Building Up the Optimization Algorithmic Infrastructure for Data-Driven Knowledge Discovery and Recovery

构建数据驱动知识发现和恢复的优化算法基础设施

• 批准号: 1115950
• 负责人: Yin Zhang
• 金额: $ 18.5万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115950&HistoricalAwards=false
• 关键词: Building; Up; Optimization; Algorithmic; Infrastructure

The investigator proposes to study a number of optimization models and algorithms that are broadly useful in data dimension reduction, latent information extractionand hidden knowledge discovery. The focus is on problems involving low-rank matrices of very large sizes, including the fundamental problem of computing principal singular value decompositions for unstructured dense matrices, as well as 3D-image processing techniques with applications to hyperspectral data processing and wireless video networks. The overall goal is to develop reliable algorithms that are much faster (by one order of magnitude or more on large problems) than those in use today. Since many of the proposed algorithms are extensions to the classic augmented Lagrangian alternating direction method (ALADM) originally designed for certain convex programs, a part of the project is devoted to a theoretical investigation on establishing a convergence theory for ALADM in more general settings.Modern technologies, such as 4D CT-scans, satellite remote sensing and DNA microarrays, are creating an explosion of data made available in massive quantities and at fast rates. Mathematical and computational techniques play a crucial role in helping make sense out of such massive data sets in a timely fashion and with minimal human interventions. The PI's work involves studying and designing new algorithms for solving several classes of mathematical models designed to help discover and extract the most useful information buried or hidden in large amounts of data. New algorithms have the potential to run much much faster than today's state-of-the-art methods, thus providing more processing power and speed to numerous data-driven applications such as medical diagnoses, agriculture planning, environment surveillance or genetic research in biosciences.

研究者建议研究一些在数据降维、潜在信息提取和隐藏知识发现方面广泛有用的优化模型和算法。重点是涉及非常大尺寸的低秩矩阵的问题，包括计算非结构化稠密矩阵的主奇异值分解的基本问题，以及应用于高光谱数据处理和无线视频网络的 3D 图像处理技术。 总体目标是开发比当今使用的算法快得多的可靠算法（在大型问题上快一个数量级或更多）。由于许多提出的算法是最初为某些凸程序设计的经典增强拉格朗日交替方向法（ALADM）的扩展，因此该项目的一部分致力于在更一般的设置中建立 ALADM 收敛理论的理论研究。现代4D CT 扫描、卫星遥感和 DNA 微阵列等技术正在快速产生大量数据。数学和计算技术在帮助以最少的人为干预及时理解如此庞大的数据集方面发挥着至关重要的作用。 PI 的工作涉及研究和设计新算法，用于解决几类数学模型，旨在帮助发现和提取隐藏在大量数据中的最有用的信息。新算法的运行速度可能比当今最先进的方法快得多，从而为医疗诊断、农业规划、环境监测或生物科学中的基因研究等众多数据驱动的应用提供更多的处理能力和速度。