A Fast Frequent Directions Algorithm for Low Rank Approximation
For practitioners needing scalable low-rank approximation, this work offers a faster variant of frequent directions, though it is an incremental improvement.
The paper proposes a fast frequent directions algorithm for low-rank approximation that integrates sparse subspace embedding to reduce computational cost while maintaining accuracy, achieving linear sketch size in the rank. Experiments on synthetic and real datasets demonstrate improved efficiency.
Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast frequent directions algorithm for the low rank approximation problem, which implants a randomized algorithm, sparse subspace embedding (SpEmb) in FD. This new algorithm makes use of FD's natural block structure and sends more information through SpEmb to each block in FD. We prove that our new algorithm produces a good low rank approximation with a sketch of size linear on the rank approximated. Its effectiveness and efficiency are demonstrated by the experimental results on both synthetic and real world datasets, as well as applications in network analysis.