cmdscale {mva}R Documentation

Classical (Metric) Multidimensional Scaling

Description

Classical multidimensional scaling of a data matrix.

Usage

cmdscale(d, k = 2, eig = FALSE)

Arguments

d a distance structure such as that returned by dist or a full symmetric matrix containing the dissimilarities.
k the dimension of the space which the data are to be represented in; must be in {1,2, .., n-1}.
eig indicates whether eigenvalues should be returned.

Details

Multidimensional scaling takes a set of dissimilarities and returns a set of points such that the distances between the points are approximately equal to the dissimilarities.

The functions isoMDS and sammon in package `MASS' provide alternative ordination techniques.

Value

If eig = FALSE, a matrix with k columns whose rows give the coordinates of the points chosen to represent the dissimilarities.
Otherwise, a list containing the following components.

points a matrix with k columns whose rows give the coordinates of the points chosen to represent the dissimilarities.
eig the eigenvalues computed during the scaling process.

Note

The S version of this function provides for computing an additional ``fiddle'' factor suggested by Torgerson. R will provide this option from version 1.5.0 on.

References

Cox, F.C. and Cox, M.A.A. (1994) Multidimensional Scaling. Chapman and Hall.

Mardia, K. V., J. T. Kent and J. M. Bibby (1979). Chapter 14 of Multivariate Analysis, London: Academic Press.

Seber, G. A. F. (1984). Multivariate Observations. New York: Wiley.

Torgerson, W. S. (1958). Theory and Methods of Scaling. New York: Wiley.

See Also

dist. Also isoMDS and sammon in package `MASS'.

Examples

data(eurodist)
loc <- cmdscale(eurodist)
x <- loc[,1]
y <- -loc[,2]
plot(x, y, type="n", xlab="", ylab="", main="cmdscale(eurodist)")
text(x, y, names(eurodist), cex=0.8)



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