Collaborative Research: OAC Core: Robust, Scalable, and Practical Low Rank Approximation

合作研究：OAC 核心：稳健、可扩展且实用的低阶近似

• 批准号: 2106738
• 负责人: Haesun Park
• 金额: $ 27.5万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-15 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2106738&HistoricalAwards=false
• 关键词: Collaborative; Research; OAC; Core; Robust

Nearly all aspects of society are affected by data being produced at a faster rate in recent years. The data from experiments, observations, and simulations are not only in more classical science and engineering domains but also in numerous other areas such as businesses tracking more and more facets of consumer behavior, and social networking capturing vast amounts of information on the relationships between people and their actions and interactions. There is a strong need to distill a set of data into a smaller representation that separates useful information from noise and captures the most important trends, patterns, and underlying relationships.  Such a representation can be used for direct interpretation of hidden patterns or as a means of simplifying other data analytic tasks.  This project addresses these challenges by studying a concept from linear algebra called low rank approximation.  The project develops techniques that faithfully distill the meaningful information within a data set.  The algorithms are also designed to exploit high-performance computers so that analysts can get results more quickly and tackle larger problems.  The overall effort in the project is expected to close the gap between algorithms that can effectively handle very large-scale problems and the data analyst’s ability to convert raw input into meaningful representations and actionable insight.The matrix and tensor low rank approximations being studied in this project serve as foundational tools in numerous science and engineering applications. Imposing constraints on the low rank approximations enables the modeling of many key problems, and designing scalable algorithms enables new applications that reach far beyond classical science and engineering disciplines. In particular, mathematical models with nonnegative data values abound, and imposing nonnegative constraints allows for more accurate and interpretable models. Variants of these constraints can be designed to reflect additional characteristics of real-life data analytics problems. The primary goals of this project are (1) to develop robust techniques for evaluating computed low rank approximations for rank and model determination, (2) to develop scalable parallel algorithms for large and robust low rank approximations on today’s extreme-scale machines, and (3) to provide end users the practical tools required to compute and analyze solutions at scale. Typical data and application scientists use Python or Matlab to iteratively compute, visualize, and evaluate solutions, and they are limited to small data sets with feasible memory and computational requirements. While high-performance algorithms and implementations exist, end users would not leverage these tools if they cannot rely on the robustness and generalizability of the results. This project aims to close this gap, developing an end-to-end system with scalable solutions for all steps of the data analytics workflow.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

近年来，社会的几乎所有方面都受到以更快的速度产生的数据的影响，来自实验、观察和模拟的数据不仅存在于更经典的科学和工程领域，而且还存在于许多其他领域，例如企业跟踪和分析。消费者行为的更多方面，以及社交网络捕获有关人与人之间的关系及其行为和交互的大量信息，因此迫切需要将一组数据提炼成更小的表示形式，以将有用信息与噪音分开并捕获最多的信息。重要的趋势、模式和潜在的关系。可用于直接解释隐藏模式或作为简化其他数据分析任务的方法，该项目通过研究线性代数中称为低秩近似的概念来解决这些挑战。这些算法还旨在利用高性能计算机，以便分析师能够更快地获得结果并解决更大的问题。该项目的总体工作预计将缩小能够有效处理超大规模问题的算法之间的差距。数据分析师的转换能力将原始输入转化为有意义的表示和可操作的见解。本项目中研究的矩阵和张量低秩近似可作为众多科学和工程应用中的基础工具，对低秩近似施加约束可以对许多关键问题进行建模，并设计可扩展的模型。算法可以实现远远超出经典科学和工程学科范围的新应用，特别是具有非负数据值的数学模型比比皆是，并且施加非负约束可以设计出更准确和可解释的模型来反映额外的模型。该项目的主要目标是（1）开发用于评估计算的低秩近似值以进行排序和模型确定的鲁棒技术，（2）为大型且鲁棒的低秩近似值开发可扩展的并行算法。 (3) 为最终用户提供大规模计算和分析解决方案所需的实用工具，典型的数据和应用科学家使用 Python 或 Matlab 迭代计算、可视化和评估解决方案。仅限于具有可行内存和计算要求的小数据集。虽然存在高性能算法和实现，但如果最终用户不能依赖结果的稳健性和普遍性，他们就不会利用这些工具。该项目旨在缩小这一差距。为数据分析工作流程的所有步骤开发一个具有可扩展解决方案的端到端系统。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。