DBSCAN
Discover arbitrarily shaped clusters from local density while labeling isolated points as noise.
01 Overview
02 The Problem
Clusters may be irregularly shaped and mixed with noise. DBSCAN defines a cluster through local density instead of requiring a fixed number of spherical groups.
03 Why It Matters
DBSCAN can discover multiple shapes and explicitly label isolated observations as noise, which makes it useful for spatial and anomaly-oriented data.
04 Intuition
Draw a circle of radius epsilon around each point. Dense points form the seeds of clusters; nearby border points join them, while isolated points remain noise.
05 Mathematical Foundation
A point is core when its epsilon neighbourhood contains at least MinPts observations. Density reachability then expands a cluster through connected core points.
06 The Equation
- \(\epsilon\) neighbourhood radius
- \(N_{\epsilon}(p)\) points within that radius
- \(\mathrm{MinPts}\) density threshold
07 How It Learns
- Choose epsilon and MinPts.
- Identify core points.
- Expand clusters through density-connected cores.
- Label unassigned points as noise or border.
08 Algorithm
09 Visual Explanation
A quick visual summary of how this model sees data and makes its prediction.
10 Worked Example
Increasing epsilon joins more points and may merge groups; increasing MinPts demands denser evidence and usually labels more points as noise.