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Hierarchical clustering in R

Another approach to clustering is to build hierarchy of all possible distances between objects in the dataset. This plot called Cluster Dendrogram. One of the advantages of these hierarchical tries (Dendogram) that it is very easy to analyse them visually without mathematical calculations and understand how different classes are appear in the set.

Calculating hierarchical tree

Using all iris data

We will use all available data for clustering by Hierarchical trees (hclust()).


library(dplyr)

unlabeled_iris <- iris %>% select(-Species)
iris_hierarchy <- hclust(dist(unlabeled_iris), method="centroid")
plot(iris_hierarchy)

As a result we will have the following dendogram:

Iris hierarchy for all data
Iris hierarchy for all data
Dendogram calculated with all available data for iris dataset. It is easy to see, how these distances are slitted into two main groups.
Original image: 568 x 695

This hierarchical tree reveals, that we have two separated group, but not three. Lets check it in more details. We will select 3 clusters from this tree and check how it is related with our species. cutree() will split our hierarchical tree into 2 groups and then table() will show relation with or real species


iris_cluster <- cutree(iris_hierarchy, 3)
table(iris_cluster, iris$Species)

#iris_cluster setosa versicolor virginica
#           1     50          0         0
#           2      0         50        48
#           3      0          0         2

setosa was separated clearly. versicolor is clearly separated as well, but almost all virginica was classified as versicolor. Clearly this is very bad clustering

Let’s check it on the plot


plot(unlabeled_iris$Petal.Length, unlabeled_iris$Petal.Width,
     pch=c(22,21,23)[iris_cluster],
     bg=c("red", "green", "blue")[iris_cluster])
Iris full dataset hierarchy cluster
Iris full dataset hierarchy cluster
Hierarchy clustering on the basis of all available data.
Original image: 566 x 624

It is possible to see how green dots are cover almost all big area, which is wrong. So really, our clustering is fail on this example.

Using Petal.Length and Petal.Width iris data

Now we will do hierarchical clustering on the basis of only Petal.Length and Petal.Width sets in our iris dataset.


library(dplyr)

unlabeled_iris2 <- iris %>% select(Petal.Length, Petal.Width)
iris_hierarchy2 <- hclust(dist(unlabeled_iris2), method="centroid")
plot(iris_hierarchy2)
Iris hierarchy for selected data
Iris hierarchy for selected data
Dendogram calculated for only on the basis of only Petal.Length and Petal.Width set of data.
Original image: 582 x 694

This hierarchy tree is more clearly shows the splitting into 3 groups and this is very promising. Now we will check it with cutree() by comparing our cauterization with original species


iris_cluster2 <- cutree(iris_hierarchy2, 3)
table(iris_cluster2, iris$Species)

#’iris_cluster2 setosa versicolor virginica
#            1     50          0         0
#            2      0         45         1
#            3      0          5        49

As it is possible to see now, the separation between three groups is almost ideal. There are some confusing between versicolor and virginica species, but this is much better than our previous solution. Let’s check it visually by plotting new clustering and original datasets


plot(unlabeled_iris2$Petal.Length, unlabeled_iris2$Petal.Width,
     pch=c(22,21,23)[iris_cluster2],
     bg=c("red", "green", "blue")[iris_cluster2])

plot(iris$Petal.Length, iris$Petal.Width,
     pch=c(22,21,23)[iris$Species],
     bg=c("red", "green", "blue")[iris$Species])
Iris hierarchy clustering for 2 data from the dataset
Iris hierarchy clustering for 2 data from the dataset
visual splitting for Hierarchy clustering on the basis of Petal.Length and Petal.Width datasets.
Original image: 570 x 626

And for reference we can compare with origina species distribution:

Iris dataset species
Iris dataset species
Species in the iris dataset
Original image: 563 x 617

Hierarchy clustering conclusion

This example shows that it is very important to be very accurate with selected data for analysis. Sometimes additional information which give identical results for different groups can give very bad addition to the final clusterization.


Published: 2021-11-18 06:20:20

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