无需调参的结构化稀疏PCA，自动学习正则化参数。
Tuning-Free Structured Sparse PCA via Deep Unfolding Networks
- 用ℓ₁和ℓ₂,₁范数结合捕捉局部与全局结构。
- 通过深度展开网络自动学习正则化参数，避免传统调参。
- 在基准数据集上优于现有方法，适合特征选择任务。
稀疏主成分分析（Sparse PCA）是一种经典的降维技术，常用于无监督特征选择（UFS）。然而，确定正则化参数极具挑战性，传统方法如网格搜索和贝叶斯优化不仅计算成本高，且对参数敏感。为此，我们首先通过整合ℓ₁-范数和ℓ₂,₁-范数，建立一种结构化稀疏PCA公式，分别捕捉局部与全局结构。基于现成的交替方向乘子法（ADMM）优化框架，我们设计了一种可解释的深度展开网络，将迭代优化步骤转化为可训练的神经架构。这一创新使正则化参数能够自动学习，有效规避了传统方法中的经验调参需求。在基准数据集上的数值实验验证了所提方法相对于现有最先进方法的优势。代码将公开于 https://github.com/xianchaoxiu/SPCA-Net。
原文摘要 · Abstract (English)
Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and conventional approaches, including grid search and Bayesian optimization, not only bring great computational costs but also exhibit high sensitivity. To address these limitations, we first establish a structured sparse PCA formulation by integrating $\ell_1$-norm and $\ell_{2,1}$-norm to capture the local and global structures, respectively. Building upon the off-the-shelf alternating direction method of multipliers (ADMM) optimization framework, we then design an interpretable deep unfolding network that translates iterative optimization steps into trainable neural architectures. This innovation enables automatic learning of the regularization parameters, effectively bypassing the empirical tuning requirements of conventional methods. Numerical experiments on benchmark datasets validate the advantages of our proposed method over the existing state-of-the-art methods. Our code will be accessible at https://github.com/xianchaoxiu/SPCA-Net.
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