In R software, standard clustering methods (partitioning and hierarchical clustering) can be computed using the R packages `stats`

and `cluster`

. However the workflow, generally, requires multiple steps and multiple lines of R codes.

This article describes some easy-to-use wrapper functions, in the `factoextra`

R package, for simplifying and improving **cluster analysis in R**. These functions include:

*get_dist*() &*fviz_dist*() for computing and visualizing distance matrix between rows of a data matrix. Compared to the standard*dist*() function, get_dist() supports*correlation-based distance measures*including “pearson”, “kendall” and “spearman” methods.*eclust*(): enhanced cluster analysis. It has several advantages:- It simplifies the workflow of clustering analysis
- It can be used to compute
*hierarchical clustering*and*partititioning clustering*in a single line function call - Compared to the standard partitioning functions (kmeans, pam, clara and fanny) which requires the user to specify the optimal number of clusters, the function eclust() computes automatically the
*gap statistic*for estimating the right number of clusters. - For hierarchical clustering, correlation-based metric is allowed
- It provides silhouette information for all partitioning methods and hierarchical clustering
- It creates beautiful graphs using ggplot2

Contents:

#### Related Book

Practical Guide to Cluster Analysis in R## Required packages

We’ll use the factoextra package for an enhanced cluster analysis and visualization.

- Install factoextra:

`install.packages("factoextra")`

- Load factoextra

`library(factoextra)`

## Data preparation

The built-in R dataset **USArrests** is used:

```
# Load and scale the dataset
data("USArrests")
df <- scale(USArrests)
head(df)
```

```
## Murder Assault UrbanPop Rape
## Alabama 1.2426 0.783 -0.521 -0.00342
## Alaska 0.5079 1.107 -1.212 2.48420
## Arizona 0.0716 1.479 0.999 1.04288
## Arkansas 0.2323 0.231 -1.074 -0.18492
## California 0.2783 1.263 1.759 2.06782
## Colorado 0.0257 0.399 0.861 1.86497
```

## Distance matrix computation and visualization

```
library(factoextra)
# Correlation-based distance method
res.dist <- get_dist(df, method = "pearson")
head(round(as.matrix(res.dist), 2))[, 1:6]
```

```
## Alabama Alaska Arizona Arkansas California Colorado
## Alabama 0.00 0.71 1.45 0.09 1.87 1.69
## Alaska 0.71 0.00 0.83 0.37 0.81 0.52
## Arizona 1.45 0.83 0.00 1.18 0.29 0.60
## Arkansas 0.09 0.37 1.18 0.00 1.59 1.37
## California 1.87 0.81 0.29 1.59 0.00 0.11
## Colorado 1.69 0.52 0.60 1.37 0.11 0.00
```

```
# Visualize the dissimilarity matrix
fviz_dist(res.dist, lab_size = 8)
```

In the plot above, similar objects are close to one another. Red color corresponds to small distance and blue color indicates big distance between observation.

## Enhanced clustering analysis

The standard R code for computing hierarchical clustering looks like this:

```
# Load and scale the dataset
data("USArrests")
df <- scale(USArrests)
# Compute dissimilarity matrix
res.dist <- dist(df, method = "euclidean")
# Compute hierarchical clustering
res.hc <- hclust(res.dist, method = "ward.D2")
# Visualize
plot(res.hc, cex = 0.5)
```

In this section we’ll describe the *eclust*() function [*factoextra* package] to simplify the workflow. The format is as follow:

`eclust(x, FUNcluster = "kmeans", hc_metric = "euclidean", ...)`

- x: numeric vector, data matrix or data frame
- FUNcluster: a clustering function including “kmeans”, “pam”, “clara”, “fanny”, “hclust”, “agnes” and “diana”. Abbreviation is allowed.
- hc_metric: character string specifying the metric to be used for calculating dissimilarities between observations. Allowed values are those accepted by the function dist() [including “euclidean”, “manhattan”, “maximum”, “canberra”, “binary”, “minkowski”] and correlation based distance measures [“pearson”, “spearman” or “kendall”]. Used only when FUNcluster is a hierarchical clustering function such as one of “hclust”, “agnes” or “diana”.
- …: other arguments to be passed to FUNcluster.

In the following R code, we’ll show some examples for enhanced k-means clustering and hierarchical clustering. Note that the same analysis can be done for PAM, CLARA, FANNY, AGNES and DIANA.

```
library("factoextra")
# Enhanced k-means clustering
res.km <- eclust(df, "kmeans", nstart = 25)
```

```
## Clustering k = 1,2,..., K.max (= 10): .. done
## Bootstrapping, b = 1,2,..., B (= 100) [one "." per sample]:
## .................................................. 50
## .................................................. 100
```

```
# Gap statistic plot
fviz_gap_stat(res.km$gap_stat)
```

```
# Silhouette plot
fviz_silhouette(res.km)
```

```
## cluster size ave.sil.width
## 1 1 8 0.39
## 2 2 16 0.34
## 3 3 13 0.37
## 4 4 13 0.27
```

```
# Optimal number of clusters using gap statistics
res.km$nbclust
```

`## [1] 4`

```
# Print result
res.km
```

```
## K-means clustering with 4 clusters of sizes 8, 16, 13, 13
##
## Cluster means:
## Murder Assault UrbanPop Rape
## 1 1.412 0.874 -0.815 0.0193
## 2 -0.489 -0.383 0.576 -0.2617
## 3 -0.962 -1.107 -0.930 -0.9668
## 4 0.695 1.039 0.723 1.2769
##
## Clustering vector:
## Alabama Alaska Arizona Arkansas California
## 1 4 4 1 4
## Colorado Connecticut Delaware Florida Georgia
## 4 2 2 4 1
## Hawaii Idaho Illinois Indiana Iowa
## 2 3 4 2 3
## Kansas Kentucky Louisiana Maine Maryland
## 2 3 1 3 4
## Massachusetts Michigan Minnesota Mississippi Missouri
## 2 4 3 1 4
## Montana Nebraska Nevada New Hampshire New Jersey
## 3 3 4 3 2
## New Mexico New York North Carolina North Dakota Ohio
## 4 4 1 3 2
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 2 2 2 2 1
## South Dakota Tennessee Texas Utah Vermont
## 3 1 4 2 3
## Virginia Washington West Virginia Wisconsin Wyoming
## 2 2 3 3 2
##
## Within cluster sum of squares by cluster:
## [1] 8.32 16.21 11.95 19.92
## (between_SS / total_SS = 71.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault" "clust_plot" "silinfo" "nbclust"
## [13] "data" "gap_stat"
```

```
# Enhanced hierarchical clustering
res.hc <- eclust(df, "hclust") # compute hclust
```

```
## Clustering k = 1,2,..., K.max (= 10): .. done
## Bootstrapping, b = 1,2,..., B (= 100) [one "." per sample]:
## .................................................. 50
## .................................................. 100
```

` fviz_dend(res.hc, rect = TRUE) # dendrogam`

` fviz_silhouette(res.hc) # silhouette plot`

```
## cluster size ave.sil.width
## 1 1 19 0.26
## 2 2 19 0.28
## 3 3 12 0.43
```

` fviz_cluster(res.hc) # scatter plot`

It’s also possible to specify the number of clusters as follow:

`eclust(df, "kmeans", k = 4)`

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