msPCA: An R Package for Sparse PCA with Multiple Components

We present msPCA: an open-source R package for sparse principal component analysis with multiple components. It implements an alternating maximization algorithm to generate a set of sparse loading vectors that collectively explain a large fraction of the variance in a dataset, while remaining non-redundant. The algorithm supports two definitions of non-redundancy: either orthogonality of the loading vectors or zero pairwise correlation between principal components (PCs). In the reported benchmarks, msPCA solves sparse PCA problems with thousands of features, achieving competitive runtimes while producing sparse components with controlled feasibility violations and a high fraction of variance explained.

A Robust Optimization Approach to Sparse Principal Component Analysis

While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data. Existing methods address this by promoting sparsity through explicit $\ell_1$-penalties, but these are not obvious to tune due to the unsupervised nature of the task. In contrast, we propose Adversarial PCA (AdvPCA), which leverages robust optimization to achieve sparsity by optimizing the reconstruction objective against bounded, worst-case latent space perturbations. We show that this formulation admits a closed-form reduction, leading to a practical iterative algorithm that alternates between adversarial linear regression-style updates for the sparse encoder and orthogonal updates for the decoder. By theoretically characterizing the solution, we derive a data-adaptive parameterization that allows the algorithm to perform effectively out of the box. We validate these claims through numerical experiments on synthetic and real-world genomics data.