### Cluster Analysis: K-means & PAM

## 7/05/26
## PAM

library(cluster)
library(ggplot2)

dat<-read.csv("food_spending.csv", header = TRUE)
pam.out<-pam(dat, 2, metric = "euclidean",  stand = TRUE)
pam.out

pam.out$medoids  # medoidi
pam.out$id.med   # indici riga medoidi
pam.out$clustering  # vettore clustering 

plot(dat, col=pam.out$clustering+1) # col=2,3
points(pam.out$medoids, pch=8)

## silhouette plot 
plot(pam.out, which=2, main="")
## average silhouette width per PAM con k=2 
pam.out$silinfo$avg.width

## ASW vs K 
min_nc<-2
max_nc<-10
asw<-array(0, c(max_nc-min_nc+1, 2))
asw[,1]<-c(min_nc:max_nc)

for(nc in min_nc:max_nc){
  res<-pam(dat, nc, metric = "euclidean", stand=TRUE)
  asw[nc-min_nc+1, 2]<-res$silinfo$avg.width
 }

# Esempio con "claims" data & distanza di Gower

d<-read.csv(file="claims.csv", header = TRUE)
#View(d)
d$litig<-as.factor(d$litig)
d$soft_injury<-as.factor(d$soft_injury)
d$emergency_tr<-as.factor(d$emergency_tr)
str(d)
# distanze di Gower
mixd<-daisy(d, metric = "gower")
str(mixd)

dmatrix<-as.matrix(mixd)  #matrice distanze

## PAm con matrice dissimilarità "dmatrix"
pam(dmatrix, 2, diss=TRUE)

## utilizzare ASW per decidere K (con k=2,3,...,15) 

min_nc<-2
max_nc<-15
asw<-array(0, c(max_nc-min_nc+1,2))
asw[,1]<-c(min_nc:max_nc)
for(nc in min_nc:max_nc){
  res<-pam(dmatrix, nc, diss=TRUE)
  asw[nc-min_nc+1, 2]<-res$silinfo$avg.width
}

ggplot(data=data.frame(x=asw[,1], y=asw[,2]), 
              mapping = aes(x=x,y=y)) + 
  geom_point() + 
  geom_line() +
  xlab("k") +
  ylab("ASW")

# oppure
#plot(asw[,1], asw[,2], type="o", xlab="K", ylab="ASW")
#abline(v=8, lty=3)