### Hierarchy of Clusters

Hierarchical clustering is another unsupervised machine learning algorithm, which is used to group the unlabeled datasets into a cluster and also known as **hierarchical cluster analysis** or HCA.In this algorithm, we develop the hierarchy of clusters in the form of a tree, and this tree-shaped structure is known as the **dendrogram**.Sometimes the results of K-means clustering and hierarchical clustering may look similar, but they both differ depending on how they work. As there is no requirement to predetermine the number of clusters as we did in the K-Means algorithm.

**The hierarchical clustering technique has two approaches:**

**Agglomerative:**Agglomerative is a**bottom-up**approach, in which the algorithm starts with taking all data points as single clusters and merging them until one cluster is left.**Divisive:**Divisive algorithm is the reverse of the agglomerative algorithm as it is a**top-down approach.**

### Why hierarchical clustering?

As we already have other clustering

algorithms such as **K-Means Clustering**

then why we need hierarchical clustering? So, as we have seen in the K-means clustering that there are some challenges with this algorithm, which are a predetermined number of clusters, and it always tries to create the clusters of the same size. To solve these two challenges, we can opt for the hierarchical clustering algorithm because, in this algorithm, we don’t need to have knowledge about the predefined number of clusters.

In this topic, we will discuss the Agglomerative Hierarchical clustering algorithm.

#### Agglomerative Hierarchical clustering

The agglomerative hierarchical clustering algorithm is a popular example of HCA. To group the datasets into clusters, it follows the **bottom-up approach**. It means, this algorithm considers each dataset as a single cluster at the beginning, and then start combining the closest pair of clusters together. It does this until all the clusters are merged into a single cluster that contains all the datasets.

This hierarchy of clusters is represented in the form of the dendrogram.

#### How the Agglomerative Hierarchical clustering Work?

The working of the AHC algorithm can be explained using the below steps:

**Step-1:**Create each data point as a single cluster. Let’s say there are N data points, so the number of clusters will also be N.

**Step-2:**Take two closest data points or clusters and merge them to form one cluster. So, there will now be N-1 clusters.

**Step-3**: Again, take the two closest clusters and merge them together to form one cluster. There will be N-2 clusters.

**Step-4:**Repeat Step 3 until only one cluster left. So, we will get the following clusters. Consider the below images:

**Step-5:**Once all the clusters are combined into one big cluster, develop the dendrogram to divide the clusters as per the problem.

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