Some Multidimensional Scaling and Related Procedures Devised at Bell Laboratories, With Ecological Applications

Abstract

A large number of multidimensional scaling (MDS) and related models, methods, and computer programs (for all of which we use the generic term “MDS procedures”) have been developed over the years at Bell Laboratories. This paper focuses on probably the most widely known and used subset of Bell Labs MDS procedures involving spatial (as opposed to tree structure, overlapping or non-overlapping clustering, or other “discrete and hybrid”) models. These are: the MDSCAL and KYST family, for two-way (metric or nonmetric) MDS of proximities (e.g., similarities or dissimilarities); INDSCAL, SINDSCAL and IDIOSCAL, for three-way MDS, primarily of proximities (but also applicable to more general multiway data, in a manner to be described); MDPREF, for “internal analysis” of preference (or other “dominance”) data for different individual “subjects” (or other data sources) in terms of a vector model; and the PREFMAP family for “external analysis” of such data (where the “stimulus” or other “object” dimensions are externally provided by prior analysis or theory, only “subject” vectors, ideal points and/or other parameters being determined from preference/dominance data). A number of these Bell Labs MDS procedures areapplied to some ecological data on seaworm species due to E. Fresi and collaborators.