# Hierarchical Clustering in R: The Essentials

## Examples of Dendrograms Visualization

As described in previous chapters, a dendrogram is a tree-based representation of a data created using hierarchical clustering methods.

In this article, we provide examples of dendrograms visualization using R software. Additionally, we show how to save and to zoom a large dendrogram.

Contents:

#### Related Book

Practical Guide to Cluster Analysis in R

## 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:

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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:

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## 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)
1. object: a dendrogram object
2. what: a character indicating what is the property of the tree that should be set/updated
3. value: a vector with the value to set in the tree (the type of the value depends on the “what”).

Possible values for the argument what include:

Value for the argument what Description
labels set the labels
labels_colors and labels_cex Set the color and the size of labels, respectively
leaves_pch, leaves_cex and leaves_col set the point type, size and color for leaves, respectively
nodes_pch, nodes_cex and nodes_col set the point type, size and color for nodes, respectively
hang_leaves hang the leaves
branches_k_color color the branches
branches_col, branches_lwd , branches_lty Set the color, the line width and the line type of branches, respectively
by_labels_branches_col, by_labels_branches_lwd and by_labels_branches_lty Set the color, the line width and the line type of branches with specific labels, respectively
clear_branches and clear_leaves Clear branches and leaves, respectively
• 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.

• Winderolow

Hi, thanks for the amazing tutorial! Would you know what the “height” on the Y-axis of the dendrogram mean? How is the value calculated? thanks!

• Kassambara

The height of the fusion, provided on the vertical axis, indicates the (dis)similarity/distance between two objects/clusters. The higher the height of the fusion, the less similar the objects are. This height is known as the cophenetic distance between the two objects. Read more: https://www.datanovia.com/en/lessons/agglomerative-hierarchical-clustering/

• Carol Buitrago

How can I modify the vertical scale? I noticed your leaves are at 0, but I cannot manage to do the same to mine

• Yiru Cheng

Hi, is there a way to color the block of different groups without coloring the name labels at the end? thanks!

• Kassambara

You need to specify the argument color_labels_by_k = FALSE.

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


• Yiru Cheng

Hi, Kassambara

thanks for you reply. I may not be clear about what I mean. I still want to keep the colored blocks for each group on the branch, but I don’t want the color to cover the labels. Is there a parameter that can do the trick? thanks!

• Yiru Cheng

just found I can adjust the lower part of the rect easily with low_rect = value. thanks!

• Luis

low_rect= 0