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.

do.mds

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
plot(output1$Y, pch=19, col=lab, main="10% random points") plot(output2$Y, pch=19, col=lab, main="25% random points")