Partitional Clustering in R: The Essentials

Data format and preparation

To compute the CLARA algorithm in R, the data should be prepared as indicated in Chapter data preparation and R packages.

Here, we’ll generate use a random data set. To make the result reproducible, we start by using the function set.seed().

set.seed(1234)
# Generate 500 objects, divided into 2 clusters.
df <- rbind(cbind(rnorm(200,0,8), rnorm(200,0,8)),
           cbind(rnorm(300,50,8), rnorm(300,50,8)))

# Specify column and row names
colnames(df) <- c("x", "y")
rownames(df) <- paste0("S", 1:nrow(df))

# Previewing the data
head(df, nrow = 6)

##         x    y
## S1  -9.66 3.88
## S2   2.22 5.57
## S3   8.68 1.48
## S4 -18.77 5.61
## S5   3.43 2.49
## S6   4.05 6.08

Required R packages and functions

The function clara() [cluster package] can be used to compute CLARA. The simplified format is as follow:

clara(x, k, metric = "euclidean", stand = FALSE, 
      samples = 5, pamLike = FALSE)

To create a beautiful graph of the clusters generated with the pam() function, will use the factoextra package.

1. Installing required packages:

install.packages(c("cluster", "factoextra"))

2. Loading the packages:

library(cluster)
library(factoextra)

Estimating the optimal number of clusters

To estimate the optimal number of clusters in your data, it’s possible to use the average silhouette method as described in PAM clustering chapter (Chapter @ref(k-medoids)). The R function fviz_nbclust() [factoextra package] provides a solution to facilitate this step.

Computing CLARA

The R code below computes PAM algorithm with k = 2:

# Compute CLARA
clara.res <- clara(df, 2, samples = 50, pamLike = TRUE)

# Print components of clara.res
print(clara.res)

## Call:     clara(x = df, k = 2, samples = 50, pamLike = TRUE) 
## Medoids:
##          x     y
## S121 -1.53  1.15
## S455 48.36 50.23
## Objective function:   9.88
## Clustering vector:    Named int [1:500] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
##  - attr(*, "names")= chr [1:500] "S1" "S2" "S3" "S4" "S5" "S6" "S7" ...
## Cluster sizes:            200 300 
## Best sample:
##  [1] S37  S49  S54  S63  S68  S71  S76  S80  S82  S101 S103 S108 S109 S118
## [15] S121 S128 S132 S138 S144 S162 S203 S210 S216 S231 S234 S249 S260 S261
## [29] S286 S299 S304 S305 S312 S315 S322 S350 S403 S450 S454 S455 S456 S465
## [43] S488 S497
## 
## Available components:
##  [1] "sample"     "medoids"    "i.med"      "clustering" "objective" 
##  [6] "clusinfo"   "diss"       "call"       "silinfo"    "data"

The output of the function clara() includes the following components:

• medoids: Objects that represent clusters
• clustering: a vector containing the cluster number of each object
• sample: labels or case numbers of the observations in the best sample, that is, the sample used by the clara algorithm for the final partition.

If you want to add the point classifications to the original data, use this:

dd <- cbind(df, cluster = clara.res$cluster)
head(dd, n = 4)

##         x    y cluster
## S1  -9.66 3.88       1
## S2   2.22 5.57       1
## S3   8.68 1.48       1
## S4 -18.77 5.61       1

You can access to the results returned by clara() as follow:

# Medoids
clara.res$medoids

##          x     y
## S121 -1.53  1.15
## S455 48.36 50.23

# Clustering
head(clara.res$clustering, 10)

##  S1  S2  S3  S4  S5  S6  S7  S8  S9 S10 
##   1   1   1   1   1   1   1   1   1   1

The medoids are S121, S455

Visualizing CLARA clusters

To visualize the partitioning results, we’ll use the function fviz_cluster() [factoextra package]. It draws a scatter plot of data points colored by cluster numbers.