This chapter describes a **cluster analysis example** using R software. We provide a quick start R code to compute and visualize K-means and hierarchical clustering.

#### Related Book

Practical Guide to Cluster Analysis in R## Loading required R packages

`cluster`

for cluster analysis`factoextra`

for cluster visualization

```
library(cluster)
library(factoextra)
```

## Data preparation

We’ll use the demo data set USArrests. We start by standardizing the data:

`mydata <- scale(USArrests) `

## K-means clustering

K-means is a clustering techniques that subdivide the data sets into a set of k groups, where k is the number of groups pre-specified by the analyst.

The following R codes show how to determine the optimal number of clusters and how to compute k-means and PAM clustering in R.

**Determining the optimal number of clusters**: use`factoextra::fviz_nbclust()`

`fviz_nbclust(mydata, kmeans, method = "gap_stat")`

Suggested number of cluster: 3

**Compute and visualize k-means clustering**:

```
set.seed(123) # for reproducibility
km.res <- kmeans(mydata, 3, nstart = 25)
# Visualize
fviz_cluster(km.res, data = mydata, palette = "jco",
ggtheme = theme_minimal())
```

## Hierarchical clustering

Hierarchical clustering is an alternative approach to partitioning clustering for identifying groups in the data set. It does not require to pre-specify the number of clusters to be generated.

The result of hierarchical clustering is a tree-based representation of the objects, which is also known as dendrogram. Observations can be subdivided into groups by cutting the dendrogram at a desired similarity level.

- Computation: R function:
`hclust()`

. It takes a dissimilarity matrix as an input, which is calculated using the function`dist()`

. - Visualization:
`fviz_dend()`

[in factoextra]

R code to compute and visualize hierarchical clustering:

```
res.hc <- hclust(dist(mydata), method = "ward.D2")
fviz_dend(res.hc, cex = 0.5, k = 4, palette = "jco")
```

A heatmap is another way to visualize hierarchical clustering. It’s also called a false colored image, where data values are transformed to color scale. Heat maps allow us to simultaneously visualize groups of samples and features. You can easily create a pretty heatmap using the R package `pheatmap`

.

In heatmap, generally, columns are samples and rows are variables. Therefore we start by transposing the data before creating the heatmap.

```
library(pheatmap)
pheatmap(t(mydata), cutree_cols = 4)
```

## Summary

This chapter presents examples of R code to compute and visualize k-means and hierarchical clustering.

## 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 Standford
- 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

### 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

Hi,

For some reason my code produces two optimal clusters.

data(“USArrests”)

df = USArrests; df = scale(df)

# k-means clustering; ####

# optimal number of clusters;

fviz_nbclust(

df,

kmeans,

method = “gap_stat”

)

I cant seem to find a difference in the code.

Same here! I suspect that the dataset got updated after the page was published.