Abhijeet Singh Rajput
Abhijeet Singh Rajput
@abhijeetsingh
Created
May 9, 2025
Last Modified
1 week ago

DB Scan Clustering Numerical

📘 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

📏 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