Landmark Multidimensional Scaling

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.

do.lmds(X, ndim = 2, npoints = max(nrow(X)/5, ndim + 1))

Arguments

X

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.

Value

a named Rdimtools S3 object containing

Y

an \((n\times ndim)\) matrix whose rows are embedded observations.

projection

a \((p\times ndim)\) whose columns are basis for projection.

algorithm

name of the algorithm.

References

Silva VD, Tenenbaum JB (2002). “Global Versus Local Methods in Nonlinear Dimensionality Reduction.” In Thrun S, Obermayer K (eds.), Advances in Neural Information Processing Systems 15, 705–712. MIT Press, Cambridge, MA.

Lee S, Choi S (2009). “Landmark MDS Ensemble.” Pattern Recognition, 42(9), 2045–2053.

See also

do.mds

Author

Kisung You

Examples

# \donttest{
## use iris data
data(iris)
X     = as.matrix(iris[,1:4])
lab   = as.factor(iris[,5])

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