This article describes how to compare **cluster dendrograms** in R using the *dendextend* R package.

The *dendextend* package provides several functions for comparing dendrograms. Here, we’ll focus on two functions:

*tanglegram*() for visual comparison of two dendrograms- and
*cor.dendlist*() for computing a correlation matrix between dendrograms.

#### Related Book

Practical Guide to Cluster Analysis in R## 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)
```

**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
)
```

Note that, “unique” nodes, with a combination of labels/items not present in the other tree, are highlighted with dashed lines.

Note that, just because we can get two trees to have horizontal connecting lines, it doesn’t mean these trees are identical (or even very similar topologically).

In the following section, we’ll perform correlation analysis to measure the similarity between dendrograms.

**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")
```

## Recommended for you

This section contains best data science and self-development resources to help you on your path.

### Coursera - Online Courses and Specialization

#### Data science

- Course: Machine Learning: Master the Fundamentals by Stanford
- Specialization: Data Science by Johns Hopkins University
- Specialization: Python for Everybody by University of Michigan
- Courses: Build Skills for a Top Job in any Industry by Coursera
- Specialization: Master Machine Learning Fundamentals by University of Washington
- Specialization: Statistics with R by Duke University
- Specialization: Software Development in R by Johns Hopkins University
- Specialization: Genomic Data Science by Johns Hopkins University

#### Popular Courses Launched in 2020

- Google IT Automation with Python by Google
- AI for Medicine by deeplearning.ai
- Epidemiology in Public Health Practice by Johns Hopkins University
- AWS Fundamentals by Amazon Web Services

#### Trending Courses

- The Science of Well-Being by Yale University
- Google IT Support Professional by Google
- Python for Everybody by University of Michigan
- IBM Data Science Professional Certificate by IBM
- Business Foundations by University of Pennsylvania
- Introduction to Psychology by Yale University
- Excel Skills for Business by Macquarie University
- Psychological First Aid by Johns Hopkins University
- Graphic Design by Cal Arts

### Amazon FBA

#### Amazing Selling Machine

### Books - Data Science

#### Our Books

- Practical Guide to Cluster Analysis in R by A. Kassambara (Datanovia)
- Practical Guide To Principal Component Methods in R by A. Kassambara (Datanovia)
- Machine Learning Essentials: Practical Guide in R by A. Kassambara (Datanovia)
- R Graphics Essentials for Great Data Visualization by A. Kassambara (Datanovia)
- GGPlot2 Essentials for Great Data Visualization in R by A. Kassambara (Datanovia)
- Network Analysis and Visualization in R by A. Kassambara (Datanovia)
- Practical Statistics in R for Comparing Groups: Numerical Variables by A. Kassambara (Datanovia)
- Inter-Rater Reliability Essentials: Practical Guide in R by A. Kassambara (Datanovia)

#### Others

- R for Data Science: Import, Tidy, Transform, Visualize, and Model Data by Hadley Wickham & Garrett Grolemund
- Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems by Aurelien Géron
- Practical Statistics for Data Scientists: 50 Essential Concepts by Peter Bruce & Andrew Bruce
- Hands-On Programming with R: Write Your Own Functions And Simulations by Garrett Grolemund & Hadley Wickham
- An Introduction to Statistical Learning: with Applications in R by Gareth James et al.
- Deep Learning with R by François Chollet & J.J. Allaire
- Deep Learning with Python by François Chollet

## No Comments