MATLAB Implementation of DBSCAN Algorithm with Density-Based Clustering

This section provides a detailed explanation of the principles and applications of the DBSCAN algorithm. DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a clustering algorithm that identifies clusters based on density disparities within datasets. The core concept revolves around defining two key parameters: epsilon (ε-radius) and MinPts (minimum number of points). The algorithm first identifies core points that contain at least MinPts within their ε-neighborhood, then expands clusters by connecting density-reachable points through border points. A key implementation aspect involves using spatial indexing (like kd-trees) for efficient neighborhood queries in MATLAB, achieved through functions like rangesearch or knnsearch. The algorithm's advantages include automatic discovery of arbitrarily shaped clusters without predefining cluster numbers, making it particularly suitable for large-scale datasets and noisy data. In MATLAB implementation, typical steps involve: 1) Computing pairwise distances using pdist or Euclidean distance calculations 2) Identifying core points through logical indexing 3) Performing region growing using queue-based connectivity checks 4) Handling noise points as outliers not belonging to any cluster. This density-based approach makes DBSCAN widely applicable in data mining and machine learning domains, especially for scenarios requiring robust noise handling and non-spherical cluster detection.