An Accelerated Algorithm for Distributed Sparse PCA Problems with $l_{2,1}\text{-norm}$ Regularization

Sparse Principal Component Analysis (Sparse PCA) is a widely adopted technique for feature extraction in high-dimensional datasets. Based on Alternating Direction Method of Multipliers (ADMM) framework, a Privacy-Aware Distributed Subspace Splitting Algorithm (DSSAL1) is recently proposed in [17] for the sparse PCA with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{l}_{\mathbf{1}}-\mathbf{norm}$</tex> regularization. In particular, the algorithm adapting a subspace-splitting strategy achieves low communication and fast convergence. In view of the group-sparsity of the latent feature of the datum, we generalize Distributed Subspace Splitting Algorithm to handle Sparse PCA model with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{l}_{\mathbf{21}}-\mathbf{norm}$</tex> regularization. Our principal technical innovation lies in integrating the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) [18] as an inertial acceleration method for solving the central node's optimization subproblem. Comprehensive experiments on synthetic datasets and real-world datasets consistently validate the algorithm's computational efficiency.