# Hierarchical Clustering in Data Mining

A **Hierarchical clustering** method works via grouping data into a tree of clusters. Hierarchical clustering begins by treating every data points as a separate cluster. Then, it repeatedly executes the subsequent steps:

- Identify the 2 clusters which can be closest together, and
- Merge the 2 maximum comparable clusters. We need to continue these steps until all the clusters are merged together.

In Hierarchical Clustering, the aim is to produce a hierarchical series of nested clusters. A diagram called **Dendrogram **(A Dendrogram is a tree-like diagram that statistics the sequences of merges or splits) graphically represents this hierarchy and is an inverted tree that describes the order in which factors are merged (bottom-up view) or cluster are break up (top-down view).

The basic method to generate hierarchical clustering are:

**1. Agglomerative:**

Initially consider every data point as an **individual** Cluster and at every step, **merge** the nearest pairs of the cluster. (It is a bottom-up method). At first everydata set set is considered as individual entity or cluster. At every iteration, the clusters merge with different clusters until one cluster is formed.

Algorithm for Agglomerative Hierarchical Clustering is:

- Calculate the similarity of one cluster with all the other clusters (calculate proximity matrix)
- Consider every data point as a individual cluster
- Merge the clusters which are highly similar or close to each other.
- Recalculate the proximity matrix for each cluster
- Repeat Step 3 and 4 until only a single cluster remains.

Let’s see the graphical representation of this algorithm using a dendrogram.

**Note:**

This is just a demonstration of how the actual algorithm works no calculation has been performed below all the proximity among the clusters are assumed.

Let’s say we have six data points **A, B, C, D, E, F**.

**Figure –**Agglomerative Hierarchical clustering

**Step-1:**

Consider each alphabet as a single cluster and calculate the distance of one cluster from all the other clusters.**Step-2:**

In the second step comparable clusters are merged together to form a single cluster. Let’s say cluster (B) and cluster (C) are very similar to each other therefore we merge them in the second step similarly with cluster (D) and (E) and at last, we get the clusters

[(A), (BC), (DE), (F)]**Step-3:**

We recalculate the proximity according to the algorithm and merge the two nearest clusters([(DE), (F)]) together to form new clusters as [(A), (BC), (DEF)]**Step-4:**

Repeating the same process; The clusters DEF and BC are comparable and merged together to form a new cluster. We’re now left with clusters [(A), (BCDEF)].**Step-5:**

At last the two remaining clusters are merged together to form a single cluster [(ABCDEF)].

**2. Divisive:**

We can say that the Divisive Hierarchical clustering is precisely the **opposite** of the Agglomerative Hierarchical clustering. In Divisive Hierarchical clustering, we take into account all of the data points as a single cluster and in every iteration, we separate the data points from the clusters which aren’t comparable. In the end, we are left with N clusters.

**Figure –**Divisive Hierarchical clustering

GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details

## Recommended Posts:

- Difference Between Data Mining and Text Mining
- Difference Between Data Mining and Web Mining
- Difference Between Data Mining and Data Visualization
- Types of Sources of Data in Data Mining
- Data Mining: Data Warehouse Process
- Difference Between Data Science and Data Mining
- Data Mining: Data Attributes and Quality
- Difference between Data Warehousing and Data Mining
- Difference Between Big Data and Data Mining
- Data Transformation in Data Mining
- Data Reduction in Data Mining
- Data Integration in Data Mining
- Data Preprocessing in Data Mining
- Data Normalization in Data Mining
- Data Mining | Set 2

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.