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Results & Implementation
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This section details the performance of our custom DBSCAN implementation and visualizes the results on various datasets.

Algorithm Logic
===============
Implementation follows the standard density-based clustering approach:

1. For each point, we find all neighbors within ``eps`` radius using Euclidean distance.
2. If a point has at least ``min_samples`` neighbors, it becomes a Core Point and starts a new cluster.
3. Using a queue visit all density-reachable neighbors to expand the cluster.
4. Points that are not reachable from any Core Point are labeled as ``-1`` (Noise).


Visual Results
==============

We tested the algorithm on synthetic datasets that are notoriously difficult for distance-based algorithms like K-Means.

Moons Dataset
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The "Moons" dataset consists of two interleaving half-circles. Standard K-Means would fail here by drawing a straight line through the middle. DBSCAN successfully follows the shape.

.. image:: ./report_moons.png
   :width: 600
   :alt: DBSCAN on Moons Dataset
   :align: center

Circles Dataset
---------------

The "Circles" dataset contains a smaller circle inside a larger one. This is a classic topology problem.

..  Note: Replace 'circles_plot.png' with your actual file name if you have one.
    If you don't have it yet, you can remove this block.

.. image:: ./report_circles.png
   :width: 600
   :alt: Clustering Comparison
   :align: center