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.