DBSCAN: Density-Based Spatial Clustering Algorithm for High-Dimensional Data

In machine learning and data mining, DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a widely-used clustering algorithm that enables cluster analysis in high-dimensional datasets without requiring pre-specification of cluster quantities. The algorithm classifies data points into three categories: core points, border points, and noise points. Core points are data instances that have sufficient neighboring points within a specified epsilon radius and minimum points threshold. Border points are data instances adjacent to core points but lack sufficient neighbors themselves. Noise points are data instances that are neither core points nor border points. From an implementation perspective, DBSCAN typically requires two key parameters: epsilon (ε) - the radius for neighborhood search, and min_samples - the minimum number of points required to form a dense region. The algorithm operates through a region query function that identifies density-connected points using spatial indexing structures like kd-trees for efficient high-dimensional processing. Due to its ability to handle high-dimensional datasets and automatically determine cluster quantities while identifying outliers, DBSCAN has become extensively adopted in practical applications including anomaly detection, spatial data analysis, and pattern recognition systems. The algorithm's implementation commonly involves iterative neighborhood expansion and connectivity checks to form density-based clusters while maintaining O(n log n) computational efficiency through optimized spatial queries.