Hierarchical cluster analysis

Hierarchical cluster analysis

library(tidyverse)

Prepare data for analysis datasets::USArrests

library(datasets)
df <- datasets::USArrests
head(df)

##            Murder Assault UrbanPop Rape
## Alabama      13.2     236       58 21.2
## Alaska       10.0     263       48 44.5
## Arizona       8.1     294       80 31.0
## Arkansas      8.8     190       50 19.5
## California    9.0     276       91 40.6
## Colorado      7.9     204       78 38.7

# check if 'NA' values present in data
any(is.na(df))

## [1] FALSE

# remove 'NA' if necessary
df <- na.omit(df)
# normalize
df <- scale(df)

Choosing optimal number of clusters

wss <- (nrow(df)-1)*sum(apply(df,2,var))
for (i in 2:15) wss[i] <- sum(kmeans(df, centers=i)$withinss)
plot(1:15, wss, type="b",
     xlab="Number of Clusters",
     ylab="Within groups sum of squares")

Choosing the best clustering model

hc2 <- cluster::agnes(df, method='complete')
hc2$ac

## [1] 0.8531583

This metric allows to estimate the quality of cluster. Closer to 1 is better.
Using this metric we can try several models and choose the best one.

m <- c( "average", "single", "complete", "ward")
names(m) <- c( "average", "single", "complete", "ward")
# function to compute coefficient
ac <- function(x) { cluster::agnes(df, method = x)$ac }

purrr::map_dbl(m, ac)

##   average    single  complete      ward 
## 0.7379371 0.6276128 0.8531583 0.9346210

As we can see the ward method gives the best clustering.

Hierarchical cluster analysis

Let’s first split data into 4 groups using clust::hclust function.

# calculate distances
d <- dist(df, method='euclidean')

# hierarchical cluster analysis
# 'ward.D2' method is equivalent of agnes 'ward'
hc1 <- hclust(d, method='ward.D2')

# Plot the obtained dendrogram
plot(hc1, hang = -1, cex = 0.6)

# show 4 clusers
rect.hclust(hc1, k=4, border="blue")

# group data by clusters
groups <- cutree(hc1, k=3)
names(groups[groups == 1])

##  [1] "Alabama"        "Alaska"         "Arizona"        "California"    
##  [5] "Colorado"       "Florida"        "Georgia"        "Illinois"      
##  [9] "Louisiana"      "Maryland"       "Michigan"       "Mississippi"   
## [13] "Nevada"         "New Mexico"     "New York"       "North Carolina"
## [17] "South Carolina" "Tennessee"      "Texas"

# check for cluster metrics
names(hc1)

## [1] "merge"       "height"      "order"       "labels"      "method"     
## [6] "call"        "dist.method"

Now we can split data into 4 groups using cluster::agnes function.

# using 'agnes' for hierarhical clustering
hc3 <- cluster::agnes(df, method='ward')
# plot slaster
cluster::pltree(hc3, hang = -1, cex = 0.6)

# split into groups
groups <- cutree(as.hclust(hc3), k = 4)
groups[groups==1]

##        Alabama        Georgia      Louisiana    Mississippi North Carolina 
##              1              1              1              1              1 
## South Carolina      Tennessee 
##              1              1

Bibliography

UC Business Analytics R Programming Guide