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 work."



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.
        *Torgerson provided the first complete explication of a MDS method.
        Although Klingberg (1941) had already performed a "crude" MDS scaling
        of data concerning the degree of hostility between nations, the first
        systematic procedure for determining the MDS map of points from
        errorful interpoint distances was provided by Torgerson.

        *This process introduced three major steps:    (Torgerson, 1952)
        Step 1)  A scale of comparative distances between all pairs of stimuli is
                      obtained [i.e. measured on an interval scale]
        Step 2)  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., ratio]
                     distances.
        Step 3)  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
    theory.
        *This very active decade included work that focused on developing
        methods for analyzing ordinal dissimilarities data known as nonmetric
        MDS.  This stage became popularized by Shepard (1962) who turned
        "MDS from a data analysis procedure familiar to a few aficionados
        into a procedure used in such diverse disciplines as architecture and
        zoology, geography and political science, and psychology and business
        administration."  Shepard pointed out the idea that one could recover
        metric information 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
    differences MDS.
        *Before this point, MDS procedures could only analyze a single matrix of
        data.  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).
        *Carroll and Chang proposed a model for representing
        cognitive/perceptual individual differences whose psychological appeal
        was very high, which displayed individual differences in an easily
        assimilated 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, 1980b).
        *Constrained MDS - introduction of constraints on the parameters of the
        model.
        *Maximum likelihood MDS - A maturing of the data analysis technology
        usually brings a desire for... an explanation of the error model involved in
        the fitting process.  (Ramsay 1977)
        *This approach changes MDS from a descriptive tool into an inferential
        tool.
        *This includes the development of significant tests to determine the
        appropriate dimensionality, appropriate MDS model, and appropriate
        error model.
        *This approach provides confidence regions for the stimuli and with
        weighted models for subjects.                                        (Young, 1987)
 

                                                    History of MDS:  An Outline
 

                                                                                             
 
 

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                 Learning is not the accumulation of knowledge.
                 Learning is movement from moment to moment.
                                         J. Krishnamurti
 
 
 

                                                                                    
                                                                                   Cummins - 2001