Advances in Multidimensional Scaling

Abstract

Multidimensional scaling (MDS) is a central technique in facet theory. The main asset of MDS is that it is a visualization technique that excels in simplicity in its interpretation: points that are close together are similar; those that are far apart differ. An important development in MDS has been the majorization algorithm SMACOF proposed by De Leeuw (1977) and its extension of constrained MDS by De Leeuw and Heiser (1980). This algorithmic framework allows for very useful applications and extensions of MDS. In this presentation, we shall discuss several advances in MDS within the majorization framework. There will be special attention to dynamic visualization of MDS, the special case of MDS of constant dissimilarities, the effect of applying weights to MDS, imposing regional restrictions from facets with MDS, and large scale MDS.