Tuning-Free Structured Sparse PCA via Deep Unfolding Networks
This work addresses a computational bottleneck in unsupervised feature selection for researchers and practitioners, though it is incremental as it builds on existing ADMM optimization.
The paper tackles the challenge of tuning regularization parameters in sparse PCA by proposing a deep unfolding network that automatically learns these parameters, bypassing empirical tuning and reducing computational costs, with numerical experiments showing advantages over state-of-the-art methods on benchmark datasets.
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.