one-s tep update for Minkowski parameters larger than 2 and use the results for d istance smoothing. We present simple ideas for finding quadratic majorizing functions. The performance of distance smoothing is investigated in severa l examples, including two simulation studies.