D S ] 22 N ov 2 01 6 A Randomized Rounding Algorithm for Sparse PCA

We present and analyze a simple, two-step algorithm to appro ximate the optimal solution of the sparse PCA problem. Our approach first solves an l1-penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized rounding strate gy to sparsify the resulting dense solution. Our main theoretical result guarantees an additive error ap p oximation and provides a tradeoff between sparsity and accuracy. Our experimental evaluation indica tes that our approach is competitive in practice, even compared to state-of-the-art toolboxes such as Sp sm.