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.

Measuring Similarity between Clusters

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.

Hierarchical Clustering: Dendrograms

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

University of Michigan - Ann Arbor

- K-means clustering
- Hierarchical clustering

Method of clustering in unsupervised statistical learning

K-Means Clustering is a form of unsupervised learning that aims to identify distinct categories in data by segmenting the data by Euclidean Distance into 'k' number of clusters.

K-Means Clustering

Hierarchical Clustering  

Some decisions must be made before performing K-means and hierarchical clustering. With these methods there is no single right answer and any solution that exposes some interesting aspects of the data should be considered.

Practical Issues in Clustering

Below is a video reference for both k-means and hierarchical clustering. It provides an easy introduction to both clustering methods and their algorithms.

[Luis Serrano]. (2019, January 27). Clustering: K-means and Hierarchical [Video File]. Retrieved from [www.youtube.com/watch?v=QXOkPvFM6NU](https://www.youtube.com/watch?v=QXOkPvFM6NU) 

Clustering: K-means and Hierarchical (Reference)

There are various applications for both k-means and hierarchical clustering using real life data. Some of these include:
- Genetics and evolutionary biology:
Genomes holds a lot of information about a species. That information can be clustered to understand how species have evolved over time
- Recommender systems:
Users can be clustered based on the similarity of their interests
- Social networks:
Demographics, behavior, and other factors can be clustered to target certain groups of users with specific types of information (echo chamber)

Applications of Clustering

Spectral Clustering is a clustering algorithm that formulates the building of clusters as a graph partitioning problem and uses the eigenvectors of a similarity matrix to break the data into clusters.

Spectral Clustering

A Gaussian mixture model (GMM) is a unsupervised learning model which states that all generated data points are derived from a mixture of a finite Gaussian distributions that has no known parameters. The parameters for Gaussian mixture models are derived from an iterative expectation-maximization algorithm. 

Gaussian Mixture Model (GMM) Clustering 

- Density based spatial clustering of applications with noise 
- Don’t need to specify # of clusters 
- Relatively efficient 
 -Identifies likely noise points 
- Parameters:
       - Neighbor count parameter: min_samples
       - Neighborhood radius parameter: eps 
- Core point: point that lie in more dense region 
- For a given data point, if there are min_sample other data points that lie within a distance of eps, that given data point is labelled as a core sample 
- All core samples with a distance of eps units apart are put in the same cluster 
- Noise: points that don’t belong in any cluster 
- Boundary point: points within a distance of eps units from core points but not core points themselves

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