Hierarchical Clustering in R: The Essentials

Computing hierarchical clustering

We start by computing hierarchical clustering using the USArrests data sets:

# Load data
data(USArrests)

# Compute distances and hierarchical clustering
dd <- dist(scale(USArrests), method = "euclidean")
hc <- hclust(dd, method = "ward.D2")

R packages and functions

To visualize the dendrogram, we’ll use the following R functions and packages:

• fviz_dend()[in factoextra R package] to create easily a ggplot2-based beautiful dendrogram.
• dendextend package to manipulate dendrograms

Before continuing, install the required package as follow:

install.packages(c("factoextra", "dendextend"))

Creating dendrograms

We’ll use the function fviz_dend()[in factoextra R package] to create easily a beautiful dendrogram using either the R base plot or ggplot2. It provides also an option for drawing circular dendrograms and phylogenic-like trees.

To create a basic dendrograms, type this:

library(factoextra)
fviz_dend(hc, cex = 0.5)

You can use the arguments main, sub, xlab, ylab to change plot titles as follow:

fviz_dend(hc, cex = 0.5, 
          main = "Dendrogram - ward.D2",
          xlab = "Objects", ylab = "Distance", sub = "")

To draw a horizontal dendrogram, type this:

fviz_dend(hc, cex = 0.5, horiz = TRUE)

It’s also possible to cut the tree at a given height for partitioning the data into multiple groups as described in the previous chapter. In this case, it’s possible to color branches by groups and to add rectangle around each group.

For example:

To change the plot theme, use the argument ggtheme, which allowed values include ggplot2 official themes [ theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void()] or any other user-defined ggplot2 themes.

fviz_dend(hc, k = 4,                 # Cut in four groups
          cex = 0.5,                 # label size
          k_colors = c("#2E9FDF", "#00AFBB", "#E7B800", "#FC4E07"),
          color_labels_by_k = TRUE,  # color labels by groups
          ggtheme = theme_gray()     # Change theme
          )

Allowed values for k_color include brewer palettes from RColorBrewer Package (e.g. “RdBu”, “Blues”, “Dark2”, “Set2”, …; ) and scientific journal palettes from ggsci R package (e.g.: “npg”, “aaas”, “lancet”, “jco”, “ucscgb”, “uchicago”, “simpsons” and “rickandmorty”).

In the R code below, we’ll change group colors using “jco” (journal of clinical oncology) color palette:

Manipulating dendrograms using dendextend

The package dendextend provide functions for changing easily the appearance of a dendrogram and for comparing dendrograms.

In this section we’ll use the chaining operator (%>%) to simplify our code. The chaining operator turns x %>% f(y) into f(x, y) so you can use it to rewrite multiple operations such that they can be read from left-to-right, top-to-bottom. For instance, the results of the two R codes below are equivalent.

• Standard R code for creating a dendrogram:

data <- scale(USArrests)
dist.res <- dist(data)
hc <- hclust(dist.res, method = "ward.D2")
dend <- as.dendrogram(hc)
plot(dend)

• R code for creating a dendrogram using chaining operator:

library(dendextend)
dend <- USArrests[1:5,] %>% # data
        scale %>% # Scale the data
        dist %>% # calculate a distance matrix, 
        hclust(method = "ward.D2") %>% # Hierarchical clustering 
        as.dendrogram # Turn the object into a dendrogram.
plot(dend)

• Functions to customize dendrograms: The function set() [in dendextend package] can be used to change the parameters of a dendrogram. The format is:

set(object, what, value)

Possible values for the argument what include:

• Examples:

library(dendextend)
# 1. Create a customized dendrogram
mycols <- c("#2E9FDF", "#00AFBB", "#E7B800", "#FC4E07")
dend <-  as.dendrogram(hc) %>%
   set("branches_lwd", 1) %>% # Branches line width
   set("branches_k_color", mycols, k = 4) %>% # Color branches by groups
   set("labels_colors", mycols, k = 4) %>%  # Color labels by groups
   set("labels_cex", 0.5) # Change label size

# 2. Create plot 
fviz_dend(dend) 

Summary

We described functions and packages for visualizing and customizing dendrograms including:

• fviz_dend() [in factoextra R package], which provides convenient solutions for plotting easily a beautiful dendrogram. It can be used to create rectangular and circular dendrograms, as well as, a phylogenic tree.
• and the dendextend package, which provides a flexible methods to customize dendrograms.

Additionally, we described how to plot a subset of large dendrograms.