Non-Negative Matrix and Tensor Approximations: Algorithms, Software and Applications

非负矩阵和张量近似：算法、软件和应用

• 批准号: 0728879
• 负责人: Inderjit Dhillon
• 金额: $ 25万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-10-01 至 2012-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0728879&HistoricalAwards=false
• 关键词: Non; Negative; Matrix; Tensor; Approximations

Title: Non-negative Matrix and Tensor Approximations: Algorithms, Software and ApplicationsApplications as diverse as data mining, chemometrics, and bioinformaticslead to the need for analysis of co-occurrence and count data.These data sets are intrinsically composed of non-negative numbers, andoften can be represented as multi-dimensional matrices. Analysis of suchdata is a major contemporary scientific challenge.This research studies approximations of non-negative matrices andtensors that reveal an easily interpretable parts-based representationof the data. Fast, numerical algorithms are developed that incorporatestate-of-the-art techniques from numerical optimization. A softwaretoolbox is made available to the public after being tested onapplications in web data mining, bioinformatics and computer vision.An emphasis of the project is to train graduate and undergraduatestudents in mathematics and computer science, and make the softwareavailable via a public web site.

职务名称：非负矩阵和张量近似：算法、软件和应用数据挖掘、化学计量学和生物信息学等各种应用都需要分析共现和计数数据。这些数据集本质上由非负数组成，通常可以表示为多维矩阵。对这些数据的分析是当代科学的一个主要挑战，本研究研究了非负矩阵和张量的近似，揭示了一种易于解释的基于部分的数据表示。快速，数值算法的开发，从数值优化的最先进的技术。一个软件工具箱在测试了网络数据挖掘、生物信息学和计算机视觉方面的应用后向公众提供，该项目的重点是培训数学和计算机科学方面的研究生和本科生，并通过公共网站提供该软件。