$L_1$-norm Regularized Indefinite Kernel Logistic Regression
This work addresses the need for more interpretable and generalizable classification methods in domains where indefinite kernels are beneficial, representing an incremental advancement.
The paper tackled the problem of improving classification with indefinite kernels by proposing an L1-norm regularized indefinite kernel logistic regression model, which achieved superior accuracy and sparsity on benchmark datasets.
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.