Secure principal component analysis in multiple distributed nodes

Privacy preservation becomes an important issue in recent big data analysis, and many secure multiparty computations have been proposed for the purpose of privacy preservation in the environment of distributed nodes. As a secure multiparty computations of principal component analysis (PCA), in this paper, we propose S-PCA, which compute PCA securely among the distributed nodes. PCA is widely used in many applications including time-series analysis, text mining, and image compression. In general, we compute PCA after concentrating all data in a single server, but this approach discloses data privacy of each node. In contrast, the proposed S-PCA computes PCA without disclosing the sensitive data of individual nodes. In S-PCA, the nodes share non-sensitive mean vectors first and compute covariance matrices and PCA securely using the shared mean vectors. In this paper, we formally prove the correctness and secureness of S-PCA and apply it to an application of secure similar document detection. Experimental results show that the performance of S-PCA is slightly worse than that of PCA due to guarantee of secureness, but it significantly improves the performance of secure similar document detection by up to two orders of magnitudes. Copyright (c) 2016 John Wiley & Sons, Ltd.