Structural interpretability in SVMs with truncated orthogonal polynomial kernels
2026-04-16 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a way to understand Support Vector Machines (SVMs) that use a special kind of kernel based on orthogonal polynomials. They develop a method called ORCA that breaks down the SVM's decision function into understandable parts without needing to retrain the model or use approximations. This method shows how different features and their interactions contribute to the model's decisions by measuring contributions in the model's coordinate system. They tested this on both a synthetic dataset and real echocardiogram data, finding insights about model complexity that normal accuracy scores miss.
Support Vector MachinesOrthogonal PolynomialsReproducing Kernel Hilbert SpaceOrthogonal Kernel ContributionModel InterpretabilityKernel MethodsPost-training AnalysisDecision FunctionInteraction EffectsPolynomial Kernels
Authors
Víctor Soto-Larrosa, Nuria Torrado, Edmundo J. Huertas
Abstract
We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product orthonormal basis, the fitted decision function can be expanded exactly in intrinsic RKHS coordinates. This leads to Orthogonal Representation Contribution Analysis (ORCA), a diagnostic framework based on normalized Orthogonal Kernel Contribution (OKC) indices. These indices quantify how the squared RKHS norm of the classifier is distributed across interaction orders, total polynomial degrees, marginal coordinate effects, and pairwise contributions. The methodology is fully post-training and requires neither surrogate models nor retraining. We illustrate its diagnostic value on a synthetic double-spiral problem and on a real five-dimensional echocardiogram dataset. The results show that the proposed indices reveal structural aspects of model complexity that are not captured by predictive accuracy alone.