**1 Answer**

written 12 months ago by |

**Hierarchical Clustering**

- This type of clustering groups together the unlabeled data points having similar characteristics.
- Hierarchical clustering treats every data point as a separate cluster.
- Then, it repeatedly executes the subsequent steps like, Identify the two clusters which can be closest together, and merging the two maximum comparable clusters.
- This process needs to continue until all the clusters are merged.
- Hence, this method creates a hierarchical decomposition of the given set of data objects.
- Based on this how the hierarchical decomposition is formed this clustering is further classified into two types,
**Agglomerative Approach****Divisive Approach**

- Hierarchical clustering typically works by sequentially merging similar clusters. This is known as agglomerative hierarchical clustering.
- In theory, it can also be done by initially grouping all the observations into one cluster, and then successively splitting these clusters. This is known as divisive hierarchical clustering.
- Divisive clustering is rarely done in practice.

**Agglomerative Approach**

- This approach is also known as the
*Bottom-Up Approach.* - This approach starts with each object forming a separate group.
- It keeps on merging the objects or groups that are close to one another.
- It keeps on doing so until all of the groups are merged into one or until the termination condition holds.
:*Algorithm for Agglomerative Hierarchical Clustering is***Step 1 -**Calculate the similarity of one cluster with all the other clusters. Calculation of Proximity Matrix.**Step 2 -**Consider every data point as an individual cluster.**Step 3 -**Merge the clusters which are highly similar or close to each other.**Step 4 -**Recalculate the proximity matrix for each cluster.**Step 5 -**Repeatuntil only a single cluster remains.*Steps 3 and 4*

- In this method, clusters are merged based on the distance between them and to calculate the distance between the clusters there are different types of linkages used such as
*Single Linkage**Complete Linkage**Average Linkage**Centroid Linkage*

**Dendrogram**

- A dendrogram is a tree-like structure used to represent hierarchical clustering.
- In this, each object is represented by leaf nodes, and the clusters are represented by root nodes.

*Letâ€™s understand Dendrogram by solving the one example:*

The above-given Distance Matrix contains all diagonals with 0's and other symmetric values.

# Step 1 -

From the above distance matrix, The shortest distance in the matrix is 1, and elements associated with are E and A. Hence, merge them to form a cluster (E, A).

Now, *calculate the distance between other elements and EA as follows:*

**Distance ((E A), C) =** Minimum_Distance[Distance(E, C), Distance(A, C)]
= Minimum_Distance[2,2]
**= 2**

**Distance ((E A), B) =** Minimum_Distance[Distance(E, B), Distance(A, B)]
= Minimum_Distance[2,5]
**= 2**

**Distance ((E A), D) =** Minimum_Distance[Distance(E, D), Distance(A, D)]
= Minimum_Distance[3,3]
**= 3**

*The new Distance Matrix after the First Cluster (EA) formation and Dendrogram formed at this step looks as follows:*

# Step 2 -

From the newly obtained distance matrix, The shortest distance in the matrix is 1, and elements associated with are B and C. Hence, merge them to form a cluster (B, C).

Now, *calculate the distance between other elements and BC as follows:*

**Distance ((B C),(E A)) =** Minimum_Distance[Distance(B, E), Distance(B, A), Distance(C E), Distance(C A)]
= Minimum_Distance[2, 5, 2, 2]
**= 2**

**Distance ((B C), D) =** Minimum_Distance[Distance(B, D), Distance(C, D)]
= Minimum_Distance[3,6]
**= 3**

*The new Distance Matrix after the Second Cluster (BC) formation and Dendrogram formed at this step looks as follows:*

# Step 3 -

From the newly obtained distance matrix, The shortest distance in the matrix is 2, and elements associated with are (B, C) and (E, A). Hence, merge them to form a cluster (B C E A).

Now, *calculate the distance between other elements and EABC as follows:*

**Distance ((E A),(B C)) =** Minimum_Distance[Distance(E, B), Distance(E, C), Distance(A B), Distance(A C)]
= Minimum_Distance[2, 2, 5, 2]
**= 2**

*The new Distance Matrix after the Third Cluster (EABC) formation and Dendrogram formed at this step looks as follows:*

# Step 4 -

Finally, **combine D with (EABC)** and the ** Final Dendrogram** formed as follows: