DBSCAN operates based on the idea of **density reachability**. It defines clusters as dense regions of data points separated by areas of lower density. Two key parameters govern its behavior: 

- **Epsilon (ε):** the radius within which you search for neighboring points; 

- **Minimum number of points (MinPts):** the minimum number of points required within the ε-radius to form a dense region (including the point itself). 

DBSCAN classifies points into three categories: 

- **Core points:** a point is a core point if it has at least MinPts within its ε-radius; 

- **Border points:** a point is a border point if it has fewer than MinPts within its ε-radius but is reachable from a core point (i.e., within the ε-radius of a core point); 
     
- **Noise points:** a point that is neither a core point nor a border point is considered a noise point.

## Algorithm

1.  Start with an arbitrary unvisited point; 

2.  Find all points within its ε-radius; 

3.  If a point has at least MinPts neighbors within an ε-radius, it's marked as a **core point**, initiating a new cluster that recursively expands by adding all **directly density-reachable** points;  

4.  If the number of points within the ε-radius is **less than MinPts**, mark the point as a **border point** (if it's within the ε-radius of a core point) or a **noise point** (if it's not);     

5.  Repeat steps 1-4 until all points are visited. 

Imagine a **scatter plot** of data points. DBSCAN would start by picking a point. If it finds enough neighbors within its ε-radius, it marks it as a **core point** and starts forming a cluster. It then expands this cluster by checking the **neighbors of the core point and their neighbors**, and so on. Points that are close to a core point but don't have enough neighbors themselves are marked as **border points**. Points that are isolated are identified as **noise**. 

In DBSCAN, what condition must be met for a point to be classified as a core point?

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Cluster Analysis

How DBSCAN Works?

Algorithm