FRG: Collaborative research: Algorithms for sparse data representations

FRG：协作研究：稀疏数据表示算法

• 批准号: 0354707
• 负责人: Ronald DeVore
• 金额: --
• 依托单位: University South Carolina Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-15 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0354707&HistoricalAwards=false
• 关键词: FRG; Collaborative; research; Algorithms; sparse

The investigators address the mathematical underpinnings of compressing large data sets using sparse representations over rich dictionaries and develop a foundation for classifying these problems in terms of their algorithmic complexity. The investigators also find efficient algorithms for computing high-quality sparse representations of data over sophisticated, commonly used dictionaries that provably perform as claimed with respect to both efficiency and correctness of output and are particularly well-suited for massive data set applications. The research proceeds at multiple levels of abstraction. It considers general factors of a representation class that guarantee or preclude such algorithms, it considers algorithms for specific common representation classes, and it finds algorithms for representation classes adapted to specific common (and diverse) applications, such as solutions of partial differential equations, image processing, and database query optimization.Over the past ten years there has been a dramatic increase in data gathering mechanisms, as well as an ever-increasing demand for finer data analysis in applications that rely on scientific and geometric modeling. Each day, literally millions of large data sets are generated in medical imaging, surveillance, and scientific acquisition. In addition, the internet has become a communication medium with vast capacity, generating massive traffic data sets. The usefulness of these data sets rests on our ability to process them efficiently, whether it be for storage, transmission, visual display, fast on-line graphical query, correlation, or registration against data from other modalities. The current state of the art in data processing is far from providing the efficient and faithful representations required in emerging applications. With few exceptions, previous work has not provided algorithms whose efficiency or output quality, though typically validated experimentally, has been analyzed rigorously and thoroughly. The investigators carry out fundamental mathematical and algorithmic research to significantly increase our capacity to process and manage large data sets. The research makes significant mathematical progress in providing rigorous algorithmic results that are of great need in this field. The research also makes significant improvements through highly efficient algorithms in the sizes of data sets that are analyzable and in the types of data processing tasks that can be carried out. Finally, the investigators create a library of software for massive data processing applications.

研究人员使用稀疏的表示属性的词典来解决压缩大数据集的数学基础，并为根据其算法复杂性而为这些问题分类而奠定了基础。 研究人员还发现，与复杂的，常用的词典相比，数据计算高质量的数据的高质量稀疏表示，这些词典在效率和产出的正确性方面所主张的效果，并且特别适合大规模的数据集应用程序。 该研究以多个抽象级别进行。 它考虑了表示或排除此类算法的代表性类别的一般因素，它考虑了特定常见表示类别的算法，并且找到了适应于特定常见（和多样）应用的表示类别的算法，例如偏差方程的解决方案，图像处理和数据库的良好机制，以及在dragasse Quartization intagiation of Dragiation nation intagiation.ul at dragiation nation intagiation.ul and dragiation。在依赖科学和几何建模的应用程序中，对更精细的数据分析的需求不断增加。 每天，在医学成像，监视和科学获取中都会产生数百万个大型数据集。此外，互联网已成为具有巨大容量的通信媒介，产生了大量的交通数据集。 这些数据集的有用性取决于我们有效地处理它们的能力，无论是用于存储，传输，视觉显示，快速的在线图形查询，相关性还是针对其他模式的数据的注册。 数据处理中的最新技术远非提供新兴应用程序中所需的高效和忠实表示。 除少数例外，以前的工作尚未提供算法的效率或产出质量，尽管通常经过实验性验证，但已被严格而彻底地分析。 研究人员进行了基本的数学和算法研究，以显着提高我们处理和管理大型数据集的能力。 该研究在提供严格的算法结果方面取得了重大数学进步，这些结果在该领域非常需要。 这项研究还通过高效的算法在可分析的数据集以及可以执行的数据处理任务的类型中进行了重大改进。 最后，研究人员创建了一个用于大规模数据处理应用程序的软件库。