Accuracy-Preserving and Scalable Column-Based Low-Rank Matrix Approximation

Column-based low-rank matrix approximation is a useful method to analyze and interpret data in machine learning and data mining. However existing methods will face some accuracy and scalability problems when dealing with large-scale data. In this paper we propose a new parallel framework for column-based low-rank matrix approximation based on divide-and-conquer strategy. It consists of three stages: (1) Dividing the original matrix into several small submatrices. (2) Performing column-based low-rank matrix approximation to select columns on each submatrix in parallel. (3) Combining these columns into the final result. We prove that the new parallel framework has (1+epsilon) relative-error upper bound. We also show that it is more scalable than existing work. The results of comparison experiments and application in kernel methods demonstrate the effectiveness and efficiency of our method on both synthetic and real world datasets.