This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel in applications such as Latent Semantic Indexing and Recommender Systems. Nonetheless, the proposed framework is purely algebraic and targets general updating problems. The algorithm presented in this paper undertakes a projection view-point and focuses on building a pair of subspaces which approximate the linear span of the sought singular vectors of the updated matrix. We discuss and analyze two different choices to form the projection subspaces. Results on matrices from real applications suggest that the proposed algorithm can lead to higher accuracy, especially for the singular triplets associated with the largest modulus singular values. Several practical details and key differences with other approaches are also discussed.

翻译：本文件审议了更新按新行和(或)列随时间推移添加新行和(或)列的矩阵排成的单体单值分解(SVD)的问题,这些矩阵问题代表了Lentnt 语义索引和建议系统等应用中一个重要的计算内核,然而,拟议框架纯粹是代数,针对的是一般更新问题。本文件所介绍的算法进行了预测观察点,并侧重于建立一对子空间,接近更新矩阵中所寻求的单向矢量的直线范围。我们讨论和分析了形成预测子空间的两种不同的选择。真实应用的矩阵结果表明,拟议的算法可以提高准确性,尤其是与最大模积单值相关的单三联数。还讨论了与其他方法的一些实际细节和关键差异。