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摘要翻译：
有效、准确和可靠地用低阶矩阵逼近矩阵是数值线性代数和信号处理应用中的一个基本任务。本文提出了一种新的矩阵分解方法--子空间轨道随机奇异值分解（SOR-SVD）,它利用随机抽样技术对低秩矩阵进行逼近。给定一个大而密集的数据矩阵，大小为$m\乘以n$，数值秩为$k$，其中$k\ll\text{min}\{m,n}$，该算法需要对数据进行几次传递，并且可以用$o(mnk)$浮点运算进行计算。此外，SOR-SVD算法可以利用先进的计算机体系结构，因此，它可以被优化以获得最大的效率。SOR-SVD算法简单、准确、可证明是正确的，在精度和效率方面优于以前报道的技术。我们的数值实验支持了这些说法。
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英文标题：
《Subspace-Orbit Randomized Decomposition for Low-rank Matrix
Approximation》
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作者：
Maboud F. Kaloorazi, Rodrigo C. de Lamare
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最新提交年份：
2018
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Numerical Analysis 数值分析
分类描述：cs.NA is an alias for math.NA. Roughly includes material in ACM Subject Class G.1.
cs.na是Math.na的别名。大致包括ACM学科类G.1的材料。
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一级分类：Electrical Engineering and Systems Science 电气工程与系统科学
二级分类：Signal Processing 信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed Subspace-Orbit Randomized singular value decomposition (SOR-SVD), which makes use of random sampling techniques to give an approximation to a low-rank matrix. Given a large and dense data matrix of size $m\times n$ with numerical rank $k$, where $k \ll \text{min} \{m,n\}$, the algorithm requires a few passes through data, and can be computed in $O(mnk)$ floating-point operations. Moreover, the SOR-SVD algorithm can utilize advanced computer architectures, and, as a result, it can be optimized for maximum efficiency. The SOR-SVD algorithm is simple, accurate, and provably correct, and outperforms previously reported techniques in terms of accuracy and efficiency. Our numerical experiments support these claims.
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PDF链接：
https://arxiv.org/pdf/1804.00462
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