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通过随机化使非常大规模的线性代数计算成为可能

Making Very Large-Scale Linear Algebraic Computations Possible Via Randomization
课程网址: http://videolectures.net/nips09_martinsson_mvll/  
主讲教师: Gunnar Martinsson
开课单位: 科罗拉多大学
开课时间: 2010-01-19
课程语种: 英语
中文简介:
随着在医学成像,分析大型网络(例如万维网),图像和视频处理以及一系列其他应用中产生越来越大的数据集,对用于分析数据的软件的需求迅速增加。为了处理这种大量数据,所使用的任何软件都必须能够充分利用以多处理器和宽容但速度慢的存储器为特征的现代硬件。计算机体系结构的发展目前正迫使算法设计的转变远离为具有随机存取存储器(RAM)中可用的所有数据的单处理器计算机设计的经典算法,以及积极地最小化通信成本的算法。本教程将描述一组最近开发的标准线性代数计算技术(如计算矩阵的部分奇异值分解),这些技术非常适合在多核或其他并行体系结构上实现,并用于处理存储在磁盘上的数据,或流式传输。这些技术基于使用随机抽样来降低数据的有效维数。值得注意的是,随机抽样不仅放松了通信限制,而且在保持甚至提高现有确定性技术的准确性和稳健性的同时也是如此。
课程简介: The demands on software for analyzing data are rapidly increasing as ever larger data sets are generated in medical imaging, in analyzing large networks such as the World Wide Web, in image and video processing, and in a range of other applications. To handle this avalanche of data, any software used must be able to fully exploit modern hardware characterized by multiple processors and capacious but slow memory. The evolution of computer architecture is currently forcing a shift in algorithm design away from the classical algorithms that were designed for single-processor computers with all the data available in Random Access Memory (RAM), towards algorithms that aggressively minimize communication costs. This tutorial will describe a set of recently developed techniques for standard linear algebraic computations (such as computing a partial singular value decomposition of a matrix) that are very well suited for implementation on multi-core or other parallel architectures, and for processing data stored on disk, or streamed. These techniques are based on the use of randomized sampling to reduce the effective dimensionality of the data. Remarkably, randomized sampling does not only loosen communication constraints, but does so while maintaining, or even improving, the accuracy and robustness of existing deterministic techniques.
关 键 词: 医学成像; 网络; 数据
课程来源: 视频讲座网
最后编审: 2020-07-30:yumf
阅读次数: 40