Hierarchical Clustering in R Programming

Hierarchical clustering in R Programming Language is an Unsupervised non-linear algorithm in which clusters are created such that they have a hierarchy(or a pre-determined ordering). For example, consider a family of up to three generations. A grandfather and mother have their children that become father and mother of their children. So, they all are grouped together to the same family i.e they form a hierarchy.

R – Hierarchical Clustering

Hierarchical clustering is of two types: 

• Agglomerative Hierarchical clustering: It starts at individual leaves and successfully merges clusters together. Its a Bottom-up approach.
• Divisive Hierarchical clustering: It starts at the root and recursively split the clusters. It’s a top-down approach.

Theory:

In hierarchical clustering, Objects are categorized into a hierarchy similar to a tree-shaped structure which is used to interpret hierarchical clustering models. The algorithm is as follows:  

1. Make each data point in a single point cluster that forms N clusters.
2. Take the two closest data points and make them one cluster that forms N-1 clusters.
3. Take the two closest clusters and make them one cluster that forms N-2 clusters.
4. Repeat steps 3 until there is only one cluster.

Dendrogram is a hierarchy of clusters in which distances are converted into heights. It clusters n units or objects each with p feature into smaller groups. Units in the same cluster are joined by a horizontal line. The leaves at the bottom represent individual units. It provides a visual representation of clusters.
Thumb Rule: Largest vertical distance which doesn’t cut any horizontal line defines the optimal number of clusters.

The Dataset

mtcars(motor trend car road test) comprise fuel consumption, performance, and 10 aspects of automobile design for 32 automobiles. It comes pre-installed with dplyr package in R. 

R

# Installing the package
install.packages("dplyr")

# Loading package
library(dplyr)

# Summary of dataset in package
head(mtcars)

Output:

Performing Hierarchical clustering on Dataset

Using Hierarchical Clustering algorithm on the dataset using hclust() which is pre-installed in stats package when R is installed.

R

# Finding distance matrix
distance_mat <- dist(mtcars, method = 'euclidean')
distance_mat

# Fitting Hierarchical clustering Model
# to training dataset
set.seed(240)  # Setting seed
Hierar_cl <- hclust(distance_mat, method = "average")
Hierar_cl

# Plotting dendrogram
plot(Hierar_cl)

# Choosing no. of clusters
# Cutting tree by height
abline(h = 110, col = "green")

# Cutting tree by no. of clusters
fit <- cutree(Hierar_cl, k = 3 )
fit

table(fit)
rect.hclust(Hierar_cl, k = 3, border = "green")

Output:

• Distance matrix:

• The values are shown as per the distance matrix calculation with the method as euclidean.
• Model Hierar_cl:

• In the model, the cluster method is average, distance is euclidean and no. of objects are 32.
• Plot dendrogram:

• The plot dendrogram is shown with x-axis as distance matrix and y-axis as height.
• Cutted tree:

• So, Tree is cut where k = 3 and each category represents its number of clusters.
• Plotting dendrogram after cutting:

• The plot denotes dendrogram after being cut. The green lines show the number of clusters as per the thumb rule.