do.lmds: Landmark Multidimensional Scaling

Description

Landmark MDS is a variant of Classical Multidimensional Scaling in that it first finds a low-dimensional embedding using a small portion of given dataset and graft the others in a manner to preserve as much pairwise distance from all the other data points to landmark points as possible.

Usage

do.lmds(
  X,
  ndim = 2,
  npoints = max(nrow(X)/5, ndim + 1),
  preprocess = c("center", "cscale", "decorrelate", "whiten")
)

Arguments

an \((n\times p)\) matrix whose rows are observations and columns represent independent variables.

ndim

an integer-valued target dimension.

npoints

the number of landmark points to be drawn.

preprocess

an option for preprocessing the data. Default is "center". See also aux.preprocess for more details.

Value

a named list containing

Y: an \((n\times ndim)\) matrix whose rows are embedded observations.
trfinfo: a list containing information for out-of-sample prediction.
projection: a \((p\times ndim)\) whose columns are basis for projection.

References

silva_global_2002Rdimtools

lee_landmark_2009Rdimtools

Examples

Run this code

# NOT RUN {
## use iris data
data(iris)
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
lab   = as.factor(iris[subid,5])

## use 10% and 25% of the data and compare with full MDS
output1 <- do.lmds(X,npoints=round(nrow(X)*0.10))
output2 <- do.lmds(X,npoints=round(nrow(X)*0.25))
output3 <- do.mds(X,ndim=2)

## vsualization
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, pch=19, col=lab, main="10% random points")
plot(output2$Y, pch=19, col=lab, main="25% random points")
plot(output3$Y, pch=19, col=lab, main="original MDS")
par(opar)

# }