Goes over three distinct algorithms and discusses them in great detail : 
[arxiv.org/pdf/1109.2378.pdf](https://arxiv.org/pdf/1109.2378.pdf) 

University of Michigan - Ann Arbor

1. Consider all data points to be their own cluster
2. Identify and merge pairs of clusters that are most similar
 3. Continue merging pairs until only one cluster remains

link: [towardsdatascience.com/understanding-the-concept-of-hierarchical-clustering-technique-c6e8243758ec](https://towardsdatascience.com/understanding-the-concept-of-hierarchical-clustering-technique-c6e8243758ec)  

Medium: Agglomerative Hierarchical Clustering Algorithm

This algorithm is the most optimal way to implement agglomerative clustering. It reduces the naive implementation's runtime O($n^3$) to O($n^2$). It is detailed below : 

1. Initalize all data points as Clusters
2. Initialize a stack K
3. While there are more than 1 clusters :
   a. If K is empty, add an arbitrary cluster to K
   b. Let A be K.top(). Find the cluster closest to A, say B.
   c. If B is already in K, it must have been added just before A (since it is closest to A). Thus, pop off A and B and merge them. 
   d. If B is not already in K, add it to K.


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