DBSCAN : points centraux, points de bord et bruit

K-Means assumes clusters are convex and roughly spherical. It fails on crescent, ring, or elongated shapes because it partitions by distance to centroids. DBSCAN (Density-Based Spatial Clustering of Applications with Noise) overcomes this by defining clusters as dense regions separated by low-density areas, discovering clusters of any shape.

DBSCAN is controlled by two parameters: eps (epsilon) defines the radius of a neighbourhood around a point, and min_samples sets the minimum number of points (including the point itself) required within that radius to be considered a dense region. Together they determine which points are cores, borders, or noise.

A point is a core point if at least min_samples points (including itself) lie within distance eps. Core points are the seeds from which clusters grow. Every point within the core's neighbourhood is directly reachable from it — the foundation for expanding the cluster.

A border point has fewer than min_samples neighbours within eps but lies within the eps-neighbourhood of a core point. It belongs to the cluster of its core point but does not expand the cluster further. A point is density-connected to another if there is a chain of directly-reachable steps linking them through core points.

Points that are neither core nor border — isolated points with too few neighbours — are labelled noise (label = -1 in scikit-learn). This makes DBSCAN a natural outlier detector: anomalies that do not belong to any dense cluster are automatically flagged as noise without any extra configuration.

Use sklearn.cluster.DBSCAN. After fitting, db.labels_ contains integer cluster IDs starting at 0, with -1 for noise. db.core_sample_indices_ lists which samples are core points. The number of clusters is determined automatically — no k needed upfront.

DBSCAN excels on datasets like two interlocking moons or concentric rings — shapes where K-Means completely fails. Because DBSCAN expands clusters along density chains, it naturally follows the curved manifold of the data. This is a fundamental algorithmic advantage for geospatial data, biological cell clusters, and anomaly-embedded datasets.

A practical way to choose eps is to plot the k-distance graph: compute the distance of each point to its kth nearest neighbour (where k = min_samples), sort these distances, and look for the knee. The distance at the knee is a good eps candidate. Points above the knee are in sparse regions (noise); below the knee are in dense regions.

Increasing eps merges clusters (eventually everything becomes one cluster). Decreasing eps creates more clusters and more noise. Increasing min_samples requires denser cores, making it harder to form clusters and generating more noise points. Tuning both parameters together is needed — the k-distance plot guides eps while min_samples is typically set to the dimensionality of the data plus one as a starting point.

Use DBSCAN when: clusters have irregular shapes, you do not know k in advance, outlier detection is important, or data has varying density. Use K-Means when: clusters are roughly spherical, the dataset is very large (DBSCAN scales as O(n log n) with a spatial index), or you need a specific number of clusters for business reasons like market segmentation into exactly 5 regions.

DBSCAN is particularly popular for geospatial clustering (finding hotspots in GPS data) because it naturally identifies dense urban areas while marking sparse rural points as noise. Use metric='haversine' and convert coordinates to radians to cluster by great-circle distance on Earth's surface. The result is geographically meaningful clusters without needing to specify their number.

In this lesson you learned: DBSCAN classifies points as core, border, or noise based on the eps radius and min_samples threshold, it discovers clusters of arbitrary shape by chaining density-reachable core points, and noise points (label -1) are automatic outliers — a feature K-Means does not provide. Next up we apply clustering end-to-end in a customer segmentation project.