论文标题
在应用Kaczmarz方法中的矩阵分解中
On Application of Block Kaczmarz Methods in Matrix Factorization
论文作者
论文摘要
矩阵分解技术计算高维数据矩阵的低级产品近似值，因此通常用于推荐系统和协作过滤应用中。但是，此任务的许多算法都使用了一个精确的最小二乘求解器，该算法的计算是耗时且廉价的。在本文中，我们讨论并测试了一个块kaczmarz求解器，该溶剂替代了矩阵分解的常见交替方案中最小二乘子例程。该变体的分数误差的增加较小，以显着更快的算法性能。在此过程中，我们发现只有一小部分运行时和工作内存要求的块尺寸可产生与最小二乘求解器相当的解决方案。
Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this task utilize an exact least-squares solver whose computation is time consuming and memory-expensive. In this paper we discuss and test a block Kaczmarz solver that replaces the least-squares subroutine in the common alternating scheme for matrix factorization. This variant trades a small increase in factorization error for significantly faster algorithmic performance. In doing so we find block sizes that produce a solution comparable to that of the least-squares solver for only a fraction of the runtime and working memory requirement.
