  We propose a new input perturbation mechanism for publishing a covariance
matrix to achieve $(\epsilon,0)$-differential privacy. Our mechanism uses a
Wishart distribution to generate matrix noise. In particular, We apply this
mechanism to principal component analysis. Our mechanism is able to keep the
positive semi-definiteness of the published covariance matrix. Thus, our
approach gives rise to a general publishing framework for input perturbation of
a symmetric positive semidefinite matrix. Moreover, compared with the classic
Laplace mechanism, our method has better utility guarantee. To the best of our
knowledge, Wishart mechanism is the best input perturbation approach for
$(\epsilon,0)$-differentially private PCA. We also compare our work with
previous exponential mechanism algorithms in the literature and provide near
optimal bound while having more flexibility and less computational
intractability.
