The image on the right below represents a dendogram. The left is a different visualization of how to interpret the data. Observations toward the bottom of the data are nested inside observations above it. 



Dendograms: vizualizing nested observations

Observations split at the bottom of the dendogram will be much more similar than observations split towards the top. In the dendogram on the left in the image below, observations 9 and 2 appear to be very similar, but when plotted on the right, it is clear that they are not very similar at all. The location of these observations towards the top of the dendogram explain this. 


Common Mistake Interpreting Dendograms

Hierarchical Clustering analysis is presented in the form of a tree based representation of the observations, which is known as a dendrogram. 

A graphical representation of a hierarchical cluster transformed to a dendrogram is pictured below.

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Method of clustering that seeks to build a hierarchy of clusters. 

Starts by treating each observation as separate cluster. Then it will repeated execute the following two steps: 

1. Identify the two clusters closest together
2. Merge the two most similar clusters 


The iterative process continues until all clusters are merged together

Hierarchical Clustering  

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

1. Divisive: Top-down approach
2. Agglomerative: Bottom down approach


Types of hierarchical clustering

Given the explorative nature of Unsupervised Learning, there may be scenarios where one not know how many clusters that may appear in a set of data. Hierarchical clustering, unlike K-means clustering, does not require a pre-determined number of clusters. 

Why Hierarchical Clustering?

Using Hierarchical clustering can lead to a great deal of bias as not all data is hierarchical in nature. Assuming that data lower in a dendogram can also be classified by properties higher on the dendogram can lead to a much worse result than using K-means clustering instead.

Assumption of Hierarchical Structure

Linkage between clusters can be determined in four main ways, three of which are pictured below:
- Simple: Find the pairwise dissimilarity between each pair of observations and select the most similar
- Average Linkage: Find all pairwise dissimilarities and use the mean value
- Complete Linkage: Compute pairwise dissimilarities and use the least similar 
- Centroid Linkage: Not pictured. Dissimilarity between the centroids of two clusters.

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