Growing some Trees

Consider here the dataset used in a previous post, about visualising a classification (with more than 2 features),

> MYOCARDE=read.table(
+ "http://freakonometrics.free.fr/saporta.csv",
+ header=TRUE,sep=";")

The default classification tree is

> arbre = rpart(factor(PRONO)~.,data=MYOCARDE)
> rpart.plot(arbre,type=4,extra=6)

We can change the options here, such as the minimum number of observations, per node

> arbre = rpart(factor(PRONO)~.,data=MYOCARDE,
+       control=rpart.control(minsplit=10))
> rpart.plot(arbre,type=4,extra=6)

or

> arbre = rpart(factor(PRONO)~.,data=MYOCARDE,
+        control=rpart.control(minsplit=5))
> rpart.plot(arbre,type=4,extra=6)

To visualize that classification, use the following code (to get a projection on the first two components)

> library(FactoMineR) # ACP (sur les var continues)
> X=MYOCARDE[,1:7]
> acp=PCA(X,ncp=ncol(X))
> M=acp$var$coord
> m=apply(X,2,mean)
> s=apply(X,2,sd)
> 
> arbre = rpart(factor(PRONO)~.,data=MYOCARDE)
> pred2=function(d1,d2,Mat,tree){
+   z=Mat %*% c(d1,d2,rep(0,ncol(X)-2))
+   newd=data.frame(t(z*s+m))
+   names(newd)=names(X)
+   predict(tree,newdata=newd,
+           type="prob")[2] }
> p=function(d1,d2) pred2(d1,d2,Minv,arbre)

> Outer <- function(x,y,fun) {
+   mat <- matrix(NA, length(x), length(y))
+   for (i in seq_along(x)) {
+     for (j in seq_along(y)) 
+       mat[i,j]=fun(x[i],y[j])}
+   return(mat)}

> xgrid=seq(-5,5,length=251)
> ygrid=seq(-5,5,length=251)
> zgrid=Outer(xgrid,ygrid,p)
> bluereds=c(
+   rgb(1,0,0,(10:0)/25),rgb(0,0,1,(0:10)/25))

> acp2=PCA(MYOCARDE,quali.sup=8,graph=TRUE)
> plot(acp2, habillage = 8,col.hab=c("red","blue"))
> image(xgrid,ygrid,zgrid,add=TRUE,col=bluereds)
> contour(xgrid,ygrid,zgrid,add=TRUE,levels=.5)

It is also possible to consider the case where

> arbre = rpart(factor(PRONO)~.,data=MYOCARDE,
+        control=rpart.control(minsplit=5))

Finaly, one can also grow more trees, obtained by sampling. This is the idea of bagging: we boostrap our observations, we grow some trees, and then, we aggregate the predicted values. On the grid

> xgrid=seq(-5,5,length=201)
> ygrid=seq(-5,5,length=201)

the code is the following,

> Z = matrix(0,201,201)
> for(i in 1:200){
+ indice = sample(1:nrow(MYOCARDE),
+          size=nrow(MYOCARDE),
+          replace=TRUE)
+ ECHANTILLON=MYOCARDE[indice,]
+ arbre_b = rpart(factor(PRONO)~.,
+   data=ECHANTILLON)
+ p2 = function(d1,d2) pred2(d1,d2, Minv,arbre_b)
+ zgrid2_b = Outer(xgrid,ygrid,p2)
+ Z = Z+zgrid2_b }
> Zgrid = Z/200

To visualize it, use

> plot(acp2, habillage = 8,
+ col.hab=c("red","blue"))
> image(xgrid,ygrid,Zgrid,add=TRUE,
+ col=bluereds)

> contour(xgrid,ygrid,Zgrid,add=TRUE,
+ levels=.5,lwd=3)

Last, but not least, it is possible to use some random forrest algorithm. The method combines Breiman’s bagging idea (mentioned previously) and the random selection of features.

> library(randomForest)
> foret = randomForest(factor(PRONO)~.,
+          data=MYOCARDE)
> pF=function(d1,d2) pred2(d1,d2,Minv,foret)
> zgridF=Outer(xgrid,ygrid,pF)
 
> acp2=PCA(MYOCARDE,quali.sup=8,graph=TRUE)
> plot(acp2, habillage = 8,col.hab=c("red","blue"))
> image(xgrid,ygrid,Zgrid,add=TRUE,
+ col=bluereds)
> contour(xgrid,ygrid,zgridF,
+ add=TRUE,levels=.5,lwd=3)