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arXiv · 2610.36691

Differentially Private Preconditioned Power Iteration Method for Principal Component Analysis that Adapts to the Coherence

Duy V. Le·Ta Duy Nguyen·Alina Ene·Huy L. Nguyen
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Abstract

In Principal Component Analysis (PCA), we are given as input a matrix $A\in\mathbb{R}^{n\times d}$ and an integer $k\leq d$, and the goal is to find the top $k$ right-singular vectors of $A$. We consider the setting where each row of $A$ is the private data of an individual, and we design an $(ε,δ)$-differentially private algorithm whose utility guarantee improves with the coherence of the input matrix. Prior works were either restricted to the case $k=1$ or ensured significantly weaker privacy protections. Our algorithm is based on a preconditioned variant of the power iteration method that is designed to significantly reduce the noise needed to ensure privacy.

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Duy V. Le, Ta Duy Nguyen, Alina Ene, Huy L. Nguyen. 2026-10-27. Differentially Private Preconditioned Power Iteration Method for Principal Component Analysis that Adapts to the Coherence. https://arxiv.org/abs/2610.36691

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