基于PiE正则化与自步学习的稀疏逻辑回归特征选择方法
Sparse Logistic Regression Feature Selection Method Based on PiE Regularization and Self-Paced Learning
摘要: 针对高维小样本、高噪声基因表达数据的特征选择与分类问题，本文提出一种融合分段指数(PiE)正则化与自步学习(SPL)机制的稀疏逻辑回归模型(PiE-SPLR)。PiE正则化能逼近 l 0 范数，具有强稀疏选择能力；SPL机制可逐步筛选低噪声样本，增强模型鲁棒性。通过交替方向优化与近端梯度法高效求解，模型在Colon、Leukemia等四个基因数据集上取得了最优分类性能，同时所选特征数最少。该方法为基因标志物挖掘与高维数据分类提供了有效工具。
Abstract: To address the feature selection and classification challenges in high-dimensional, small-sample, and high-noise gene expression data, this paper proposes a sparse logistic regression model (PIE-SPLR) that integrates Piecewise Exponential (PiE) regularization with Self-Paced Learning (SPL). The PiE regularization approximates the l 0 norm, providing strong sparse selection capability, while the SPL mechanism progressively filters low-noise samples to enhance model robustness. Through efficient alternating direction optimization and proximal gradient methods, the model achieves optimal classification performance on four gene datasets (Colon, Leukemia, etc.), while selecting the fewest features. This method provides an effective tool for biomarker discovery and high-dimensional data classification.
文章引用：马娟玲. 基于PiE正则化与自步学习的稀疏逻辑回归特征选择方法[J]. 应用数学进展, 2026, 15(2): 247-256. https://doi.org/10.12677/aam.2026.152066

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