Abstract

In this paper, we address the column-based low-rank matrix approximation problem using a novel parallel approach. Our approach is based on the divide-and-combine idea. We first perform column selection on submatrices of an original data matrix in parallel, and then combine the selected columns into the final output. Our approach enjoys a theoretical relative-error upper bound. In addition, our column-based low-rank approximation partitions data in a deterministic way and makes no assumptions about matrix coherence. Compared with other traditional methods, our approach is scalable on large-scale matrices. Finally, experiments on both simulated and real world data show that our approach is both efficient and effective.

A Scalable Approach to Column-Based Low-Rank Matrix Approximation / 1600 Yifan Pi, Haoruo Peng, Shuchang Zhou, Zhihua Zhang In this paper, we address the column-based low-rank matrix approximation problem using a novel parallel approach. Our approach is based on the divide-and-combine idea. We first perform column selection on submatrices of an original data matrix in parallel, and then combine the selected columns into the final output. Our approach enjoys a theoretical relative-error upper bound. In addition, our column-based low-rank approximation partitions data in a deterministic way and makes no assumptions about matrix coherence. Compared with other traditional methods, our approach is scalable on large-scale matrices. Finally, experiments on both simulated and real world data show that our approach is both efficient and effective.