Day 14: Clustering Exercises.R

# ------------------------------------------------------------------
# DAY 14: CLUSTERING EXERCISES
# ------------------------------------------------------------------
# ------------------------------------------------------------------
# EXERCISE 1
# Use kk Means Clustering to group the observations in the mtcars data. Is it 
#important to standardise these data first? Vary the number of clusters and choose 
# an appropriate value for kk. Interpret the clusters.
# ------------------------------------------------------------------ 

(mtcars.kmeans <- kmeans(mtcars, 3, nstart = 20))
summary(mtcars) #looks like we should standardize so that the features are treated
#somewhat equally.

scaled.cars <- scale(mtcars)

ratios = sapply(1:10, function(k) {
  with(kmeans(scaled.cars, k, nstart = 20), betweenss / totss)
})

plot(1:10, ratios) #it seems like 3-4 clusters seems to be optimal
clusters <- kmeans(scaled.cars, 4)
clusters$centers

#the first cluster has poor mpg, a high number of cylinders, a lighter weight.

#the second cluster has the worst mpg, the highest number of cylinders + horsepower, #the greatest weight, more likely to be automatic.

#the third cluster has the best mpg, the lowest number of cylinders, the least
#horsepower, the lightest weight, the most likely to be manual

#the fourth cluster is pretty much average everything.

# ------------------------------------------------------------------
# EXERCISE 2
# Use the animals data from the cluster package to perform hierarchical clustering. 
#Try different distance measures and select the one that makes the most sense. Check
#?dist to ensure that you understand how missing values are treated.
# ------------------------------------------------------------------ 

library(cluster)
animals #looks like there are some NA values.
rownames(animals) #looks like names are also just abbreviated
animals <- na.omit(animals)

kmeans(animals,2)

animals.dist <- dist(animals, method = "euclidean")
(animals.hclust <- hclust(animals.dist))
plot(animals.hclust)


# ------------------------------------------------------------------
# EXERCISE 3
# Perform hierarchical clustering on the mtcars data. Plot the dendrogram. Does the 
#structure make sense?
# ------------------------------------------------------------------
 
scaled.cars #the standardized mtcars data we were working with

cars.dist <- dist(scaled.cars, method = "euclidean")
(cars.hclust <- hclust(cars.dist))
plot(cars.hclust) 
#i think so. the toyota corolla and volvo are in the same
#data clusters. another cluster has luxury sports cars in them.

# ------------------------------------------------------------------
# EXERCISE 4
# Perform hierarchical clustering on the USArrests data. Try all possible linkage 
#methods and see what effect they have on the results
# ------------------------------------------------------------------

scaled.arrests <- scale(USArrests)

arrests.dist <- dist(scaled.arrests, method = "euclidean")
(arrests.hclust <- hclust(arrests.dist, method = "complete"))
plot(arrests.hclust) #

#In complete-link clustering or complete-linkage clustering , the 
#similarity of two clusters is the similarity of their most dissimilar 
#members.