提出稀疏不定核逻辑回归模型，提升分类精度与可解释性。
$L_1$-norm Regularized Indefinite Kernel Logistic Regression
- 用L1正则化实现不定核逻辑回归的特征选择
- 在多个数据集上同时提高准确率与模型稀疏度
- 适合需要高可解释性的分类任务
核逻辑回归（KLR）是一种广泛应用于各领域的强大分类方法。在许多实际场景中，不定核比正定核能捕捉更多领域特定的结构信息。本文提出一种新型的L1范数正则化不定核逻辑回归（RIKLR）模型，通过引入L1范数惩罚扩展了现有IKLR框架，实现特征稀疏性。该正则化提升了模型可解释性与泛化能力，但也带来了优化问题的非光滑性和非凸性。为此，我们设计了一种理论严谨且计算高效的近端线性化算法。在多个基准数据集上的实验结果表明，所提方法在准确率和稀疏性方面均表现更优。
原文摘要 · Abstract (English)
Kernel logistic regression (KLR) is a powerful classification method widely applied across diverse domains. In many real-world scenarios, indefinite kernels capture more domain-specific structural information than positive definite kernels. This paper proposes a novel $L_1$-norm regularized indefinite kernel logistic regression (RIKLR) model, which extends the existing IKLR framework by introducing sparsity via an $L_1$-norm penalty. The introduction of this regularization enhances interpretability and generalization while introducing nonsmoothness and nonconvexity into the optimization landscape. To address these challenges, a theoretically grounded and computationally efficient proximal linearized algorithm is developed. Experimental results on multiple benchmark datasets demonstrate the superior performance of the proposed method in terms of both accuracy and sparsity.
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