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-s...
| Authors | David Vävinggren, Francis Bach, André M. H. Teixeira et al. |
|---|---|
| Primary category | stat.ML |
| Published | 2 June 2026 |
| Last updated at source | 2 June 2026 |
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