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...

A simple geometry allows the main properties of matrix approximations used in biplot displays to be developed. It establishes orthogonal components of an analysis of variance, from which different contributions to approximations may be assessed. Particular attention is paid to approximations...