Two-Dimensional Multi-Density Grid Clustering Algorithm

The Two-Dimensional Multi-Density Grid Clustering Algorithm is an efficient clustering method designed for two-dimensional data, particularly suitable for scenarios with uneven data distribution or significant density variations. By partitioning the data space into regular grid cells and incorporating a multi-density strategy to dynamically adjust clustering decisions in neighboring regions, this algorithm effectively identifies cluster structures across varying densities.

The core methodology consists of three key steps: Spatial Grid Partitioning: Divide the two-dimensional data space into uniformly sized grid cells, where each cell computes the distribution density of data points to form a density histogram. Noise cells are filtered out by setting density thresholds, retaining only valid data regions. In code implementation, this can be achieved using histogram binning functions (e.g., numpy.histogram2d in Python) followed by threshold-based filtering to eliminate low-density cells. Multi-Density Adaptation: Dynamically adjust neighborhood search ranges based on regional density differences. High-density regions employ smaller neighborhood radii to prevent over-merging, while low-density areas use expanded radii to connect sparse but related points. Algorithmically, this involves implementing adaptive epsilon parameters similar to DBSCAN, where radius selection is density-dependent via k-distance graphs or local density estimators. Cluster Merge Optimization: Merge adjacent grid cells satisfying density connectivity constraints. Final clustering results are generated through hierarchical processing or graph traversal algorithms (e.g., a grid-based version of DBSCAN), maintaining clear cluster boundaries. Code implementation typically uses union-find data structures or connected-component labeling algorithms to efficiently merge dense grid regions.

The algorithm’s strength lies in balancing computational efficiency and clustering accuracy—grid-based preprocessing reduces the computational complexity of traditional density algorithms, while the multi-density strategy enhances adaptability to heterogeneous data. Typical applications include geographic information analysis, image region segmentation, and other scenarios requiring processing of non-uniformly distributed data.