Title: ExDBSCAN: Explaining DBSCAN with Counterfactual Reasoning -- Additional Material

Abstract:

Clustering serves as an unsupervised method for organizing data points based on their similarity. Although explainability techniques are well-established for supervised machine learning, they cannot be directly transferred to clustering tasks, creating significant difficulties in interpreting how clusters are formed. This lack of interpretability is especially pronounced in DBSCAN, a widely used density-based algorithm that categorizes points as either inliers (members of dense clusters) or outliers (noise in sparse areas). DBSCAN fails to offer insights into the rationale behind specific point assignments or to determine if those assignments remain stable under minor data perturbations.

To bridge this explainability gap, we propose ExDBSCAN, a post-hoc explanation framework designed with density awareness. This method delivers actionable counterfactual explanations backed by theoretical guarantees of validity. ExDBSCAN constructs multiple counterfactuals via a density-connected weighted graph. It employs a physics-inspired approach that simultaneously encourages diversity by repelling candidate counterfactuals from each other and ensures proximity by drawing them toward the instance being explained. In empirical tests across 30 tabular datasets, ExDBSCAN surpassed all four baseline methods, achieving perfect validity while successfully retrieving counterfactuals that were both diverse and close to the original instances.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC