# Hierarchical Clustering

Original article was published on Deep Learning on Medium

## Introduction: It is a specific type of clustering, or it can be said that it is a specific way to perform clustering. This type of clustering is good for small sized datasets, and they are very intuitive.

I will suggest that before this reading this article, please go through my other article which explains clustering in detail, because then you will have a strong base of the clustering.

## Explanation of Hierarchical Clustering

This type of clustering starts to make clusters of data in Tree format.

Internally Hierarchical clustering try to construct a tree where each node can be considered as a cluster of its child nodes.

Hierarchical Clustering can be further divided into 2 categories which are:

1. Agglomerative
2. Divisive

## Agglomerative Hierarchical Clustering

It is based on the bottom to top approach of tree formation.

This approach starts at the bottom of the tree & keep on constructing the cluster Tree upwards. It, first of all, finds the 2 or more features which are most similar and combine them as one by creating a node of the Cluster Tree, they can be found out let’s say by the distance between them, let’s say there are multiple points, then the 2 features having the minimum distance will be considered as the down-most node of the Tree.

By continuing the above-explained approach recursively, a complete tree is formed which can be easily interpreted & multiple insights can be easily extracted from that Tree.

## Divisive Hierarchical Clustering

It is opposite to the Agglomerative approach & works oppositely as compared to the Agglomerative approach.

It is based on the top to bottom approach of cluster tree formation. First of all it creates a cluster of the items which are far apart, & then move downwards in the cluster tree & continues the above step until the complete tree is formed.

Generally most popular approach among the two is Agglomerative one, as it is more relatable to form clusters of the items first which are similar to each other.

## Example of the Agglomerative Approach

In this example, I have shown the practical example of Hierarchical Clustering on fruits. Generally, the output of Hierarchical clustering is represented as a “Dendrogram”, which is a way to represent trees, or we can say diagrammatic representation of trees.

In the above figure, the “y” axis represents the similarity between the clusters, as the value of y increases, dissimilarity increases. “x” axis represents the clusters.

## Explanation of the above Dendrogram

Clusters of pairs of (“Plum” and “Sweet Lime”) & (“Strawberry” and “Lychee”) are formed first (using agglomerative approach) because they are most similar.

Now, both of the above pairs can be treated as an individual entity, and the similarity of other fruits will be compared to them & further cluster tree grows. In the present example, pair of (“Plum” and “Sweet Lime”) is clustered with “Orange”, on the other hand, pair of (“Strawberry” and “Lychee”) is clustered with “Cherry”, based on the similarity between them.

In this fashion, hierarchical clustering executes and makes clusters of the data.