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.

翻译：我们研究了基于截断正交多项式核的支持向量机（SVM）在训练后的可解释性。由于关联的再生核希尔伯特空间是有限维的，并拥有显式的张量积标准正交基，因此拟合的决策函数可以在固有RKHS坐标中精确展开。由此引出基于标准化的正交核贡献（OKC）指数的诊断框架——正交表示贡献分析（ORCA）。这些指数量化了分类器的RKHS范数平方在交互阶数、总多项式次数、边际坐标效应以及成对贡献上的分布。该方法完全属于训练后分析，既不需要代理模型，也无需重新训练。我们通过一个合成双螺旋问题和一个真实五维心回波数据集展示了其诊断价值。结果表明，所提出的指数能够揭示预测准确性本身无法捕捉的模型复杂性结构特征。