The DBSCAN algorithm classifies data points into three categories based on two parameters: **neighborhood radius ($$\epsilon$$)** and **minimum points ($$min\_samples$$)**.

- **Core Point:** A point with at least $$min\_samples$$ points within its $$\epsilon$$-neighborhood.
- **Border Point:** A point within $$\epsilon$$ distance of a core point, but with fewer than $$min\_samples$$ neighbors itself.
- **Noise:** A point that is neither a core point nor a border point.

Point Classifications in DBSCAN 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.

University of Michigan - Ann Arbor

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- 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  

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)

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.

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