Geometric Feature Selection for Interpretable SVM Classifiers in Cyber-Physical Systems

Abstract

Identifying mode-transition conditions in Cyber-Physical Systems (CPS) is fundamental to model-based diagnosis, but learning them from scarce, multivariate time-series data requires boundary expressions that remain interpretable in physical variables. A central challenge is that some features are actively detrimental: their inclusion distorts the orientation of the learned boundary, degrading robustness to future crossings without affecting training accuracy. We introduce SVM-GRFE (Geometric Recursive Feature Elimination for SVM), a feature selection method that operates on polynomial monomials rather than raw variables, jointly assessing accuracy and geometric criteria that capture each monomial’s structural role in boundary orientation; the boundary is back-projected analytically to an explicit polynomial inequality in physical variables. We prove SVM-GRFE returns an interpretable, geometrically stable, and robust boundary. On seven synthetic scenarios, SVM-GRFE achieves 33%-85% monomial reduction, matches or outperforms SVM-RFE in five out of seven scenarios and consistently outperforms SVM-RFE under noise at equal complexity, most notably under heteroscedastic noise.