AdaBox: Adaptive Density-Based Box Clustering with Parameter Generalization

Ahmed Elmahdi

cs.LGMar 6, 2026

AdaBox: Adaptive Density-Based Box Clustering with Parameter Generalization

Authors: Ahmed Elmahdi

Organizations: Independent Researcher

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.

Figures & tables

Method	Arbitrary Shapes	Noise Handling	Variable Density	Params	Generalization
DBSCAN	Yes	Yes	Partial	2	No
HDBSCAN	Yes	Yes	Yes	2–3	No
OPTICS	Yes	Yes	Yes	2–3	No
DENCLUE	Yes	Partial	Yes	2+	No
DPC	Yes	Partial	Partial	2	No
AdaBox	Yes	Yes	Yes	6	Yes

Table 1: Comparison of AdaBox with related methods.

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.

Parameter	Description	Stage
n_boxes	Grid resolution (cells per dimension)	Grid Construction
min_density	Minimum cell density for clustering	Seed & Growth
regular_threshold_factor	Growth threshold multiplier	Iterative Growth
merge_adjacent	Enable statistical merging	Cluster Merging
refinement_sigma	Gaussian smoothing bandwidth	Boundary Refinement
min_cluster_size	Minimum cluster size filter	Post-processing

Table 2: AdaBox hyperparameters with descriptions.

Metric	AdaBox	DBSCAN	HDBSCAN	$\boldsymbol{p}$ -value
ARI	0.724	0.640	0.676	$1.31\times 10^{-7}$
NMI	0.726	0.674	0.695	$1.40\times 10^{-5}$
AMI	0.724	0.670	0.692	$1.09\times 10^{-5}$
V-Measure	0.726	0.674	0.695	$1.40\times 10^{-5}$
Fowlkes-Mallows	0.752	0.678	0.713	$2.87\times 10^{-6}$

Table 3: Average performance across 62 datasets. Best results in bold.

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.

Algorithm	Sample ARI	Full ARI	$\boldsymbol{\Delta}$ ARI	% Change
AdaBox	0.724	0.778	+0.053	+7.3%
DBSCAN	0.575	0.176	$-0.399$	$-69.4\%$
HDBSCAN	0.697	0.204	$-0.493$	$-70.7\%$

Table 4: Protocol A results—parameter transfer from 500-point samples to 15K–50K datasets.

Figure 6: Protocol A Parameter Generalization Results. Four-panel visualization showing: (a) Full dataset ARI across 10 datasets, (b) $\Delta$ ARI per dataset, (c) Aggregate performance comparison, (d) Average generalization gap with error bars.

Algorithm	Datasets Tested	Mean $\Delta$ ARI	Mean ARI at 100K	Transfer Success
AdaBox	10/10	$-0.001$	0.733	10/10 (100%)
DBSCAN	2/10	$-0.257$	0.193	1/10 (10%)
HDBSCAN	4/10	$-0.156$	0.522	2/10 (20%)

Table 5: Protocol B Stage 2 results—parameter transfer to 100K points.

Figure 7: Protocol B Staged Transfer Results. Four-panel visualization showing: (a) $\Delta$ ARI distribution at 100K, (b) Stage 1 pass rates, (c) Head-to-head wins at 100K, (d) Per-dataset $\Delta$ ARI comparison.

Component Removed	Mean ARI	$\boldsymbol{\Delta}$ ARI	% Change	$\boldsymbol{p}$ -value
Full AdaBox	0.880	—	—	—
No Adaptive Merging	0.695	$-0.186$	$-21.1\%$	$<0.0005$
No Boundary Refinement	0.800	$-0.080$	$-9.1\%$	$<0.0001$
Fixed Grid	0.716	$-0.165$	$-18.8\%$	$<0.0001$

Table 6: Ablation study results across 24 datasets.

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Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN), a multiscale density-based clustering algorithm that replaces HDBSCAN*'s fixed minimum cluster size pruning of a mutual-reachability linkage hierarchy with a persistence-based cluster selection procedure. Effectively, PLSCAN identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. In concept, PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher median ARI, is less sensitive to changes in the number of mutual reachability neighbours, and has higher stability under resampling. Additionally, we compare PLSCAN's computational costs to

k

-Means++, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.

Abstract

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