Differentially Private Singular Value Decomposition for Training Support Vector Machines

Support vector machine (SVM) is an efficient classification method in machine learning. The traditional classification model of SVMs may pose a great threat to personal privacy, when sensitive information is included in the training datasets. Principal component analysis (PCA) can project instances into a low-dimensional subspace while capturing the variance of the matrix A as much as possible. There are two common algorithms that PCA uses to perform the principal component analysis, eigenvalue decomposition (EVD) and singular value decomposition (SVD). The main advantage of SVD compared with EVD is that it does not need to compute the matrix of covariance. This study presents a new differentially private SVD algorithm (DPSVD) to prevent the privacy leak of SVM classifiers. The DPSVD generates a set of private singular vectors that the projected instances in the singular subspace can be directly used to train SVM while not disclosing privacy of the original instances. After proving that the DPSVD satisfies differential privacy in theory, several experiments were carried out. The experimental results confirm that our method achieved higher accuracy and better stability on different real datasets, compared with other existing private PCA algorithms used to train SVM.