ACT/SGER: Algorithms for Large-Scale Approximate Nonnegative Matrix Factorization in Data Analysis

ACT/SGER：数据分析中大规模近似非负矩阵分解的算法

• 批准号: 0442065
• 负责人: Yin Zhang
• 金额: --
• 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: 2004
• 资助国家: 美国
• 起止时间: 2004-09-15 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0442065&HistoricalAwards=false
• 关键词: ACT; SGER; Algorithms; Large; Scale; ACT; SGER; Algorithms; Large; Scale

In data analysis applications where physical data can only take nonnegative values such as pixels in imagery data, it is desirable to obtain physically meaningful ``nonnegative principal parts'', and then represent data as additive combinations of these parts. This leads to the approximate nonnegative matrix factorization (ANMF) problem, which is a constrained, nonconvex global minimization problem. The existing algorithms for ANMF are relatively expensive and not suitable for large-scale, real-time applications. The investigator proposes to reformulate a normalized ANMF problem into a low-dimensional optimization problem, thus reducing the problem size by a potentially very large factor. With the help of geometric insights from the new formulation, the project will focus on developing robust and efficient new algorithms suitable for very large-scale and real-time applications. The goal is to advance the fundamentals of ANMF and realize its full potential as a powerful data analysis tool.Can a computer identify a person, in a few seconds and with a high degree of confidence, by comparing a snapshot of his to some, perhaps old and low-quality, photos stored in a database? Approximate nonnegative matrix factorization (ANMF) is an emerging technique that may help solve this face detection problem and other real-time data analysis problems. In this project, the investigator will study novel mathematical formulations and develop new computer algorithms for solving the ANMF problems more quickly and more reliably.This award is supported jointly by the NSF and the Intelligence Community. The Approaches to Terrorism program in the Directorate for Mathematics and Physical Sciences supports new concepts in basic research and workforce development with the potential to contribute to national security.

在数据分析应用程序中，物理数据只能在图像数据中使用非负值（例如像素），希望获得物理有意义的``非负主部分''，然后将数据表示为这些部分的加法组合。 这导致了近似的非负矩阵分解（ANMF）问题，这是一个受约束的非凸全局最小化问题。 ANMF的现有算法相对昂贵，不适合大规模的实时应用。 研究人员建议将归一化的ANMF问题重新制定为低维优化问题，从而将问题大小减少到潜在的大因素。 在新配方的几何见解的帮助下，该项目将着重于开发适用于非常大规模和实时应用的稳健有效的新算法。 目的是推进ANMF的基本原理，并实现其作为强大的数据分析工具的全部潜力。计算机可以在几秒钟内将一个人与某些（可能是古老且低质量）的快照相提并论，并具有高度的信心，并存储在数据库中？ 近似非负矩阵分解（ANMF）是一种新兴技术，可以帮助解决此面部检测问题和其他实时数据分析问题。 在这个项目中，研究人员将研究新颖的数学表述，并开发新的计算机算法，以更快，更可靠地解决ANMF问题。该奖项由NSF和情报界共同支持。数学和物理科学局中恐怖主义计划的方法支持基础研究和劳动力发展中的新概念，有可能为国家安全做出贡献。