分布高/瘦数据的奇异值分解方法综述
A Survey of Singular Value Decomposition Methods for Distributed Tall/Skinny Data
摘要：
奇异值分解（SVD）是最重要的矩阵分解之一，在众多应用领域中有着广泛的应用。在统计学和数据分析中，奇异值分解的常见应用如主成分分析（PCA）和线性回归。通常这些应用程序出现在行比列多得多的数据上，即所谓的“高/瘦”矩阵。在大数据分析背景下，这可能采取数亿到数十亿行的形式，只有几百列。因此，需要能够充分利用现代计算资源的快速、准确和可扩展的高/瘦SVD实现。为此，我们提出了一个调查的三种不同的算法来计算SVD的这些种高/瘦的数据布局使用MPI通信。我们将这些与常见的大数据分析技术（主要是PCA）结合起来。最后，我们提出了CPU和GPU的首脑会议超级计算机的时间结果，并讨论可能的替代方法。
英文摘要：
The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as Principal Components Analysis (PCA) and linear regression. Usually these applications arise on data that has far more rows than columns, so-called "tall/skinny" matrices. In the big data analytics context, this may take the form of hundreds of millions to billions of rows with only a few hundred columns. There is a need, therefore, for fast, accurate, and scalable tall/skinny SVD implementations which can fully utilize modern computing resources. To that end, we present a survey of three different algorithms for computing the SVD for these kinds of tall/skinny data layouts using MPI for communication. We contextualize these with common big data analytics techniques, principally PCA. Finally, we present both CPU and GPU timing results from the Summit supercomputer, and discuss possible alternative approaches.
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。
