  We present and analyze a simple, two-step algorithm to approximate the
optimal solution of the sparse PCA problem. Our approach first solves a L1
penalized version of the NP-hard sparse PCA optimization problem and then uses
a randomized rounding strategy to sparsify the resulting dense solution. Our
main theoretical result guarantees an additive error approximation and provides
a tradeoff between sparsity and accuracy. Our experimental evaluation indicates
that our approach is competitive in practice, even compared to state-of-the-art
toolboxes such as Spasm.
