###########################################################################################

# Alimenti

###########################################################################################

originale<-read.table(file.choose(), header=TRUE,sep="\t")

dataset<-as.matrix(originale[,-c(1:2)])

Alimento<-originale$Alimento
Categoria<-originale$Categoria

levels(as.factor(Categoria))

############################


#-- Riduzione del numero di variabili con PCA

PCA<-prcomp(dataset, center= TRUE, scale=TRUE)


varianze<-PCA$sdev^2

varianzecum<-cumsum(varianze/sum(varianze)*100) 

#-- Scree plot

plot(varianze,pch=16,type="o")

abline(h=1,col="gray")

#-- Varianza cumulata %

plot(varianzecum,pch=16,type="o")
abline(h=c(50,75),col="gray")

#-- Plot loadings

plot(PCA$rotation[,1], PCA$rotation[,2],pch=16)
text(PCA$rotation[,1], PCA$rotation[,2],labels=colnames(dataset),cex=0.8,pos=3)
abline(h=0,col="gray")
abline(v=0,col="gray")

#-- Plot scores

plot(PCA$x[,1], PCA$x[,2],pch=16)
text(PCA$x[,1], PCA$x[,2],labels=Alimento,cex=0.6,pos=3)
abline(h=0,col="gray")
abline(v=0,col="gray")


plot(PCA$x[,1], PCA$x[,2],type="n")
text(PCA$x[,1], PCA$x[,2],labels=Categoria,cex=0.8)
abline(h=0,col="gray")
abline(v=0,col="gray")


#-- Per raggruppamento in base alle prime 3 PC:

datasetPCA<-PCA$x[,c(1:3)]


#-- Kmeans selezione numero cluster


Tot<-NULL
for(i in c(1:15)) {set.seed(7); km<- kmeans(datasetPCA, centers=i,iter.max=50);
Tot<-c(Tot,km$tot.withinss)}


plot(Tot, xlab="K",ylab="Somma dei quadrati delle distanze intra-cluster", pch=16, type="o",
main="Elbow plot")

#--5  Cluster
set.seed(7)
KM5PCA<- kmeans(datasetPCA, centers=5,iter.max=50)


#-- Plot scores

#-- a colori

Color<-as.factor(KM5PCA$cluster)
levels(Color)<-c("red","blue","green","purple","orange")
Color<-as.character(Color)

plot(PCA$x[,1], PCA$x[,2],type="n")
points(PCA$x[,1], PCA$x[,2],col=Color,cex=1.2,pch=16)
text(PCA$x[,1], PCA$x[,2],labels=Categoria,pos=3,cex=0.5)
abline(h=0,col="gray")
abline(v=0,col="gray")

##### Seconda vs. terza componente

plot(PCA$rotation[,2], PCA$rotation[,3],pch=16)
text(PCA$rotation[,2], PCA$rotation[,3],labels=colnames(dataset),cex=0.8,pos=3)
abline(h=0,col="gray")
abline(v=0,col="gray")


#-- Plot scores

#-- a colori

Color<-as.factor(KM5PCA$cluster)
levels(Color)<-c("red","blue","green","purple","orange")
Color<-as.character(Color)

plot(PCA$x[,2], PCA$x[,3],type="n")
points(PCA$x[,2], PCA$x[,3],col=Color,cex=1.2,pch=16)
text(PCA$x[,2], PCA$x[,3],labels=Categoria,pos=3,cex=0.5)
abline(h=0,col="gray")
abline(v=0,col="gray")


### Newdata

Newdata<-data.frame(KM5PCA$cluster,originale)
View(Newdata)

Newdata2<-Newdata[order(Newdata$KM5PCA.cluster),]
View(Newdata2)