Cluster Analysis
DEVINE FATHY MAE S. GRINO
2024-05-17
library(factoextra)## Warning: package 'factoextra' was built under R version 4.3.3## Loading required package: ggplot2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBaData 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 1.24256408 0.7828393 -0.5209066 -0.003416473
## Alaska 0.50786248 1.1068225 -1.2117642 2.484202941
## Arizona 0.07163341 1.4788032 0.9989801 1.042878388
## Arkansas 0.23234938 0.2308680 -1.0735927 -0.184916602
## California 0.27826823 1.2628144 1.7589234 2.067820292
## Colorado 0.02571456 0.3988593 0.8608085 1.864967207Distance 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)
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:
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)
# Gap statistic plot
fviz_gap_stat(res.km$gap_stat)
# Silhouette plot
fviz_silhouette(res.km)## cluster size ave.sil.width
## 1 1 13 0.37
## 2 2 20 0.26
## 3 3 17 0.32
# Optimal number of clusters using gap statistics
res.km$nbclust## [1] 3# Print result
res.km## K-means clustering with 3 clusters of sizes 13, 20, 17
##
## Cluster means:
## Murder Assault UrbanPop Rape
## 1 -0.9615407 -1.1066010 -0.9301069 -0.9667633
## 2 1.0049340 1.0138274 0.1975853 0.8469650
## 3 -0.4469795 -0.3465138 0.4788049 -0.2571398
##
## Clustering vector:
## Alabama Alaska Arizona Arkansas California
## 2 2 2 3 2
## Colorado Connecticut Delaware Florida Georgia
## 2 3 3 2 2
## Hawaii Idaho Illinois Indiana Iowa
## 3 1 2 3 1
## Kansas Kentucky Louisiana Maine Maryland
## 3 1 2 1 2
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 2 1 2 2
## Montana Nebraska Nevada New Hampshire New Jersey
## 1 1 2 1 3
## New Mexico New York North Carolina North Dakota Ohio
## 2 2 2 1 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 3 2
## South Dakota Tennessee Texas Utah Vermont
## 1 2 2 3 1
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 1 1 3
##
## Within cluster sum of squares by cluster:
## [1] 11.95246 46.74796 19.62285
## (between_SS / total_SS = 60.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault" "clust_plot"
## [11] "silinfo" "nbclust" "data" "gap_stat" # Enhanced hierarchical clustering
res.hc <- eclust(df, "hclust") # compute hclust## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
## Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated. 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
eclust(df, "kmeans", k = 4)
## K-means clustering with 4 clusters of sizes 8, 13, 16, 13
##
## Cluster means:
## Murder Assault UrbanPop Rape
## 1 1.4118898 0.8743346 -0.8145211 0.01927104
## 2 -0.9615407 -1.1066010 -0.9301069 -0.96676331
## 3 -0.4894375 -0.3826001 0.5758298 -0.26165379
## 4 0.6950701 1.0394414 0.7226370 1.27693964
##
## Clustering vector:
## Alabama Alaska Arizona Arkansas California
## 1 4 4 1 4
## Colorado Connecticut Delaware Florida Georgia
## 4 3 3 4 1
## Hawaii Idaho Illinois Indiana Iowa
## 3 2 4 3 2
## Kansas Kentucky Louisiana Maine Maryland
## 3 2 1 2 4
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 4 2 1 4
## Montana Nebraska Nevada New Hampshire New Jersey
## 2 2 4 2 3
## New Mexico New York North Carolina North Dakota Ohio
## 4 4 1 2 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 3 1
## South Dakota Tennessee Texas Utah Vermont
## 2 1 4 3 2
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 2 2 3
##
## Within cluster sum of squares by cluster:
## [1] 8.316061 11.952463 16.212213 19.922437
## (between_SS / total_SS = 71.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault" "clust_plot"
## [11] "silinfo" "nbclust" "data"