Approximate Multiplication of Sparse Matrices with Limited Space

arXiv:2009.03527v2 Announce Type: replace
Abstract: Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has introduced co-occuring directions (COD) to reduce the approximation error for this problem. Although it enjoys the space complexity of $O((m_x+m_y)\ell)$ for two input matrices $X\in\mathbb{R}^{m_x\times n}$ and $Y\in\mathbb{R}^{m_y\times n}$ where $\ell$ is the sketch size, its time complexity is $O\left(n(m_x+m_y+\ell)\ell\right)$, which is still very …

abstract algorithm applications approximation arxiv attention cs.lg emergence error ever matrix matrix multiplication popular problem reduce replace scale space stat.ml type work