A fast and efficient algorithm for low-rank approximation of a matrix

The low-rank matrix approximation problem involves finding of a rank k version of a m ? n matrix AAA, labeled AAAk, such that AAAk is as "close" as possible to the best SVD approximation version of AAA at the same rank level. Previous approaches approximate matrix AAA by non-uniformly adaptive sampling some columns (or rows) of AAA, hoping that this subset of columns contain enough information about AAA. The sub-matrix is then used for the approximation process. However, these approaches are often computationally intensive due to the complexity in the adaptive sampling. In this paper, we propose a fast and efficient algorithm which at first pre-processes matrix AAA in order to spread out information (energy) of every columns (or rows) of AAA, then randomly selects some of its columns (or rows). Finally, a rank-k approximation is generated from the row space of these selected sets. The preprocessing step is performed by uniformly randomizing signs of entries of AAA and transf...

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Nam H. Nguyen, Thong T. Do, Trac D. Tran
• Keywords: Algorithms, Low-rank Matrix Approximation, Matrix Aaa, Pre-processes Matrix Aaa, STOC 2009