Hierarchical Analysis in R
Javier Aguilar
2025-10-4
Data Preparation
df <- USArrestsdf <- na.omit(df)df <- scale(df)
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 1.864967207Hierarchical Clustering with R
d <- dist(df, method = "euclidean")
hc1 <- hclust(d, method = "complete" )
plot(hc1, cex = 0.6, hang = -1)
hc2 <- agnes(df, method = "complete")
hc2$ac## [1] 0.8531583m <- c( "average", "single", "complete", "ward")
names(m) <- c( "average", "single", "complete", "ward")
ac <- function(x) {
agnes(df, method = x)$ac
}
map_dbl(m, ac)## average single complete ward
## 0.7379371 0.6276128 0.8531583 0.9346210hc3 <- agnes(df, method = "ward")
pltree(hc3, cex = 0.6, hang = -1, main = "Dendrogram of agnes")
hc4 <- diana(df)
hc4$dc## [1] 0.8514345## [1] 0.8514345
pltree(hc4, cex = 0.6, hang = -1, main = "Dendrogram of diana")
Working with Dendrograms
hc5 <- hclust(d, method = "ward.D2" )
sub_grp <- cutree(hc5, k = 4)
table(sub_grp)## sub_grp
## 1 2 3 4
## 7 12 19 12USArrests %>%
mutate(cluster = sub_grp) %>%
head## Murder Assault UrbanPop Rape cluster
## Alabama 13.2 236 58 21.2 1
## Alaska 10.0 263 48 44.5 2
## Arizona 8.1 294 80 31.0 2
## Arkansas 8.8 190 50 19.5 3
## California 9.0 276 91 40.6 2
## Colorado 7.9 204 78 38.7 2plot(hc5, cex = 0.6)
rect.hclust(hc5, k = 4, border = 2:5)
fviz_cluster(list(data = df, cluster = sub_grp))
hc_a <- agnes(df, method = "ward")
cutree(as.hclust(hc_a), k = 4)## Alabama Alaska Arizona Arkansas California
## 1 2 2 3 2
## Colorado Connecticut Delaware Florida Georgia
## 2 3 3 2 1
## Hawaii Idaho Illinois Indiana Iowa
## 3 4 2 3 4
## Kansas Kentucky Louisiana Maine Maryland
## 3 3 1 4 2
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 2 4 1 3
## Montana Nebraska Nevada New Hampshire New Jersey
## 4 4 2 4 3
## New Mexico New York North Carolina North Dakota Ohio
## 2 2 1 4 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 3 1
## South Dakota Tennessee Texas Utah Vermont
## 4 1 2 3 4
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 4 4 3hc_d <- diana(df)
cutree(as.hclust(hc_d), k = 4)## Alabama Alaska Arizona Arkansas California
## 1 2 2 3 2
## Colorado Connecticut Delaware Florida Georgia
## 2 3 3 2 1
## Hawaii Idaho Illinois Indiana Iowa
## 3 4 2 3 4
## Kansas Kentucky Louisiana Maine Maryland
## 3 4 1 4 2
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 2 4 1 2
## Montana Nebraska Nevada New Hampshire New Jersey
## 4 4 2 4 3
## New Mexico New York North Carolina North Dakota Ohio
## 2 2 1 4 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 3 1
## South Dakota Tennessee Texas Utah Vermont
## 4 1 2 3 4
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 4 4 3res.dist <- dist(df, method = "euclidean")
hc1 <- hclust(res.dist, method = "complete")
hc2 <- hclust(res.dist, method = "ward.D2")
dend1 <- as.dendrogram (hc1)
dend2 <- as.dendrogram (hc2)
tanglegram(dend1, dend2)## Loading required namespace: colorspace
dend_list <- dendlist(dend1, dend2)
tanglegram(dend1, dend2,
highlight_distinct_edges = FALSE, # Turn-off dashed lines
common_subtrees_color_lines = FALSE, # Turn-off line colors
common_subtrees_color_branches = TRUE, # Color common branches
main = paste("entanglement =", round(entanglement(dend_list), 2))
)
Determining Optimal Clusters
Elbow Method
fviz_nbclust(df, FUN = hcut, method = "wss")
Average Silhouette Method
fviz_nbclust(df, FUN = hcut, method = "silhouette")
Gap Statistic Method
gap_stat <- clusGap(df, FUN = hcut, nstart = 25, K.max = 10, B = 50)
fviz_gap_stat(gap_stat)## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## 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.
Code taken from: Hierarchical Cluster Analysis.