Flexible matrix compression algorithm based on fast CUR decomposition

• 1、College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082

Abstract：Matrix data is extensively utilized across various domains, nonetheless, the increasing size of matrix data can lead to extensive storage and bandwidth costs. It is worth noting that most matrix data in nature exhibit a low-rank structure that can be exploited for matrix compression using decomposition techniques.This paper presents a compression algorithm for low-rank matrices based on CUR decomposition offering enhanced interpretability compared to SVD compression. However, existing CUR solutions lack fast and flexible compression that can dynamically adjust the matrix according to size compression requirements while preserving maximal approximation accuracy. %and addresses the CUR row and column selection issue %by formulating a deterministic CUR matrix decomposition problem involving a selection matrix $\textbf{W}$. To achieve rapid compression, this paper proposes an algorithm that effectively accelerates the process of solving the parameter matrix $\textbf{W}$. The approach in this paper reveals that the vectors in $\textbf{W}$ can indicate the importance of a row and a column in forming the row subspace and column subspace. Leveraging this insight, this paper develops a flexible compression algorithm based on the sorted vectors in the selection matrix $\textbf{W}$. This method ensures the required compression ratio while maintaining maximal approximation accuracy. The experiments on synthesized and real data illustrate that the algorithm can deliver fast and precise matrix compression under the desired Compression ratio.

Keywords： Artificial intelligence Matrix compression Matrix decomposition CUR decomposition