#########    correction exercice II - exemple 3   #######################
M = matrix(c(0,23,15,22,30,26,20,23,0,26,25,16,25,33,15,26,0,28,37,28,20,22,25,28,
0,22,7,28,30,16,37,22,0,20,22,26,25,28,7,20,0,18,20,33,20,28,22,18,0),byrow=T,ncol=7)
rownames(M)=c("A","F","O","H","R","J","Oy")
colnames(M)=c("A","F","O","H","R","J","Oy")
M
M1=cbind(M,(M[,4]+M[,6])/2)
M1=rbind(M1,c(M1[,8],0))
M1=M1[c(-4,-6),c(-4,-6)]
rownames(M1)=c("A","F","O","R","Oy","HJ")
colnames(M1)=c("A","F","O","R","Oy","HJ")
M1

M2=cbind(M1,(M1[,1]+M1[,3])/2)
M2=rbind(M2,c(M2[,7],0))
M2=M2[c(-1,-3),c(-1,-3)]
rownames(M2)=c("F","R","Oy","HJ","AO")
colnames(M2)=c("F","R","Oy","HJ","AO")
M2
M3=cbind(M2,(M2[,1]+M2[,2])/2)
M3=rbind(M3,c(M3[,6],0))
M3=M3[c(-1,-2),c(-1,-2)]
rownames(M3)=c("Oy","HJ","AO","FR")
colnames(M3)=c("Oy","HJ","AO","FR")
M3
M4=cbind(M3,(M3[,1]+M3[,3])/2)
M4=rbind(M4,c(M4[,5],0))
M4=M4[c(-1,-3),c(-1,-3)]
rownames(M4)=c("HJ","FR","AOOy")
colnames(M4)=c("HJ","FR","AOOy")
M4
M5=cbind(M4,(M4[,1]+M4[,2])/2)
M5=rbind(M5,c(M5[,4],0))
M5=M5[c(-1,-2),c(-1,-2)]
rownames(M5)=c("AOOy","HJFR")
colnames(M5)=c("AOOy","HJFR")
M5



M=as.dist(M)
cah=hclust(M,"average")
names(cah)
cah$height
cah$merge
plot(cah,hang=-1,main="moyenne")
rect.hclust(cah,h=25)

par(mfrow=c(2,2))
possible <- c( "single", "complete", "average")
for(k in 1:3)  plot(hclust(M,possible[k]),hang=-1,main=possible[k])
plot(hclust(M^2,"ward"),hang=-1,main="Inertie intra-classe")



############ correction exercice II - exemple 5 #####################

M = matrix(c(1,8/12,10/12,8/11,6/11,8/12,1,8/12,8/11,10/11,10/12,
8/12,1,6/11,6/11,8/11,8/11,6/11,1,8/10,6/11,10/11,6/11,8/10,1),byrow=T,ncol=5)
rownames(M)=c("A","B","C","D","E")
colnames(M)=c("A","B","C","D","E")
M
M*11
M=1-M

M1=cbind(M,apply(M[,c(2,5)],1,max))
M1=rbind(M1,c(M1[,6],0))
M1=M1[c(-2,-5),c(-2,-5)]
rownames(M1)=c("A","C","D","BE")
colnames(M1)=c("A","C","D","BE")
M1

M2=cbind(M1,apply(M1[,c(1,2)],1,max))
M2=rbind(M2,c(M2[,5],0))
M2=M2[c(-1,-2),c(-1,-2)]
rownames(M2)=c("D","BE","AC")
colnames(M2)=c("D","BE","AC")
M2

M3=cbind(M2,apply(M2[,c(1,2)],1,max))
M3=rbind(M3,c(M3[,4],0))
M3=M3[c(-1,-2),c(-1,-2)]
rownames(M3)=c("AC","DBE")
colnames(M3)=c("AC","DBE")
M3



M=as.dist(M)
cah=hclust(M,"complete")
names(cah)
cah$height
cah$merge

plot(cah,hang=-1,main="complete")
rect.hclust(cah,h=0.25)


######## correction exercice II - exemple 6 #########################"""

M = matrix(c(0,16,1,9,10,16,0,17,25,2,1,17,0,4,9,9,25,4,0,13,10,2,9,13,0),ncol=5)
M = as.dist(M)
par(mfrow=c(2,2))
possible <- c( "single", "complete", "average")
for(k in 1:3)  plot(hclust(M,possible[k]),hang=-1,main=possible[k])
plot(hclust(M^2,"ward"),hang=-1,main="Inertie intra-classe")

# correction manuelle
M = matrix(c(0,16,1,9,10,16,0,17,25,2,1,17,0,4,9,9,25,4,0,13,10,2,9,13,0),ncol=5)
rownames(M)=c("A","B","C","D","E")
colnames(M)=c("A","B","C","D","E")
M1=cbind(M,apply(M[,c(1,3)],1,mean))
M1=rbind(M1,c(M1[,6],0))
M1=M1[c(-1,-3),c(-1,-3)]
rownames(M1)=c("B","D","E","AC")
colnames(M1)=c("B","D","E","AC")
M1
M2=cbind(M1,apply(M1[,c(1,3)],1,mean))
M2=rbind(M2,c(M2[,5],0))
M2=M2[c(-1,-3),c(-1,-3)]
rownames(M2)=c("D","AC","BE")
colnames(M2)=c("D","AC","BE")
M2
M3=cbind(M2,apply(M2[,c(1,2)],1,mean))
M3=rbind(M3,c(M3[,4],0))
M3=M3[c(-1,-2),c(-1,-2)]
rownames(M3)=c("BE","ACD")
colnames(M3)=c("BE","ACD")
M3
M=as.dist(M)
cah=hclust(M,"average")
plot(cah,hang=-1)
cah$height


############## correction Exercice II exemple 7 #####


tab <- matrix(c(0,sqrt(2),0,0,0,0,-sqrt(2),0,sqrt(2),sqrt(2),-sqrt(2),-sqrt(2)),c(4,3),byrow=T)
colnames(tab) <- c("X","Y","Z")
rownames(tab) <- c("A","B","C","D")
tab
dist.tab=dist(tab)
cah.tab=hclust(dist.tab^2,method="ward")
plclust(cah.tab,hang=-1)
rect.hclust(cah.tab,h=5)
unclass(cah.tab)
cutree(cah.tab,h=5)
cl=kmeans(tab,2)
plot(tab, col = cl$cluster, pch=3)
points(cl$centers, col = 1:2, pch = 7, lwd=3)
segments(tab[cl$cluster==1,1],tab[cl$cluster==1,2],cl$centers[1,1],cl$centers[1,2])
library(cluster)
clusplot( tab, pam(tab, 2)$clustering )


############## correction Exercice III  Application : acp sur cidre #####

### individus ###
cidre=read.table("cidre.txt")
cidreR=scale(cidre)*sqrt(10/9)
library(ade4)
acp = dudi.pca(cidre,scannf=FALSE)
d=dist.dudi(acp)
round(d,1)
dist(cidreR)
dist(cidre)
cah=hclust(d^2,"ward")
names(cah)
cah$height
sum(cah$height)/20
par(mfrow=c(2,1))
barplot(cah$height[order(cah$height,decreasing=TRUE)])
plot(cah,hang=-1)
cutree(cah,h=20)
rect.hclust(cah,h=20)
par(mfrow=c(2,1))
s.class(dfxy=acp$li,fac=as.factor(cutree(cah,h=20)))
s.label(acp$li)

### variables ####
d=dist.dudi(acp,amongrow=FALSE)
round(d,1)

cah=hclust(d^2,"ward")
sum(cah$height)
barplot(cah$height[order(cah$height,decreasing=TRUE)])
plot(cah,hang=-1)
cutree(cah,h=3)
rect.hclust(cah,h=3)

s.corcircle(acp$co)
plclust(cah,hang=-1)
s.class(dfxy=acp$co,fac=as.factor(cutree(cah,h=2)))



###  Application : AFC et CSP ####

csp=read.table("csp.txt")
afc=dudi.coa(csp,scannf=FALSE)
d=dist.dudi(afc)
d
cah=hclust(d^2,"ward")
names(cah)
cah$height
plot(cah,hang=-1)
cutree(cah,h=0.05)
rect.hclust(cah,h=0.05)
""
par(mfrow=c(2,1))

s.label(afc$li)
s.class(dfxy=afc$li,fac=as.factor(cutree(cah,h=0.05)))

d=dist.dudi(afc,amongrow=FALSE)
cah=hclust(d^2,"ward")
names(cah)
cah$height
plot(cah,hang=-1)
cutree(cah,h=0.05)
rect.hclust(cah,h=0.05)
par(mfrow=c(2,1))
s.label(afc$co)
s.class(dfxy=afc$co,fac=as.factor(cutree(cah,h=0.05)))