The following is a decision that must be made before performing K-means clustering:
How many clusters should we look for in the data?

Issues in regular K-means clustering

1) Every observation is assigned to a cluster in both K-means and hierarchical clustering, but this may not be the best option. Both methods force every observation into a cluster, but are also sensitive to outliers and may create distorted clusters as a result.

2) Clustering is not very robust to disturbances in the data. For instance, taking out a subset of n observations may cause undesired changes between the original cluster and resulting cluster.


Disadvantages to Clustering

The following decisions must be made before performing hierarchical clustering:
1. What dissimilarity measure should be used?
2. What type of linkage should be used?
3. Where should we cut the dendrogram in order to obtain clusters?

Decisions Before Performing Hierarchical Clustering

Before applying K-means or hierarchical clustering, several decisions must be made, and there is no single correct answer—any solution that reveals interesting structure in the data can be worthwhile. Key practical issues include choosing how many clusters to look for (K-means), selecting a dissimilarity measure and linkage and deciding where to cut the dendrogram (hierarchical), and recognizing the disadvantages of these methods, such as sensitivity to outliers and lack of robustness to small changes in the data.

University of Michigan - Ann Arbor

Google

- 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

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  

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)

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 

Clustering algorithms, such as K-means and hierarchical clustering, are used to group real-world data. Key applications include:

- **Genetics and evolutionary biology**: Clustering genomes to understand how species have evolved over time.
- **Recommender systems**: Clustering users based on similar interests to recommend relevant items.
- **Social networks**: Clustering demographics and user behaviors to target specific groups with tailored information.

Real-World Applications of Clustering

**Density-Based Spatial Clustering of Applications with Noise (DBSCAN)** is an unsupervised clustering method. It groups data points that are closely packed together based on distance and density.

**Key Characteristics:**
- Does not require pre-specifying the number of clusters.
- Efficiently identifies noise and outliers in the data.

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