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Fundamentals of Machine Learning: A Pythonic Introduction

DBSCAN Walk-Through Example

Explore the DBSCAN clustering process from scratch by learning how to identify neighborhood points, classify core, border, and noise points, and assign clusters using density-based criteria. This lesson provides hands-on implementation and visualization, enhancing your understanding of how DBSCAN partitions datasets and compares to other clustering techniques like K-means.

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In this lesson, we will execute a step-by-step walk-through of the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. We will use a small dataset and manually apply the key concepts like neighborhood identification, point type classification, and cluster assignment, to see how DBSCAN partitions data based on density, unlike K-means which relies on centroids.

Dry running an example

Let’s run DBSCANS on the following dataset shown in the graph:

The actual dataset
The actual dataset

Distance calculation

First, let’s choose the value of eps and minPts.

eps = 1.2
minPts = 2
The distance calculation of a point
The distance calculation of a point

Simple enough, let’s calculate the distance of all the points from each other. For the sake of ease, we’re going to calculate for (2,1.5)(2, 1.5)

Euclidean Distance From (2, 1.5)

Data Points

Euclidean Distance From (2, 1.5)

1, 2

1.118033989

2, 1

0.5

2, 1.5

0

2.5, 3.5

2.061552813

3, 4

2.692582404

4, 3.5

2.828427125

4, 7.5

6.32455532

5, 6

5.408326913

5, 7

6.264982043

5.5, 2

3.535533906

6, 1.5

4

6, 3

4.272001873

6, 5.5

5.656854249

6.5, 5

5.700877125

7, 2.5

5.099019514

1,8

6.57647322

Enter any data point from the above table as input using the format Px,Py to the following program to get its Euclidean distance from all the data points:

Python 3.10.4
# Importing required packages
from sklearn.metrics.pairwise import euclidean_distances as dis_score
import numpy as np
x = np.array([1, 2, 2, 2.5, 3, 4, 4, 5, 5, 5.5, 6, 6, 6, 6.5, 7, 1])
y = np.array([2, 1, 1.5, 3.5, 4, 3.5, 7.5, 6, 7, 2, 1.5, 3, 5.5, 5, 2.5, 8])
data_points = [[x[i], y[i]] for i in range(len(x))]
Pt = input()
Px, Py = Pt.split(',')
print(f"Dissimilarity scores for point ({Px}, {Py}):\n",dis_score(data_points, [[Px, Py]]))
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Identification of neighborhood points

Once we compute the Euclidean distance between the data point (2,1.5)(2,1.5) and all other data points, we can identify which data points have a distance less than or equal to our threshold value eps. In the table above, we can see that two data points, (1,2)(1,2) ...