We consider the task of matrix sketching, which is obtaining a significantly smaller representation of matrix A while retaining most of its information (or in other words, approximates A well). In particular, we investigate a recent approach called Frequent Directions (FD) initially proposed by Liberty [5] in 2013, which has drawn wide attention due to its elegancy, nice theoretical guarantees and outstanding performance in practice. Two follow-up papers [3] and [2] in 2014 further refined the theoretical bounds as well as improved the practical performance. In this report, we summarize the three papers and propose a Generalized Frequent Directions (GFD) algorithm for matrix sketching, which captures all the previous FD algorithms as special cases without losing any of the theoretical bounds. Interestingly, our additive error bound seems to apply to the previously non-guaranteed well-performing heuristic iSVD.
Frequent Directions: Simple and Deterministic Matrix Sketching
