Revisiting Co-Occurring Directions: Sharper Analysis and Efficient Algorithm for Sparse Matrices

We study the streaming model for approximate matrix multiplication (AMM). are interested in scenario that algorithm can only take one pass over data with limited memory. The state-of-the-art deterministic sketching AMM is co-occurring directions (COD), which has much smaller approximation errors than randomized algorithms and outperforms other methods empirically. In this paper, we provide a tighter error bound COD whose leading term considers potential low-rank structure correlation of input matrices. prove space optimal respect to our improved bound. also propose variant sparse matrices theoretical guarantees. experiments on real-world datasets show proposed more efficient baseline methods.