Analysis of a privacy-preserving PCA algorithm using random matrix theory
To generate useful summarization of data while maintaining privacy of sensitive information is a challenging task, especially in the big data era. The privacy-preserving principal component algorithm proposed in [1] is a promising approach when a low rank data summarization is desired. However, the analysis in [1] is limited to the case of a single principal component, which makes use of bounds on the vector-valued Bingham distribution in the unit sphere. By exploring the non-commutative structure of data matrices in the full Stiefel manifold, we extend the analysis to an arbitrary number of principal components. Our results are obtained by analyzing the asymptotic behavior of the matrix-variate Bingham distribution using tools from random matrix theory.
