提出一种动态方法，可逐步消除特定特征空间影响，保留其余结构。
Shorting Dynamics and Structured Kernel Regularization
- 通过非线性算子动态逐步移除指定特征子空间影响
- 在有限样本下实现核岭回归的规范形式与抗干扰不变性
- 适用于需要去除噪声或无关特征的数据分析场景
本文提出一种非线性算子动态，能逐步消除指定特征子空间的影响，同时最大程度保留其他部分的结构。生成的正算子序列单调递增，具备精确残差分解，并收敛至经典短化算子。将该动态引入再生核希尔伯特空间，得到一组收敛于原核中最大且在给定子空间上为零的核函数。在有限样本设置下，对应的格拉姆算子继承结构化残差分解，导出核岭回归的规范形式，并提供一种有原则的方法来强制实现无关特征不变性。该方法为数据中不变核构造与结构化正则化提供了统一的算子分析框架。
原文摘要 · Abstract (English)
This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced sequence of positive operators is monotone, admits an exact residual decomposition, and converges to the classical shorted operator. Transporting this dynamic to reproducing kernel Hilbert spaces yields a corresponding family of kernels that converges to the largest kernel dominated by the original one and annihilating the given subspace. In the finite-sample setting, the associated Gram operators inherit a structured residual decomposition that leads to a canonical form of kernel ridge regression and a principled way to enforce nuisance invariance. This gives a unified operator-analytic approach to invariant kernel construction and structured regularization in data analysis.
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