DB Scan Clustering Numerical

PUBLISHED: MAY 2, 2026•2 MIN READ

📘 DBSCAN Clustering (Numerical Solution)🧠 DBSCAN Concepts Recapε (epsilon): Radius of neighborhoodMinPts: Minimum number of points (including the point itself

Abhishek SinghAuthor

giratina-altered

📘 DBSCAN Clustering (Numerical Solution)

🧠 DBSCAN Concepts Recap

ε (epsilon): Radius of neighborhood
MinPts: Minimum number of points (including the point itself) to be considered a core point
Core Point: A point that has at least MinPts points (including itself) within ε distance
Border Point: A point that is within ε of a core point but doesn't have enough neighbors to be a core point itself
Noise Point: A point that is not a core and not reachable from any core point

📌 Given Parameters

ε = 1.9
MinPts = 4

📍 Points (with coordinates)

Point	x	y
P1	7	4
P2	6	4
P3	5	6
P4	4	2
P5	6	3
P6	5	2
P7	3	3
P8	4	5
P9	6	5
P10	3	6
P11	4	4
P12	8	2

DBSCAN numerical example showing labeled data points p1 to p12 plotted on a 2D coordinate grid for clustering analysis

d(A,B)=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

📏 12x12 Euclidean Distance Matrix (rounded to 2 decimals)

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12
P1	0.00	1.00	2.83	3.61	1.41	2.83	4.12	3.16	1.41	4.47	3.00	2.24
P2	1.00	0.00	2.24	2.83	1.00	2.24	3.16	2.24	1.00	3.61	2.00	2.83
P3	2.83	2.24	0.00	4.12	3.16	4.00	3.61	1.41	1.41	2.00	2.24	5.00
P4	3.61	2.83	4.12	0.00	2.24	1.00	1.41	3.00	3.61	4.12	2.00	4.00
P5	1.41	1.00	3.16	2.24	0.00	1.41	3.00	2.83	2.00	4.24	2.24	2.24
P6	2.83	2.24	4.00	1.00	1.41	0.00	2.24	3.16	3.16	4.47	2.24	3.00
P7	4.12	3.16	3.61	1.41	3.00	2.24	0.00	2.24	3.61	3.00	1.41	5.10
P8	3.16	2.24	1.41	3.00	2.83	3.16	2.24	0.00	2.00	1.41	1.00	5.00
P9	1.41	1.00	1.41	3.61	2.00	3.16	3.61	2.00	0.00	3.16	2.24	3.61
P10	4.47	3.61	2.00	4.12	4.24	4.47	3.00	1.41	3.16	0.00	2.24	6.40
P11	3.00	2.00	2.24	2.00	2.24	2.24	1.41	1.00	2.24	2.24	0.00	4.47
P12	2.24	2.83	5.00	4.00	2.24	3.00	5.10	5.00	3.61	6.40	4.47	0.00

🔍 Core, Border, and Noise Classification (ε = 1.9, MinPts = 4)

Core Point: ≥ 4 neighbors within distance ≤ 1.9
Border Point: < 4 neighbors, but neighbor of core
Noise: Neither core nor border

🔍 Point-wise Explanation

🔸 P1 (7, 4)

Neighbors P2, P5, P9
Count: 4
✅ Since 4 ≥ MinPts → P1 is a Core Point

🔸 P2 (6, 4)

Neighbors P1, P5, P9
Count: 4
✅ 4 ≥ MinPts → P2 is a Core Point

🔸 P3 (5, 6)

Neighbors P8, P9
Count: 3
⚠️ 3 < MinPts → P3 is not a core point
But it lies within ε of P8 and P9 which are a core point
🔁 Therefore, P3 is a Border Point

🔸 P4 (4, 2)

Neighbors P6, P7
Count: 3
❌ 3 < MinPts, and not within ε of any core point
❌ So, P4 is a Noise Point

🔸 P5 (6, 3)

Neighbors P1, P2, P6
Count: 4
✅ 4 ≥ MinPts → P5 is a Core Point

🔸 P6 (5, 2)

Neighbors P4, P5
Count: 3
⚠️ 3 < MinPts → P6 is not a core point
But it lies within ε of P5 which is core points
🔁 So, P6 is a Border Point

🔸 P7 (3, 3)

Neighbors P4, P11
Count: 3
❌ 3 < MinPts, and not within ε of any core point
❌ So, P7 is a Noise Point

🔸 P8 (4, 5)

Neighbors P3, P10, P11
Count: 4
✅ 4 ≥ MinPts → P8 is a Core Point

🔸 P9 (6, 5)

Neighbors P1, P2, P3
Count: 4
✅ 4 ≥ MinPts → P9 is a Core Point

🔸 P10 (3, 6)

Neighbors P8
Count: 2
⚠️ 2 < MinPts → Not core
But within ε of P8, a core point
🔁 So, P10 is a Border Point

🔸 P11 (4, 4)

Neighbors P7, P8
Count: 3
⚠️ 2 < MinPts → Not core
But within ε of P8, a core point
🔁 So, P10 is a Border Point

🔸 P12 (8, 2)

Neighbors within ε = 1.9 (NONE)
Count: 1
❌ 1 < MinPts, and not within ε of any core point
❌ So, P12 is a Noise Point

🧠 Final Classification Summary:

Type	Points
Core	P1, P2, P5, P8, P9
Border	P3, P6, P10, P11
Noise	P4, P7, P12

Point	Neighbors (within ε=1.9)	Count	Type
P1	P2, P5, P9	4	✅ Core
P2	P1, P5, P9	4	✅ Core
P3	P8, P9	3	⚠️ Border of (P8, P9)
P4	P6, P7	3	❌ Noise
P5	P1, P2, P6	4	✅ Core
P6	P4, P5	3	⚠️ Border of (P5)
P7	P4, P11	3	❌ Noise
P8	P3, P10, P11	4	✅ Core
P9	P1, P2, P3	4	✅ Core
P10	P8	2	⚠️ Border of (P8)
P11	P7, P8	3	⚠️ Border of (P8)
P12	None	1	❌ Noise