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

Area of Science:

• Data Science
• Machine Learning
• Computational Statistics

Background:

• Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a popular unsupervised learning algorithm.
• Accurate selection of the neighborhood parameter epsilon is crucial for DBSCAN performance.
• Traditional epsilon estimation methods struggle with high-dimensional and varying-density data.

Purpose of the Study:

• To develop a robust method for selecting the DBSCAN neighborhood parameter epsilon.
• To address limitations of traditional epsilon estimation in complex data scenarios.
• To provide a principled framework for hyperparameter tuning in DBSCAN.

Main Methods:

• A three-level perspective (algorithmic, modeling, causal) for DBSCAN hyperparameter selection.
• Approximation of the ordered k-distance signal using a surrogate dynamical system inspired by mass-spring-damper models.
• Modeling epsilon variation with ordinary differential equations and system identification via L-BFGS-B optimization.
• Analysis of causal effects using Pearl's do-calculus and computation of Average Causal Effect (ACE).

Main Results:

• The proposed method effectively models epsilon variation and identifies structurally informative transition regions.
• Evaluations on synthetic and real-world datasets (Covtype) demonstrate improved epsilon selection.
• Achieved ACE values of +0.9352, +0.5148, and +0.9246 indicate significant performance gains over geometric baselines.
• Computational complexity is near O(N log N) under optimal conditions.

Conclusions:

• The surrogate dynamical estimation framework offers a principled and effective approach to DBSCAN epsilon selection.
• This method enhances clustering reliability in challenging high-dimensional and multi-density datasets.
• The causal inference perspective provides a deeper understanding of the hyperparameter selection mechanism.