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，社会几乎所有方面都受到更快的数据的影响。来自实验，观察和模拟的数据不仅在更古典的科学和工程领域中，而且在许多其他领域（例如企业跟踪越来越多的消费者行为方面），以及社交网络捕获有关人们及其行动和互动之间关系的大量信息。非常需要将一组数据提炼成较小的表示，该数据将有用的信息与噪声分开，并捕获最重要的趋势，模式和基本关系。这种表示形式可用于直接解释隐藏模式或简化其他数据分析任务的手段。该项目通过研究一个称为低等级近似的线性代数的概念来解决这些挑战。该项目开发了完全不同的数据集中有意义信息的技术。该算法还旨在探索高性能计算机，以便分析师可以更快地获得结果并解决更大的问题。预计该项目中的总体努力将弥合算法之间的差距，这些算法可以有效地处理非常大规模的问题，以及数据分析师将原始输入转换为有意义的表示和可行的见解的能力。在该项目中，矩阵和张量低级别近似值在众多科学和工程应用中都可以作为基础。对低等级近似的约束可以实现许多关键问题的建模，并且设计可扩展的算法可以使新应用程序能够远远超出古典科学和工程学科。特别是，具有非负数据值的数学模型充斥着，并施加非负约束可以提供更准确和可解释的模型。可以设计这些约束的变体以反映该项目的主要目标的其他特征是（1），以开发可靠的级别和模型确定的计算低等级近似值的强大技术，（2）以在当今的极端尺度机器上为当今的极端尺度机器和（3）提供量表和分析的实用工具，以开发大型且强大的低等级近似值的可扩展平行算法，以便提供实践的范围。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，并且仅限于具有可行的内存和计算要求的小型数据集。尽管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，则不会利用这些工具。该项目旨在缩小这一差距，开发一个针对数据分析工作流程的所有步骤的端到端系统。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子和更广泛的影响审查标准来通过评估来诚实地获得支持。