Tuning-Free Structured Sparse PCA via Deep Unfolding Networks

TL;DR

This paper introduces a deep unfolding network for structured sparse PCA that automatically learns regularization parameters, reducing computational costs and tuning sensitivity, and demonstrating superior performance on benchmark datasets.

Contribution

It proposes a novel deep unfolding network for structured sparse PCA that eliminates the need for manual parameter tuning by translating optimization steps into trainable neural modules.

Findings

Outperforms existing state-of-the-art methods on benchmark datasets.

Automatically learns regularization parameters, reducing tuning effort.

Demonstrates computational efficiency and robustness in feature selection.

Abstract

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.