R: Classical (Metric) Multidimensional Scaling

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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