MATLAB Implementation of DBSCAN Density-Based Clustering Algorithm

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering algorithm particularly effective for discovering arbitrarily shaped clusters and efficiently handling noisy data. Unlike distance-based clustering methods like K-means, DBSCAN identifies cluster structures by defining "neighborhood density," enabling it to adapt to complex data distributions.

Core concepts include: - Neighborhood Radius (Eps): Defines a radius threshold to determine whether sample points belong to the same dense region - Minimum Points (MinPts): The minimum number of neighboring points required within Eps radius for a point to be considered a core point - Core Points, Border Points, and Noise Points: Core points satisfy MinPts condition; border points lie within core points' neighborhoods but don't meet MinPts themselves; noise points are isolated points not belonging to any cluster

MATLAB implementation typically follows these steps: 1. Data Preprocessing: Apply standardization or normalization to ensure consistent distance measurement using functions like zscore or normalize 2. Distance Matrix Calculation: Compute pairwise distances using Euclidean distance (pdist2 function) or other metrics to determine neighborhood relationships 3. Cluster Expansion Logic: Implement recursive neighborhood search starting from core points, using queue-based or recursive algorithms to merge density-reachable points 4. Noise Identification: Points not assigned to any cluster are labeled as noise using logical indexing

Key advantages and limitations: - Advantages: No need to predefine number of clusters, strong noise resistance, ability to identify non-spherical clusters - Limitations: Sensitivity to Eps and MinPts parameters, performance degradation in high-dimensional data due to the "curse of dimensionality"

MATLAB toolboxes or custom scripts allow flexible parameter tuning using functions like dbscan (Statistics and Machine Learning Toolbox) or manual implementation with knnsearch for neighborhood queries. The algorithm finds applications in geographic information systems, image segmentation, and anomaly detection. Practical implementation should include visualization (e.g., scatter plots with cluster-colored labels) to validate results and may incorporate quality metrics like silhouette coefficients using evalclusters function for performance evaluation.