投影成本保持草图：证明策略和构造
Projection-Cost-Preserving Sketches: Proof Strategies and Constructions
摘要：
在本文中，我们将说明常见的矩阵近似方法，如随机投影和随机采样，如何产生投影成本保持草图，如[FSS 13，CEM+15]中所介绍的。投影成本保持草图是一种矩阵近似，对于给定的参数$k$，它近似地保持目标矩阵到所有$k$维子空间的距离。这样的草图可以应用于线性代数、数据科学和机器学习的可扩展算法。我们的目标是简化在[CEM+15]和[CMM17]中介绍的证明技术，以便它们可以作为未来工作的指南。我们也请读者参考[CYD19]，它对第2节中的证明给出了类似的简化说明。
英文摘要：
In this note we illustrate how common matrix approximation methods, such as random projection and random sampling, yield projection-cost-preserving sketches, as introduced in [FSS13, CEM+15]. A projection-cost-preserving sketch is a matrix approximation which, for a given parameter $k$, approximately preserves the distance of the target matrix to all $k$-dimensional subspaces. Such sketches have applications to scalable algorithms for linear algebra, data science, and machine learning. Our goal is to simplify the presentation of proof techniques introduced in [CEM+15] and [CMM17] so that they can serve as a guide for future work. We also refer the reader to [CYD19], which gives a similar simplified exposition of the proof covered in Section 2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
