Multidimensional scaling: Difference between revisions

Revision as of 12:08, 19 March 2024

Revision as of 12:12, 19 March 2024

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{{Short description|Set of related ordination techniques used in information visualization}}

[[File:RecentVotes.svg|thumb|400px|An example of classical multidimensional scaling applied to voting patterns in the [[United States House of Representatives]]. Each red dot represents one Republican member of the House, and each blue dot one Democrat.]]

'''Multidimensional scaling''' ('''MDS''') is a means of visualizing the level of [[Similarity measure|similarity]] of individual cases of a data set. MDS is used to translate "information about the pairwise 'distances' amongbetween aeach setpair of <math display="inline"> n </math> objects orin individuals"a set into a configuration of <math display="inline"> n </math> points mapped into an abstract [[Cartesian coordinate system|Cartesian space]].<ref name="MS_history">{{cite journal |last= Mead|first=A |date= 1992|title= Review of the Development of Multidimensional Scaling Methods |journal= Journal of the Royal Statistical Society. Series D (The Statistician)|volume= 41|issue=1 |pages=27–39 |quote= Abstract. Multidimensional scaling methods are now a common statistical tool in psychophysics and sensory analysis. The development of these methods is charted, from the original research of Torgerson (metric scaling), Shepard and Kruskal (non-metric scaling) through individual differences scaling and the maximum likelihood methods proposed by Ramsay. |jstor=2348634 }}</ref>

More technically, MDS refers to a set of related [[Ordination (statistics)|ordination]] techniques used in [[information visualization]], in particular to display the information contained in a [[distance matrix]]. It is a form of [[non-linear dimensionality reduction]].