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This paper introduces Adversarial PCA (AdvPCA), a method that replaces difficult-to-tune sparsity penalties with robust optimization against worst-case perturbations to achieve dimensionality reduction. By deriving a closed-form reduction and data-adaptive parameterization, the approach offers a practical iterative algorithm that performs effectively out of the box on high-dimensional datasets. The technique is validated through experiments on both synthetic data and real-world genomics applications, providing a theoretically grounded alternative to standard PCA variants.
A Robust Optimization Approach to Sparse Principal Component Analysis
arXiv:2606.03553v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2606.03553 [stat.ML]
(or arXiv:2606.03553v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2606.03553 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 238 words
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