# Hierarchical Clustering: Dendograms

What are dendograms? How de we interpret them? By looking at the dendograms, how can we decide the number of clusters to be formed?

Dendrograms are tree-like diagrams used to represent the arrangement of the clusters produced by hierarchical clustering. They are particularly useful in visualizing the data and understanding the structure of the clusters.

Interpreting a dendrogram involves understanding its structure. Each leaf of the dendrogram represents one data point. As you move up the tree, leaves that merge together do so because they belong to the same cluster. The height of the merge (represented by the vertical lines) indicates the distance between the two clusters, with lower merges indicating that the clusters are closer together.

To decide the number of clusters by looking at the dendrogram, you can use a simple strategy called the "largest vertical distance without crossing any horizontal line". Essentially, you draw a horizontal line across the dendrogram and count the number of vertical lines it crosses. This will give you the number of clusters. The idea is to choose a cut such that the distance (or difference) between two clusters is maximum, which means they are the most dissimilar and hence should be separate clusters.

However, the decision also depends on the context and the specific problem you are trying to solve. Sometimes, domain knowledge can also help in deciding the number of clusters.

Dendrograms are visual representations of hierarchical clustering results. They illustrate the hierarchical relationships between data points by showing how they group together at different levels of similarity. Dendrograms are commonly used in cluster analysis to assist in understanding the clustering structure and determining the number of clusters.

Interpreting dendrograms involves examining the vertical lines (branches) and horizontal lines (called fusions or f-fusions) that connect the branches. The height of the vertical lines represents the similarity or dissimilarity between the data points or clusters. The longer the line, the greater the dissimilarity.

To determine the number of clusters from a dendrogram, you can follow these steps:

1. Identify the longest vertical lines that do not intersect with any other lines. These lines represent the largest distances or dissimilarities.
2. Draw a horizontal line across the longest vertical lines, and count the number of times it intersects with the vertical lines.
3. The number of intersections corresponds to the number of clusters you can form. The point at which you draw the horizontal line is subjective and depends on your desired level of granularity or the specific problem you are trying to solve. You can choose to draw the line at a height that gives you a suitable number of clusters.

Another approach is to look for significant increases in the vertical line lengths. If there is a substantial increase in line length compared to the previous level, it may suggest that the clusters are forming at that point, indicating a possible number of clusters.

Keep in mind that dendrograms provide a visual representation, and deciding the number of clusters can still involve some level of subjectivity and domain knowledge. It's important to consider the specific context and objectives of your analysis when interpreting dendrograms and determining the appropriate number of clusters.