Hierarchical Clustering in R: The Essentials

Data preparation

We’ll use the R base USArrests data sets and we start by standardizing the variables using the function scale() as follow:

df <- scale(USArrests)

To make readable the plots, generated in the next sections, we’ll work with a small random subset of the data set. Therefore, we’ll use the function sample() to randomly select 10 observations among the 50 observations contained in the data set:

# Subset containing 10 rows
set.seed(123)
ss <- sample(1:50, 10)
df <- df[ss,]

Dendrograms comparison

We start by creating a list of two dendrograms by computing hierarchical clustering (HC) using two different linkage methods (“average” and “ward.D2”). Next, we transform the results as dendrograms and create a list to hold the two dendrograms.

library(dendextend)

# Compute distance matrix
res.dist <- dist(df, method = "euclidean")

# Compute 2 hierarchical clusterings
hc1 <- hclust(res.dist, method = "average")
hc2 <- hclust(res.dist, method = "ward.D2")

# Create two dendrograms
dend1 <- as.dendrogram (hc1)
dend2 <- as.dendrogram (hc2)

# Create a list to hold dendrograms
dend_list <- dendlist(dend1, dend2)

1. Visual comparison of two dendrograms

To visually compare two dendrograms, we’ll use the following R functions [dendextend package]:

• untangle(): finds the best layout to align dendrogram lists, using heuristic methods
• tanglegram(): plots the two dendrograms, side by side, with their labels connected by lines.
• entanglement(): computes the quality of the alignment of the two trees. Entanglement is a measure between 1 (full entanglement) and 0 (no entanglement). A lower entanglement coefficient corresponds to a good alignment.
• Draw a tanglegram:

# Align and plot two dendrograms side by side
dendlist(dend1, dend2) %>%
  untangle(method = "step1side") %>% # Find the best alignment layout
  tanglegram()                       # Draw the two dendrograms

# Compute alignment quality. Lower value = good alignment quality
dendlist(dend1, dend2) %>%
  untangle(method = "step1side") %>% # Find the best alignment layout
  entanglement()                     # Alignment quality

## [1] 0.0384

• Customized the tanglegram using many other options as follow:

dendlist(dend1, dend2) %>%
  untangle(method = "step1side") %>% 
  tanglegram(
    highlight_distinct_edges = FALSE, # Turn-off dashed lines
    common_subtrees_color_lines = FALSE, # Turn-off line colors
    common_subtrees_color_branches = TRUE # Color common branches 
    )

2. Correlation matrix between a list of dendrogams

The function cor.dendlist() is used to compute “Baker” or “Cophenetic” correlation matrix between a list of trees. The value can range between -1 to 1. With near 0 values meaning that the two trees are not statistically similar.

# Cophenetic correlation matrix
cor.dendlist(dend_list, method = "cophenetic")

##       [,1]  [,2]
## [1,] 1.000 0.965
## [2,] 0.965 1.000

# Baker correlation matrix
cor.dendlist(dend_list, method = "baker")

##       [,1]  [,2]
## [1,] 1.000 0.962
## [2,] 0.962 1.000

The correlation between two trees can be also computed as follow:

# Cophenetic correlation coefficient
cor_cophenetic(dend1, dend2)

## [1] 0.965

# Baker correlation coefficient
cor_bakers_gamma(dend1, dend2)

## [1] 0.962

It’s also possible to compare simultaneously multiple dendrograms. A chaining operator %>% is used to run multiple function at the same time. It’s useful for simplifying the code:

# Create multiple dendrograms by chaining
dend1 <- df %>% dist %>% hclust("complete") %>% as.dendrogram
dend2 <- df %>% dist %>% hclust("single") %>% as.dendrogram
dend3 <- df %>% dist %>% hclust("average") %>% as.dendrogram
dend4 <- df %>% dist %>% hclust("centroid") %>% as.dendrogram
# Compute correlation matrix
dend_list <- dendlist("Complete" = dend1, "Single" = dend2,
                      "Average" = dend3, "Centroid" = dend4)
cors <- cor.dendlist(dend_list)
# Print correlation matrix
round(cors, 2)

##          Complete Single Average Centroid
## Complete     1.00   0.76    0.99     0.75
## Single       0.76   1.00    0.80     0.84
## Average      0.99   0.80    1.00     0.74
## Centroid     0.75   0.84    0.74     1.00

# Visualize the correlation matrix using corrplot package
library(corrplot)
corrplot(cors, "pie", "lower")