**Agglomerative Clustering Technique:**

In Hierarchical clustering algorithms, either top down or bottom up approach is followed. In Bottom up approach, every object is considered to be a cluster and in subsequent iterations they are merged into single cluster. Therefore it is also called as Hierarchical Agglomerative Clustering.

An HAC clustering is typically visualised as a dendrogram , where each merge is represented by a horizontal line.

**Flowchart:**

**Numerical:**

**Given:**

**Distance matrix:**

**Step 1:** From above given distance matrix, E and A clusters are having minimum distance, so merge them together to form cluster(E,A).

**Distance matrix:**

$\begin{aligned}
\text{dist((E A), C)} &= \text{MIN(dist(E,C), dist(A,C))} \\
&= \text{MIN(2,2)} \\
&= 2 \\
\text{} \\
\text{dist((E A), B)} &= \text{MIN(dist(E,B), dist(A,B))} \\
&= \text{MIN(2,5)} \\
&= 2 \\
\text{} \\
\text{dist((E A), D)} &= \text{MIN(dist(E,D), dist(A,D))} \\
&= \text{MIN(3,3)} \\
&= 3 \\
\end{aligned}$

**Step 2:** Consider the distance matrix obtained in step 1. Since B,C distance is minimum, we combine B and C.

$\begin{aligned}
\text{dist((B C), (E A))} &= \text{MIN(dist(B,E), dist(B,A), dist(C E), dist(C A))} \\
&= \text{MIN(2,5, 2, 2)} \\
&= 2 \\
\text{} \\
\text{dist((B C), D)} &= \text{MIN(dist(B, D), dist(C,D))} \\
&= \text{MIN(3,6)} \\
&= 3 \\
\end{aligned}$

**Step 3:** Consider the distance matrix obtained in step 2. Since (E,A) and (B,C) distance is minimum, we combine them

$\begin{aligned}
\text{dist((E A), (B C))} &= \text{MIN(dist(E,B), dist(E,C), dist(A B), dist(A C))} \\
&= \text{MIN(2, 2, 2, 5, 2)} \\
&= 2 \\
\end{aligned}$

**Step 4:** Finally combine D with (E A B C)