spa (version 2.0)

predict.spa: Inductive Predict Procedure For SPA

Description

This implements the inductive prediction for an spa object. The impact of the observation(s) on the existing labeled and unlabeled data is ignored.

For transductive predicton use update function.

Usage

"predict"(object,xnew,gnew,type=c("vector","probs","both"),...)

Arguments

object

an existing object of type spa

xnew

the new xdata to predict, of diminsion ngXdim(object[2]) (only applicable if object was called with x data)

gnew

the new graph links. The diminsion on this matrix is ngX dim(object)[1] with ng as the number of observations to predict.

type

the type of prediction to return.

...

additional arguments passed into the function.

References

M. Culp (2011). spa: A Semi-Supervised R Package for Semi-Parametric Graph-Based Estimation. Journal of Statistical Software, 40(10), 1-29. URL http://www.jstatsoft.org/v40/i10/.

Examples

## Use simulated example (two moon) and generate a contour plot of the border
set.seed(100)
dat=spa.sim(type="moon") 

L=which(!is.na(dat$y))
U=which(is.na(dat$y))
Dij=as.matrix(daisy(dat[,-1]))

##Use spa to train with a supervised/transductive kernel smoother
gsup<-spa(dat$y[L],graph=Dij[L,L],control=spa.control(gcv="lGCV"))
gsemi<-spa(dat$y,graph=Dij,control=spa.control(gcv="aGCV"))

##Use predict to define a grid for contour plot
gsize=100
a1<-seq(min(dat$x1),max(dat$x1),length=gsize)
a2<-seq(min(dat$x2),max(dat$x2),length=gsize)

zsup=matrix(0,gsize,gsize)
for(i in 1:gsize){
  val=sqrt(t(sapply(1:gsize,function(j)(dat$x1[L]-a1[i])^2+(dat$x2[L]-a2[j])^2)))
  zsup[i,]=predict(gsup,gnew=val)  ##supervised prediction with k-smoother
}
zsemi=matrix(0,gsize,gsize)
for(i in 1:gsize){
  val=sqrt(t(sapply(1:gsize,function(j)(dat$x1-a1[i])^2+(dat$x2-a2[j])^2)))
  zsemi[i,]=predict(gsemi,gnew=val) ##inductive prediction with transductive rule
}

## Plot results
gr=c(2,4)
plot(0,1,cex=1.5,xlab="x1",ylab="x2",type="n",
     xlim=c(-0.5,6.5),ylim=c(-6.5,3.5))
gr=gray(c(.7,.9))
points(dat$x1,dat$x2,pch=16,col=8,cex=1)
points(dat$x1[L],dat$x2[L],pch=16,col=gr[dat$y[L]+1],cex=2)
points(dat$x1[L],dat$x2[L],pch=1,col=1,cex=2)
contour(a1,a2,zsup, levels=.5,add=TRUE,lty=1,method="edge",drawlabels=FALSE,lwd=2,col=gray(0.6))
contour(a1,a2,zsemi,levels=.5,add=TRUE,lty=1,method="edge",drawlabels=FALSE,lwd=2,col=1)
exp1=expression(hat(Y)*"="*hat(f)(G[X]))
exp2=expression(Y[L]*"="*f(X[L])+epsilon)
legend(4.25,par()$usr[4],c(exp1,exp2),cex=1.24,fill=gray(c(0,0.6)),bg="white")
legend(4.25,par()$usr[4],c(exp1,exp2),cex=1.24,fill=gray(c(0,0.6)))

title(switch(attr(dat,"type"),moon="Two Moon Simulated Data",supervised="Supervised Border Simulated set"))
title("\n\nInductive Prediction with a Transductive Model",cex.main=1.1)
box()