Constrained Density-Based Spatial Clustering of Applications with Noise (DBSCAN) using hyperparameter optimization

Abstract

This article proposes a hyperparameter optimization method for density-based spatial clustering of applications with noise (DBSCAN) with constraints, termed HC-DBSCAN. While DBSCAN is effective at creating non-convex clusters, it cannot limit the number of clusters. This limitation is difficult to address with simple adjustments or heuristic methods. We approach constrained DBSCAN as an optimization problem and solve it using a customized alternating direction method of multipliers Bayesian optimization (ADMMBO). Our custom ADMMBO enables HC-DBSCAN to reuse clustering results for enhanced computational efficiency, handle integer-valued parameters, and incorporate constraint functions that account for the degree of violations to improve clustering performance. Furthermore, we propose an evaluation metric, penalized Davies–Bouldin score, with a computational cost of $O\left(N\right)$. This metric aims to mitigate the high computational cost associated with existing metrics and efficiently manage noise instances in DBSCAN. Numerical experiments demonstrate that HC-DBSCAN, equipped with the proposed metric, generates high-quality non-convex clusters and outperforms benchmark methods on both simulated and real datasets.