Subset Selection Algorithms: Randomized vs. Deterministic

Abstract. Subset selection is a method for selecting a subset of columns from a real matrix, so that the subset represents the entire matrix well and is far from being rank deficient. We begin by extending a deterministic subset selection algorithm to matrices that have more columns than rows. Then we investigate a two-stage subset selection algorithm that utilizes a randomized stage to pick a smaller number of candidate columns, which are forwarded for to the deterministic stage for subset selection. We perform extensive numerical experiments to compare the accuracy of this algorithm with the best known deterministic algorithm. We also introduce an iterative algorithm that systematically determines the number of candidate columns picked in the randomized stage, and we provide a recommendation for a specific value. Motivated by our experimental results, we propose a new two stage deterministic algorithm for subset selection. In our numerical experiments, this new algorithm appears to be as accurate as the best deterministic algorithm, but it is faster, and it is also easier to implement than the randomized algorithm.