Laplace Input and Output Perturbation for Differentially Private Principal Components Analysis

Algorithm 2

Laplace output perturbation (LOP).

	Input: matrix , number of samples n, attributes d, privacy parameter ε;
	Output: : the rank-k approximation matrix
(1)	Compute covariance matrix ;
(2)	Compute eigenvalues and corresponding eigenvectors ;
(3)	Given a threshold α, select top k eigenvectors of A, low-dimensional data ;
(4)	Noise matrix is a matrix where the whole elements are i.i.d. samples from
(5)	Add noise ;
(6)	The rank-k approximation matrix ;