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AdaBox: Adaptive Density-Based Box Clustering with Parameter Generalization

Ahmed Elmahdi

Abstract

Density-based clustering algorithms like DBSCAN and HDBSCAN are foundational tools for discovering arbitrarily shaped clusters, yet their practical utility is undermined by acute hyperparameter sensitivity -- parameters tuned on one dataset frequently fail to transfer to others, requiring expensive re-optimization for each deployment. We introduce AdaBox (Adaptive Density-Based Box Clustering), a grid-based density clustering algorithm designed for robustness across diverse data geometries. AdaBox features a six-parameter design where parameters capture cluster structure rather than pairwise point relationships. Four parameters are inherently scale-invariant, one self-corrects for sampling bias, and one is adjusted via a density scaling stage, enabling reliable parameter transfer across 30-200x scale factors. AdaBox processes data through five stages: adaptive grid construction, liberal seed initialization, iterative growth with graduation, statistical cluster merging, and Gaussian boundary refinement. Comprehensive evaluation across 111 datasets demonstrates three key findings: (1) AdaBox significantly outperforms DBSCAN and HDBSCAN across five evaluation metrics, achieving the best score on 78\% of datasets with p < 0.05; (2) AdaBox uniquely exhibits parameter generalization. Protocol A (direct transfer to 30-100x larger datasets) shows AdaBox maintains performance while baselines collapse. (3) Ablation studies confirm the necessity of all five architectural stages for maintaining robustness.

AdaBox: Adaptive Density-Based Box Clustering with Parameter Generalization

Abstract

Density-based clustering algorithms like DBSCAN and HDBSCAN are foundational tools for discovering arbitrarily shaped clusters, yet their practical utility is undermined by acute hyperparameter sensitivity -- parameters tuned on one dataset frequently fail to transfer to others, requiring expensive re-optimization for each deployment. We introduce AdaBox (Adaptive Density-Based Box Clustering), a grid-based density clustering algorithm designed for robustness across diverse data geometries. AdaBox features a six-parameter design where parameters capture cluster structure rather than pairwise point relationships. Four parameters are inherently scale-invariant, one self-corrects for sampling bias, and one is adjusted via a density scaling stage, enabling reliable parameter transfer across 30-200x scale factors. AdaBox processes data through five stages: adaptive grid construction, liberal seed initialization, iterative growth with graduation, statistical cluster merging, and Gaussian boundary refinement. Comprehensive evaluation across 111 datasets demonstrates three key findings: (1) AdaBox significantly outperforms DBSCAN and HDBSCAN across five evaluation metrics, achieving the best score on 78\% of datasets with p < 0.05; (2) AdaBox uniquely exhibits parameter generalization. Protocol A (direct transfer to 30-100x larger datasets) shows AdaBox maintains performance while baselines collapse. (3) Ablation studies confirm the necessity of all five architectural stages for maintaining robustness.
Paper Structure (23 sections, 7 figures, 6 tables)

This paper contains 23 sections, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Density-Based Clustering
  4. Grid-Based Clustering
  5. Parameter Selection for Clustering
  6. Positioning
  7. Method
  8. Algorithm Overview
  9. Adaptive Grid Construction
  10. Liberal Seed Initialization
  11. Iterative Growth with Graduation
  12. Statistical Cluster Merging
  13. Gaussian Boundary Refinement
  14. Hyperparameters
  15. Complexity Analysis
  16. ...and 8 more sections

Figures (7)

  • Figure 1: AdaBox Algorithm Pipeline. Five-stage processing pipeline showing: Adaptive Grid Construction $\rightarrow$ Liberal Seed Initialization $\rightarrow$ Iterative Growth with Graduation $\rightarrow$ Statistical Cluster Merging $\rightarrow$ Gaussian Boundary Refinement.
  • Figure 2: AdaBox achieves the highest average score on all five metrics.
  • Figure 3: Visual clustering comparison on the TrafficFlow_Urban dataset showing AdaBox (ARI: 0.70) vs. DBSCAN (0.15) vs. HDBSCAN (0.53).
  • Figure 4: Clustering comparison on the Pendigits benchmark. The Pendigits dataset (16D original, reduced to 2D via PCA) presents a challenging 10-class clustering problem with overlapping cluster boundaries. (a) Ground truth labels. (b) AdaBox achieves ARI = 0.431. (c) DBSCAN with optimized ARI. (d) HDBSCAN with ARI = 0.246.
  • Figure 5: AdaBox's advantage grows on challenging datasets. Win rates across Groups 7--9 (15 large-scale real-world datasets) show AdaBox achieving 80--100% on both ARI and SCOPE, while baselines cluster near 10--40%---a wider margin than observed on synthetic benchmarks.
  • ...and 2 more figures