The algorithm can either start with **each point in its own cluster** and successively merge them (agglomerative clustering), or start with **all points in one cluster** and recursively split them into smaller clusters (divisive clustering).

Since **agglomerative clustering** is the more commonly used approach, we'll focus on it.

The most common type of hierarchical clustering is the **bottom-up** approach. The algorithm is as follows:

1.  **Initialization:** each data point is treated as a single cluster; 

2.  **Calculate proximity matrix:** compute the distance between each pair of clusters; 

3.  **Merge clusters:** the two closest clusters are merged into a single cluster; 

4.  **Update proximity matrix:** recalculate the distances between the new cluster and all remaining clusters; 

5.  **Repeat:** steps 3 and 4 are repeated until all data points are merged into a single cluster. 

## Linkage Types 

The proximity between two clusters is defined by the **linkage type**. Common linkage methods used in hierarchical clustering are:
 

*   **Single linkage:** the distance between the closest two points in the two clusters; 

*   **Complete linkage:** the distance between the farthest two points in the two clusters;    

*   **Average linkage:** the average distance between all pairs of points in the two clusters;

*   **Ward's method:** minimizes the increase in the total within-cluster variance when merging two clusters.

The choice of linkage method can impact the **shape** and **structure** of the resulting clusters. Experimentation and domain knowledge are often helpful in selecting the best method for your data.

## Dendrogram

The results of hierarchical clustering are often visualized using a **dendrogram**.

What is the primary characteristic of the bottom-up (agglomerative) hierarchical clustering approach?

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Clusteranalyse

How Hierarchical Clustering Works?

Linkage Types

Dendrogram