zoo_data <- read.csv("zoo.csv",
                     header = TRUE, sep = ",")

head(zoo_data)

# Remove or exclude the 'type' column
clustering_data <- zoo_data[, -which(names(zoo_data) == "type")]
# Remove or exclude the 'type' column
clustering_data <- clustering_data[, -which(names(clustering_data) == "name")]
clustering_data <- clustering_data[, -which(names(clustering_data) == "legs")]
clustering_data[] <- lapply(clustering_data, function(x) ifelse(x == "yes", 1, 0))
clustering_data$legs <- zoo_data$legs

#1. Elbow Method

wss <- sapply(1:10, function(k){
  kmeans(clustering_data, centers = k)$tot.withinss
})

plot(1:10, wss, type = "b", pch = 19,
     xlab = "Number of clusters (k)",
     ylab = "Total within-clusters sum of squares",
     main = "Elbow Method for Choosing k",
     ylim = c(0,max(wss)))


#2. Silhouette Method

library(cluster)

sil_widths <- sapply(2:10, function(k){
  km <- kmeans(clustering_data, centers = k)
  ss <- silhouette(km$cluster, dist(clustering_data))
  mean(ss[, 3])
})

plot(2:10, sil_widths, type='b', pch=19,
     xlab='Number of clusters (k)',
     ylab='Average silhouette width',
     main='Silhouette Method for Choosing k')


#3. Gap Statistic
library(cluster)

set.seed(123)
gap_stat <- clusGap(clustering_data, FUN = kmeans, nstart = 25, K.max = 10, B = 50)
print(gap_stat)
plot(gap_stat)