论文标题
随机奇异值分解的一致性定理
A Consistency Theorem for Randomized Singular Value Decomposition
论文作者
论文摘要
单数值分解（SVD）和主要组件分析是基本工具，也可能是降低数据维度的最流行方法。数据矩阵大小的快速增长导致需要开发有效的大型SVD算法。提出了随机的SVD，并证明了其潜力用于计算低级SVD（Rokhlin等，2009）。在本文中，我们为随机的SVD算法提供了一个一致性定理，以及一个数字示例，以说明向低维的随机投影如何影响一致性。
The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for developing efficient large-scale SVD algorithms. Randomized SVD was proposed, and its potential was demonstrated for computing a low-rank SVD (Rokhlin et al., 2009). In this article, we provide a consistency theorem for the randomized SVD algorithm and a numerical example to show how the random projections to low dimension affect the consistency.
