# Chapter 10 Lab 1: Principal Components Analysis states=row.names(USArrests) states names(USArrests) apply(USArrests, 2, mean) apply(USArrests, 2, var) pr.out=prcomp(USArrests, scale=TRUE) names(pr.out) pr.out\$center pr.out\$scale pr.out\$rotation dim(pr.out\$x) biplot(pr.out, scale=0) pr.out\$rotation=-pr.out\$rotation pr.out\$x=-pr.out\$x biplot(pr.out, scale=0) pr.out\$sdev pr.var=pr.out\$sdev^2 pr.var pve=pr.var/sum(pr.var) pve plot(pve, xlab="Principal Component", ylab="Proportion of Variance Explained", ylim=c(0,1),type='b') plot(cumsum(pve), xlab="Principal Component", ylab="Cumulative Proportion of Variance Explained", ylim=c(0,1),type='b') a=c(1,2,8,-3) cumsum(a) # Chapter 10 Lab 2: Clustering # K-Means Clustering set.seed(2) x=matrix(rnorm(50*2), ncol=2) x[1:25,1]=x[1:25,1]+3 x[1:25,2]=x[1:25,2]-4 km.out=kmeans(x,2,nstart=20) km.out\$cluster plot(x, col=(km.out\$cluster+1), main="K-Means Clustering Results with K=2", xlab="", ylab="", pch=20, cex=2) set.seed(4) km.out=kmeans(x,3,nstart=20) km.out plot(x, col=(km.out\$cluster+1), main="K-Means Clustering Results with K=3", xlab="", ylab="", pch=20, cex=2) set.seed(3) km.out=kmeans(x,3,nstart=1) km.out\$tot.withinss km.out=kmeans(x,3,nstart=20) km.out\$tot.withinss # Hierarchical Clustering hc.complete=hclust(dist(x), method="complete") hc.average=hclust(dist(x), method="average") hc.single=hclust(dist(x), method="single") par(mfrow=c(1,3)) plot(hc.complete,main="Complete Linkage", xlab="", sub="", cex=.9) plot(hc.average, main="Average Linkage", xlab="", sub="", cex=.9) plot(hc.single, main="Single Linkage", xlab="", sub="", cex=.9) cutree(hc.complete, 2) cutree(hc.average, 2) cutree(hc.single, 2) cutree(hc.single, 4) xsc=scale(x) plot(hclust(dist(xsc), method="complete"), main="Hierarchical Clustering with Scaled Features") x=matrix(rnorm(30*3), ncol=3) dd=as.dist(1-cor(t(x))) plot(hclust(dd, method="complete"), main="Complete Linkage with Correlation-Based Distance", xlab="", sub="") # Chapter 10 Lab 3: NCI60 Data Example # The NCI60 data library(ISLR) nci.labs=NCI60\$labs nci.data=NCI60\$data dim(nci.data) nci.labs[1:4] table(nci.labs) # PCA on the NCI60 Data pr.out=prcomp(nci.data, scale=TRUE) Cols=function(vec){ cols=rainbow(length(unique(vec))) return(cols[as.numeric(as.factor(vec))]) } par(mfrow=c(1,2)) plot(pr.out\$x[,1:2], col=Cols(nci.labs), pch=19,xlab="Z1",ylab="Z2") plot(pr.out\$x[,c(1,3)], col=Cols(nci.labs), pch=19,xlab="Z1",ylab="Z3") summary(pr.out) plot(pr.out) pve=100*pr.out\$sdev^2/sum(pr.out\$sdev^2) par(mfrow=c(1,2)) plot(pve, type="o", ylab="PVE", xlab="Principal Component", col="blue") plot(cumsum(pve), type="o", ylab="Cumulative PVE", xlab="Principal Component", col="brown3") # Clustering the Observations of the NCI60 Data sd.data=scale(nci.data) par(mfrow=c(1,3)) data.dist=dist(sd.data) plot(hclust(data.dist), labels=nci.labs, main="Complete Linkage", xlab="", sub="",ylab="") plot(hclust(data.dist, method="average"), labels=nci.labs, main="Average Linkage", xlab="", sub="",ylab="") plot(hclust(data.dist, method="single"), labels=nci.labs, main="Single Linkage", xlab="", sub="",ylab="") hc.out=hclust(dist(sd.data)) hc.clusters=cutree(hc.out,4) table(hc.clusters,nci.labs) par(mfrow=c(1,1)) plot(hc.out, labels=nci.labs) abline(h=139, col="red") hc.out set.seed(2) km.out=kmeans(sd.data, 4, nstart=20) km.clusters=km.out\$cluster table(km.clusters,hc.clusters) hc.out=hclust(dist(pr.out\$x[,1:5])) plot(hc.out, labels=nci.labs, main="Hier. Clust. on First Five Score Vectors") table(cutree(hc.out,4), nci.labs)