Visualize Silhouette Information from Clustering

Silhouette (Si) analysis is a cluster validation approach that measures how well an observation is clustered and it estimates the average distance between clusters. fviz_silhouette() provides ggplot2-based elegant visualization of silhouette information from i) the result of silhouette(), pam(), clara() and fanny() [in cluster package]; ii) eclust() and hcut() [in factoextra].

Read more: Clustering Validation Statistics.

fviz_silhouette(sil.obj, label = FALSE, print.summary = TRUE, ...)

Arguments

sil.obj

an object of class silhouette: pam, clara, fanny [in cluster package]; eclust and hcut [in factoextra].
label

logical value. If true, x axis tick labels are shown
print.summary

logical value. If true a summary of cluster silhouettes are printed in fviz_silhouette().
...

other arguments to be passed to the function ggpubr::ggpar().

Value

return a ggplot

Details

- Observations with a large silhouhette Si (almost 1) are very well clustered.

- A small Si (around 0) means that the observation lies between two clusters.

- Observations with a negative Si are probably placed in the wrong cluster.

See also

fviz_cluster, hcut, hkmeans, eclust, fviz_dend

Examples

set.seed(123)

# Data preparation
# +++++++++++++++
data("iris")
head(iris)
#>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> 1          5.1         3.5          1.4         0.2  setosa
#> 2          4.9         3.0          1.4         0.2  setosa
#> 3          4.7         3.2          1.3         0.2  setosa
#> 4          4.6         3.1          1.5         0.2  setosa
#> 5          5.0         3.6          1.4         0.2  setosa
#> 6          5.4         3.9          1.7         0.4  setosa
# Remove species column (5) and scale the data
iris.scaled <- scale(iris[, -5])

# K-means clustering
# +++++++++++++++++++++
km.res <- kmeans(iris.scaled, 3, nstart = 2)

# Visualize kmeans clustering
fviz_cluster(km.res, iris[, -5], ellipse.type = "norm")+
theme_minimal()

# Visualize silhouhette information
require("cluster")
sil <- silhouette(km.res$cluster, dist(iris.scaled))
fviz_silhouette(sil)
#>   cluster size ave.sil.width
#> 1       1   50          0.64
#> 2       2   47          0.35
#> 3       3   53          0.39

# Identify observation with negative silhouette
neg_sil_index <- which(sil[, "sil_width"] < 0)
sil[neg_sil_index, , drop = FALSE]
#>      cluster neighbor   sil_width
#> [1,]       2        3 -0.01058434
#> [2,]       2        3 -0.02489394
if (FALSE) {
# PAM clustering
# ++++++++++++++++++++
require(cluster)
pam.res <- pam(iris.scaled, 3)
# Visualize pam clustering
fviz_cluster(pam.res, ellipse.type = "norm")+
theme_minimal()
# Visualize silhouhette information
fviz_silhouette(pam.res)

# Hierarchical clustering
# ++++++++++++++++++++++++
# Use hcut() which compute hclust and cut the tree
hc.cut <- hcut(iris.scaled, k = 3, hc_method = "complete")
# Visualize dendrogram
fviz_dend(hc.cut, show_labels = FALSE, rect = TRUE)
# Visualize silhouhette information
fviz_silhouette(hc.cut)
}