History of MDS
Literature addressing the history of multidimensional
scaling is heavily based upon the viewpoints of the individuals with firsthand
involvement in it's the developments. One such individual, Forrest
W. Young (1987), provides the following historical framework for MDS.
He has divided the history of "multidimensional scaling into four stages,
each roughly corresponding to a decade, and each demarcated by highly innovated
1. The first decade was pioneered by the seminal
work of Torgerson
(1952), he defined the multidimensional
scaling problem and
provided the first metric solution.
provided the first complete explication of a MDS method.
(1941) had already performed a "crude" MDS scaling
of data concerning
the degree of hostility between nations, the first
procedure for determining the MDS map of points from
distances was provided by Torgerson.
introduced three major steps: (Torgerson, 1952)
A scale of comparative distances between all pairs of stimuli is
obtained [i.e. measured on an interval scale]
Distances between each pair of stimuli are located on a
distance continuum. In paired comparisons, the procedures for
obtaining a scale of comparative distances leave the true zero
point undetermined. A comparative distance is not a distance in
the usual sense of the term, but is a distance minus an unknown
constant. When the unknown constant is obtained, the
comparative distances can be converted into absolute [i.e.,
The dimensionality of the psychological space necessary to
account for these absolute distances is determined, and the
projections of stimuli on axes of this space are obtained.
2. The second decade of work was heralded in
by the innovative work of
Shepard (1962) and Kruskal (1964)
on nonmetric multidimensional
scaling, and saw the highly illuminating
work of Coombs (1964) on data
active decade included work that focused on developing
analyzing ordinal dissimilarities data known as nonmetric
This stage became popularized by Shepard (1962) who turned
a data analysis procedure familiar to a few aficionados
into a procedure
used in such diverse disciplines as architecture and
and political science, and psychology and business
Shepard pointed out the idea that one could recover
from nonmetric information.
3. The third decade included 25 years of developments
by Takane, Young,
and De Leeuw (1977), and by the
De Leeuw and Heiser (1980). The
trend setting work came from Carroll
and Chang (1970) on individual
point, MDS procedures could only analyze a single matrix of
Leading to the development of "individual differences" MDS.
(i.e. procedures that were able to simultaneously analyze a number of data
matrices without the
necessity of any type of averaging process).
Chang proposed a model for representing
individual differences whose psychological appeal
was very high,
which displayed individual differences in an easily
and parsimonious fashion.
4. The fourth decade presented the development
of constrained MDS and
maximum likelihood multidimensional
scaling, as exemplified by
Ramsay (1982) and Takane (1980a,
MDS - introduction of constraints on the parameters of the
MDS - A maturing of the data analysis technology
a desire for... an explanation of the error model involved in
process. (Ramsay 1977)
changes MDS from a descriptive tool into an inferential
the development of significant tests to determine the
dimensionality, appropriate MDS model, and appropriate
provides confidence regions for the stimuli and with
of MDS: An Outline
Learning is not the accumulation of knowledge.
Learning is movement from moment to moment.
Cummins - 2001