Laplace Input and Output Perturbation for Differentially Private Principal Components Analysis
Algorithm 1
Laplace input perturbation (LIP).
Input: matrix , number of samples n, attributes d, privacy parameter ε;
Output: : the rank-k approximation matrix
(1)
Compute covariance matrix ;
(2)
Noise matrix is a symmetric matrix where the upper triangle is i.i.d. sample from , and each lower triangle entry is copied from the opposite position;
(3)
Add noise ;
(4)
Compute eigenvalues and corresponding eigenvectors of the noised covariance matrix ;
(5)
Given a threshold α, select top k eigenvectors of , low-dimensional data ;
