isoMDS {MASS} | R Documentation |
One form of non-metric multidimensional scaling
isoMDS(d, y = cmdscale(d, k), k = 2, niter = 50, trace = TRUE)
d |
distance structure of the form returned by dist , or a full, symmetric
matrix. Data are assumed to be dissimilarities or relative distances,
but must be positive except for self-distance.
|
y |
An initial configuration. If none is supplied, cmdscale is used to provide
the classical solution.
|
k |
The dimension of the configuration. |
niter |
The maximum number of iterations. |
trace |
Logical for tracing optimization. Default true .
|
This chooses a two-dimensional configuration to minimize the stress, the square root of the ratio of the the sum of squared differences between the input distances and those of the configuration to the sum of configuration distances squared. However, the input distances are allowed a monotonic transformation.
An iterative algorithm is used, which will usually converge in around 10 iterations. As this is necessarily an O(n^2) calculation, it is slow for large datasets. Further, since the configuration is only determined up to rotations and reflections (by convention the centroid is at the origin), the result can vary considerably from machine to machine.
points |
A two-column vector of the fitted configuration. |
stress |
The final stress achieved (in percent). |
If trace is true, the initial stress and the current stress are printed out every 5 iterations.
T. F. Cox and M. A. A. Cox (1994) Multidimensional Scaling. Chapman & Hall.
library(mva) # for dist data(swiss) swiss.x <- as.matrix(swiss[, -1]) swiss.dist <- dist(swiss.x) swiss.mds <- isoMDS(swiss.dist) plot(swiss.mds$points, type="n") text(swiss.mds$points, labels=as.character(1:nrow(swiss.x))) swiss.sh <- Shepard(swiss.dist, swiss.mds$points) plot(swiss.sh) lines(swiss.sh$x, swiss.sh$yf, type="S")