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Multidimensional Scaling
Multidimensional scaling (MDS)—also called principal coordinates analysis—transforms a data table of distances (or dissimilarities) measured between a set of observations into a set of (Euclidean) coordinates for these observations that can, in turn, be used to plot the observations on a map, so that the (Euclidean) distances on the map between the observations best approximate their distances in the original distance matrix (see Figure 1 for a sketch of the method).
Definitions and Notations
MDS exists in two variations: metric multidimensional scaling (MMDS) to be used when the data are real distances (preferably Euclidean) and nonmetric multidimensional scaling (NMDS) when the data are simply dissimilarities. But first, some definitions are needed to describe the different varieties of MDS and their properties.
Figure 1The Main Steps of Multidimensional Scaling: ...
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