On Application of Block Kaczmarz Methods in Matrix Factorization
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Publication:6351832
arXiv2010.10635MaRDI QIDQ6351832
Jamie Haddock, Edwin Chau
Publication date: 20 October 2020
Abstract: 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.
Has companion code repository: https://github.com/chaue/mf-algorithms
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