# A Robust Optimization Approach to Sparse Principal Component Analysis

arXiv: https://arxiv.org/abs/2606.03553 · HTML: https://mlsanity.com/paper/2606.03553/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 55 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [On the Convergence and Robustness of Adversarial Training](https://mlsanity.com/paper/2112.08304/) (2021)
- [Precise Tradeoffs in Adversarial Training for Linear Regression](https://mlsanity.com/paper/2002.10477/) (2020)
- [The Curious Case of Adversarially Robust Models: More Data Can Help, Double Descend, or Hurt Generalization](https://mlsanity.com/paper/2002.11080/) (2020)
- [On the folded normal distribution](https://mlsanity.com/paper/1402.3559/) (2014)
- [An Overview of Robust Subspace Recovery](https://mlsanity.com/paper/1803.01013/) (2018)
- [Overparameterized Linear Regression under Adversarial Attacks](https://mlsanity.com/paper/2204.06274/) (2022)
- [Regularization properties of adversarially-trained linear regression](https://mlsanity.com/paper/2310.10807/) (2023)
- [Efficient Optimization Algorithms for Linear Adversarial Training](https://mlsanity.com/paper/2410.12677/) (2024)
- [Kernel Learning with Adversarial Features: Numerical Efficiency and Adaptive Regularization](https://mlsanity.com/paper/2510.20883/) (2025)

## Abstract (arXiv)

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 ℓ1-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.