cmdscale {mva} | R Documentation |
Classical multidimensional scaling of a data matrix.
cmdscale(d, k = 2, eig = FALSE, add = FALSE, x.ret = FALSE)
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. |
add |
logical indicating if an additive constant c* should be computed, and added to the non-diagonal dissimilarites such that all n-1 eigenvalues are non-negative. |
x.ret |
indicates whether the doubly centered symmetric distance matrix should be returned. |
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.
When add = TRUE
, an additive constant c* is computed, and
the dissimilarities d[i,j] + c* are used instead of
the original d[i,j]'s.
Whereas S-PLUS computes this constant using an approximation suggested by Torgerson, R uses the exact analytical solution of Cailliez (1983), see also Cox and Cox (1994).
If eig = FALSE
and x.ret = FALSE
(default), 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 n-1 eigenvalues computed during the scaling process if
eig is true. |
x |
the doubly centered distance matrix if x.ret is true. |
GOF |
a numeric vector of length 2, equal to say (g.1,g.2), where g.i = (sum{j=1..k} lambda[j]) / (sum{j=1..n} T.i(lambda[j])), where lambda[j] are the eigenvalues (sorted decreasingly), T.1(v) = abs(v), and T.2(v) = max(v, 0). |
Cox, T. F. and Cox, M. A. A. (1994) Multidimensional Scaling. Chapman and Hall.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (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.
Cailliez, F. (1983) The analytical solution of the additive constant problem. Psychometrika 48, 343349.
dist
.
Also isoMDS
and sammon
in package MASS.
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) cmdsE <- cmdscale(eurodist, k=20, add = TRUE, eig = TRUE, x.ret = TRUE) str(cmdsE)