Causal Interpretation of DBSCAN Algorithm: A Dynamic Modeling for Epsilon Estimation

-distance curve, while the system dynamics are solved with the fourth-order Runge-Kutta method. The resulting estimator identifies transition regions that are structurally informative for ε selection in DBSCAN. To analyze the estimator at the intervention level, Pearl's do-calculus is used to compute the Average Causal Effect (ACE). The method was evaluated on synthetic benchmarks and on the Covtype dataset, including scenarios with multi-density overlap and dimensionality up to R10. The resulting ACE values, +0.9352, +0.5148, and +0.9246, indicate that the proposed estimator improves intervention-based ε selection relative to the geometric baseline across the evaluated datasets. Its practical computational cost is dominated by nearest-neighbor search, behaving approximately as O(NlogN) under favorable indexing conditions and degrading toward O(N2) in high-dimensional or weak-pruning regimes.