Principal Component Analysis in the Stochastic Differential Privacy Model

Abstract

In this paper, we study the differentially private Principal Component Analysis (PCA) problem in stochastic optimization settings. We first propose a new stochastic gradient perturbation PCA mechanism (DP-SPCA) for the calculation of the right singular subspace to achieve $(\epsilon,\delta)$-differential privacy. For achieving a better utility guarantee and performance, we then present a new differential privacy stochastic variance reduction mechanism (DP-VRPCA) with gradient perturbation for PCA. To the best of our knowledge, this is the first work of stochastic gradient perturbation for $(\epsilon,\delta)$-differentially private PCA. We also compare the proposed algorithms with existing state-of-the-art methods, and experiments on real-world datasets and on classification tasks confirm the improved theoretical guarantees of our algorithms.