densitybased

Density-based refers to a class of clustering and anomaly detection methods that define clusters as contiguous regions with a higher data point density than the surrounding space. In these methods, a point's cluster membership depends on the density of its neighborhood rather than distance alone, allowing clusters of arbitrary shape and robustness to noise.

Core concepts include core points, border points, and noise points. A core point has at least minPts neighbors within a radius eps; dense regions are connected via density-reachability and density-connectivity. Algorithms such as DBSCAN (Density-Based Spatial Clustering of Applications with Noise) use these ideas to grow clusters from core points by iteratively adding density-reachable points. OPTICS provides a reachability plot to reveal cluster structure at multiple density levels, and HDBSCAN extends DBSCAN to handle clusters of varying density by constructing a hierarchical clustering and extracting stable clusters. DENCLUE uses kernel density estimation to identify high-density regions; other methods adapt density notions to different data types.

Key advantages include the ability to discover clusters with irregular shapes, to identify outliers as noise, and not requiring a fixed number of clusters. Limitations include sensitivity to parameter choices (eps and minPts in DBSCAN), difficulty with varying density within the same data, reduced effectiveness in high-dimensional spaces due to distance concentration, and scalability challenges for very large datasets without indexing structures.

Applications span geographic information systems, astronomy, biology, image and video analysis, and sensor networks. The density-based paradigm emphasizes local density structure, making it a popular tool when cluster boundaries are not well described by simple geometric shapes.