CIF: Medium: Collaborative Research: Advances in the Theory and Practice of Low-Rank Matrix Recovery and Modeling

CIF：中：协作研究：低阶矩阵恢复和建模的理论与实践进展

• 批准号: 0963835
• 负责人: Emmanuel Candes
• 金额: $ 49.03万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-05-01 至 2016-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0963835&HistoricalAwards=false
• 关键词: CIF; Medium; Collaborative; Research; Advances

This project concerns one of the fundamental challenges facingcontemporary science and engineering today, namely, the efficientprocessing and analysis of massive amounts of high-dimensional data,such as images, videos, web pages, and bioinformatics data. In short,data now routinely lie in thousands or even billions of dimensions. Onthe one hand, massive data collection is motivated by 1) scientificdiscovery and 2) the need for better engineering systems. On the otherhand, the difficult task now is to conduct meaningful inference insuch high dimensions, and draw correct conclusions from limitedamounts of sample data and with limited computationalresources. Fortunately, scientific or engineering data often have verylow intrinsic complexity and dimensionality. This project addressesthe opportunities offered by this common situation, establishesconditions under which reliable inference is actually possible, anddevelops computational tools for extracting key information from hugedata sets.This interdisciplinary project is expected to have three outcomes: 1)the development of innovative mathematics needed to study the recoveryof data matrices from partial and corrupted information 2) thedevelopment of effective algorithms for recovering low-rank matricesand performing accurate dimensionality reduction with corrupted dataand 3) the development of novel applications in which these techniquesare expected to considerably advance the state-of-the-art. With thesenew tools, scientists and engineers will be able to efficientlyextract correct information from data, which was previouslyinaccessible or intractable by conventional techniques. This willenable the development of far better computer vision systems for facerecognition, better compression schemes of video sequences, a betterunderstanding of gene expression data, or better search engines forweb documents and images.

该项目涉及当今临时科学和工程面临的基本挑战之一，即对大量高维数据的有效过程和分析，例如图像，视频，网页和生物信息信息数据。简而言之，现在的数据通常在数千甚至数十亿个维度上。一方面，大量数据收集是由1）科学发现和2）需要更好的工程系统的需要。另一方面，现在艰巨的任务是进行有意义的推理，并从限量性示例数据和有限的计算率中得出正确的结论。幸运的是，科学或工程数据通常具有非常高的内在复杂性和维度。 这个共同情况提供的这个项目的寻址机会，建立可靠的推理实际上是可能的，并且开发了用于从Hugedata集合中提取关键信息的计算工具。此跨学科项目预计将具有三个结果：1）需要研究创新数学的开发，以研究逐步恢复数据的创新数学，以恢复型数据，并有效地恢复了有效的信息2）使用损坏的数据和数据进行准确的维度降低3）新型应用程序的开发，这些技术期望这些技术可以大大推动最新的技术。 借助这些工具，科学家和工程师将能够从数据中有效地从数据中提取正确的信息，而数据以前可以通过传统技术来访问或棘手。可以开发更好的计算机视觉系统，以进行面部识别，视频序列的更好的压缩方案，对基因表达数据的更好地理解或更好的搜索引擎forweb文档和图像。