Mahmoud Abas, Full-Stack Software Engineer & AI

Machine Learning & AI - DBSCAN Clustering Algorithm Lab

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Machine Learning and AI - Lab 5

DBSCAN Clustering Algorithm Lab

Density-based clustering that finds arbitrary shapes and flags outliers

Introduction

DBSCAN: Density-Based Spatial Clustering of Applications with Noise
Groups together points that are closely packed
Unlike K-Means: no need to pick the number of clusters upfront
Naturally identifies outliers as noise

Key Concepts: Point Types

Core Point: Has at least minPts points within distance ε (including itself).

Border Point: Not a core point, but lies within ε of a core point.

Noise Point: Neither a core point nor within ε of any core point.

Algorithm Parameters

epsilon (ε): The neighborhood radius. Points within this distance are neighbors.

minPts: The minimum neighbor count required to call a point core.

Algorithm Workflow

Pick unvisited point

Count neighbors

within ε

≥ minPts?

including the point itself

yes

Mark Core, expand cluster

recursively add each core neighbor's neighbors

Classify remainder

Border or Noise

Distance Calculation

DBSCAN uses Euclidean distance between points

Distance(A, B) = √(X₂ - X₁)² + (Y₂ - Y₁)²

The full pairwise distance matrix drives every neighbor lookup

Solved Example

Dataset and Parameters

12 points P1 through P12 with (x, y) coordinates
Parameters: minPts = 4, epsilon = 1.9

Point	Coordinates
P1	(3, 7)
P2	(4, 6)
P3	(5, 5)
P4	(6, 4)
P5	(7, 3)
P6	(6, 2)
P7	(7, 2)
P8	(8, 4)
P9	(3, 3)
P10	(2, 6)
P11	(3, 5)
P12	(2, 4)

Step 1 computes the full pairwise Euclidean distance matrix (12x12)

Solved Example

Identifying Neighbors

For each point, list neighbors within epsilon = 1.9

Point	Neighbors within ε = 1.9
P1	P2, P10
P2	P1, P3, P11
P3	P2, P4
P4	P3, P5
P5	P4, P6, P7, P8
P6	P5, P7
P7	P5, P6
P8	P5
P9	P12
P10	P1, P11
P11	P2, P10, P12
P12	P9, P11

P5's neighbors: P4, P6, P7, P8, four neighbors
P9's neighbors: P12 only, one neighbor

Solved Example

Classifying Points

With minPts = 4, a point needs at least 4 neighbors including itself to be Core

Point	Neighbors (excl. self)	Total incl. self	Core?
P1	2	3	No
P2	3	4	Yes
P3	2	3	No
P4	2	3	No
P5	4	5	Yes
P6	2	3	No
P7	2	3	No
P8	1	2	No
P9	1	2	No
P10	2	3	No
P11	3	4	Yes
P12	2	3	No

Core Points: P2, P5, P11
Most remaining points become Border Points
P9 has no core point nearby, so it is classified as Noise

Final Classification and Clusters

Point	Cluster	Role
P1	Cluster 2	Border
P2	Cluster 2	Core
P3	Cluster 2	Border
P4	Cluster 1	Border
P5	Cluster 1	Core
P6	Cluster 1	Border
P7	Cluster 1	Border
P8	Cluster 1	Border
P9	-	Noise
P10	Cluster 2	Border
P11	Cluster 2	Core
P12	Cluster 2	Border

Cluster 1 forms around Core Point P5, and includes Border Points P4, P6, P7, P8
Cluster 2 forms around Core Points P2, P11, and includes Border Points P1, P3, P10, P12
P9 remains unclustered, a genuine noise/outlier point
DBSCAN produced 2 clusters plus 1 noise point from 12 raw points, with no k specified upfront

Advantages

No need to specify the number of clusters in advance
Finds arbitrarily shaped clusters, not just spherical ones
Robust to outliers, explicitly labels them as noise
Only two parameters to tune: epsilon and minPts

Disadvantages

Very sensitive to the choice of epsilon and minPts
Struggles when clusters have very different densities
Performance degrades in high-dimensional spaces
Cannot handle large density differences between clusters well

Key Takeaways

DBSCAN discovers cluster count automatically from data density
It explicitly separates noise and outliers from real clusters
Core Points drive cluster growth; Border Points only join, never expand
Works well on arbitrarily shaped clusters, a key advantage over K-Means
Careful tuning of epsilon and minPts is essential for good results

Open this lesson

Mahmoud AbasDBSCAN Clustering Algorithm Lab

Point

Coordinates

(3, 7)

(4, 6)

(5, 5)

(6, 4)

(7, 3)

(6, 2)

(7, 2)

(8, 4)

(3, 3)

P10

(2, 6)

P11

(3, 5)

P12

(2, 4)

Point

Neighbors within ε = 1.9

P2, P10

P1, P3, P11

P2, P4

P3, P5

P4, P6, P7, P8

P5, P7

P5, P6

P12

P10

P1, P11

P11

P2, P10, P12

P12

P9, P11

Point

Neighbors (excl. self)

Total incl. self

Core?

Yes

P10

P11

Yes

P12

Point

Cluster

Role

Cluster 2

Border

Cluster 2

Core

Cluster 2

Border

Cluster 1

Border

Cluster 1

Core

Cluster 1

Border

Cluster 1

Border

Cluster 1

Border

Noise

P10

Cluster 2

Border

P11

Cluster 2

Core

P12

Cluster 2

Border

Point	Neighbors (excl. self)	Total incl. self	Core?
P1	2	3	No
P2	3	4	Yes
P3	2	3	No
P4	2	3	No
P5	4	5	Yes
P6	2	3	No
P7	2	3	No
P8	1	2	No
P9	1	2	No
P10	2	3	No
P11	3	4	Yes
P12	2	3	No

Point	Neighbors (excl. self)	Total incl. self	Core?
P1	2	3	No
P2	3	4	Yes
P3	2	3	No
P4	2	3	No
P5	4	5	Yes
P6	2	3	No
P7	2	3	No
P8	1	2	No
P9	1	2	No
P10	2	3	No
P11	3	4	Yes
P12	2	3	No

Point	Neighbors (excl. self)	Total incl. self	Core?
P1	2	3	No
P2	3	4	Yes
P3	2	3	No
P4	2	3	No
P5	4	5	Yes
P6	2	3	No
P7	2	3	No
P8	1	2	No
P9	1	2	No
P10	2	3	No
P11	3	4	Yes
P12	2	3	No

Point	Neighbors (excl. self)	Total incl. self	Core?
P1	2	3	No
P2	3	4	Yes
P3	2	3	No
P4	2	3	No
P5	4	5	Yes
P6	2	3	No
P7	2	3	No
P8	1	2	No
P9	1	2	No
P10	2	3	No
P11	3	4	Yes
P12	2	3	No

Point	Neighbors (excl. self)	Total incl. self	Core?
P1	2	3	No
P2	3	4	Yes
P3	2	3	No
P4	2	3	No
P5	4	5	Yes
P6	2	3	No
P7	2	3	No
P8	1	2	No
P9	1	2	No
P10	2	3	No
P11	3	4	Yes
P12	2	3	No

Point	Neighbors (excl. self)	Total incl. self	Core?
P1	2	3	No
P2	3	4	Yes
P3	2	3	No
P4	2	3	No
P5	4	5	Yes
P6	2	3	No
P7	2	3	No
P8	1	2	No
P9	1	2	No
P10	2	3	No
P11	3	4	Yes
P12	2	3	No