DBSCAN

After exploring K-means, a form of partitional clustering that relies on distance to a central point, we now move to density-based clustering. This approach groups together data points that are closely packed (high density) while marking points that lie alone in low-density regions as outliers. The most popular algorithm in this category is DBSCAN (Density-Based Spatial Clustering of Applications with Noise). A key advantage of DBSCAN is that it does not require prior knowledge of the number of clusters and is robust against noise.

DBSCAN clustering

In density-based clustering, the dataset is partitioned into dense regions separated by areas of low density. Density is quantified using two crucial hyperparameters:

• Epsilon ($\epsilon$): Specifies the maximum distance between two points to be considered neighbors. If the distance between two points is $\le \epsilon$, they are considered to be in each other’s neighborhood.
• MinPoints ($m$): Specifies the minimum number of neighbors a point must have (including itself) within the $\epsilon$ distance to be considered a core point.

Density at a point

The density at any data point $\mathbf{x}$ is defined as the number of data points in the dataset $D$ within a circle of radius $\epsilon$ centered at $\mathbf{x}$.

The image below illustrates the concept of density by showing the points enclosed within a circle of a specified radius centered at point $C$ ...