superMDS (version 1.0.2)

superMDS-package: Supervised multidimensional scaling for visualization, classification, and bipartite ranking

Description

A method for implementing the supervised multidimensional scaling proposal of Witten and Tibshirani (2011)

Details

Package:

superMDS

Type:

Package

Version:

1.0.2

Date:

2013-01-02

License:

GPL-2

LazyLoad:

yes

Supervised multidimensional scaling (MDS) is a supervised version of least squares MDS. Suppose that we have a nxn dissimilarity matrix D and we want to find a set of n configuration points z1,...,zn, each a vector of length s, so that D is well-approximated by the Euclidean distances between the configuration points. Then least squares MDS can be used. However, suppose that we also have a vector of binary class labels associated with the dissimilarity matrix, yi = 1 or 2 for i=1,...,n. Then we might want configuration points whose Euclidean dsitances approximate D, and also that have the property that zis > zjs when yi > yj. This is the objective of supervised MDS. It leads to a method for visualizing observations, as well as a classification method. Details can be found in the paper below.

References

Witten and Tibshirani (2011) Supervised multidimensional scaling for visualization, classification, and bipartite ranking. Computational Statistics and Data Analysis 55(1): 789-801.

Examples

########### Generate some data  ############
n <- 30
p <- 10
x <- matrix(rnorm(n*p),ncol=p)
y <- c(rep(1,n/2),rep(2,n/2))
xte <- matrix(rnorm(n*p),ncol=p)
yte <- c(rep(1,n/2),rep(2,n/2))
x[y==1,1:(p)] <-  x[y==1,1:(p)] + .4
x[y==2,1:(p)] <-  x[y==2,1:(p)] - .4
xte[yte==1,1:(p)] <-  xte[yte==1,1:(p)] + .4
xte[yte==2,1:(p)] <-  xte[yte==2,1:(p)] - .4    
# Done generating data  #

########### Perform SuperMDS ##############
out <- TrainSuperMDS(x=x,y=y,alpha=.4,S=2, silent=TRUE)
# A plot of the training configuration points #
par(mfrow=c(1,2))
plot(out$z, col=yte, main="Training Data", xlab="Dimension 1", ylab="Dimension 2")
testout <- TestSuperMDS(trout=out,xte=xte)
ytehat <- testout$ytehat
# A table showing the true vs predicted class labels #
print(table(ytehat,yte)) 
# A plot of the test configuration points #
plot(testout$zte, col=yte, main="Test Data", xlab="Dimension 1", ylab="Dimension 2")