MATLAB Implementation of DBSCAN Algorithm with Code Examples

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based spatial clustering algorithm particularly suitable for handling datasets with irregular shapes and noise. Unlike distance-based methods such as K-means, DBSCAN identifies clusters by analyzing density distributions around sample points, relying on two key parameters: neighborhood radius (eps) and minimum number of points (minPts).

Implementing DBSCAN in MATLAB typically involves the following steps: First, calculate the number of neighboring points within the eps radius for each data point, marking points that meet the minPts condition as core points. This can be efficiently implemented using MATLAB's pdist2 function for distance calculations and logical indexing to identify neighbors. Then, expand density-connected regions through core points by progressively merging directly density-reachable points to form clusters. This expansion process can be implemented using queue-based or recursive algorithms to traverse connected components. Points not included in any cluster are classified as noise.

The algorithm's advantages include not requiring preset cluster numbers and the ability to identify arbitrarily shaped clusters and outliers. However, it remains sensitive to parameters eps and minPts. MATLAB's matrix operations efficiently handle neighborhood queries, and performance can be further optimized using spatial indexing structures like k-d trees through functions such as rangesearch. In practical applications, attention should be paid to data standardization using zscore or similar functions, and parameter tuning through methods like k-distance graphs to determine optimal eps values.