Collaborative Research: Non-negative Matrix Factorizations for Data Mining: Foundations, Capabilities, and Applications

协作研究：数据挖掘的非负矩阵分解：基础、功能和应用

• 批准号: 0915228
• 负责人: Chris Ding
• 金额: $ 20万
• 依托单位: University of Texas at Arlington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0915228&HistoricalAwards=false
• 关键词: Collaborative; Research; Non; negative; Matrix

Nonnegative matrix factorization (NMF) factorizes an input nonnegative matrix into two nonnegative matrices of lower rank. It was recently discovered that NMF has unique ability to solve challenging data mining and machine learning problems. The advantage of NMF over existing unsupervised learning methods are (1) NMF can model widely varying data distributions, (2) NMF performs both hard and soft clustering simultaneously. (3) Many other data mining problems such as semi-supervised clustering problems can be reformulated as NMF problem. Building upon these foundations, the investigators propose to establish a NMF-based comprehensive framework for data mining: (a) Provide deeper understanding of NMF's clustering capability;(b) Extend data mining capability of NMF for solving various data mining and machine learning problems; (c) Develop fast numerical algorithms which incorporate the state-of-the-art developments from numerical optimization for various matrix factorization models; (d) Develop novel and rigorous proof strategies to prove the correctness and convergence properties of the numerical algorithms; (e) Apply and evaluate these new algorithms in real-world applications.The proposed work creates a new paradigm of analyzing vast amount of data and discovering new knowledge from the data by transforming established matrix computational methodologies. This new technology can automatically group news articles into meaningful categories, discover protein modules in protein networks, extract weather patterns in climate data, segment pictures into distinct objects, detect communities on the Web, and enable many other scientific discoveries and new technologies creation. On a fundamental level, the proposed work establishes that a simple matrix factorization in fact solves challenging data mining problems. This research reinforces the importance of mathematics in today's data centric world and encourages students to learn mathematics.

非负矩阵分解 (NMF) 将输入非负矩阵分解为两个较低秩的非负矩阵。最近发现 NMF 具有解决具有挑战性的数据挖掘和机器学习问题的独特能力。 与现有无监督学习方法相比，NMF 的优点是（1）NMF 可以对广泛变化的数据分布进行建模，（2）NMF 同时执行硬聚类和软聚类。 (3) 许多其他数据挖掘问题，例如半监督聚类问题，可以重新表述为 NMF 问题。在此基础上，研究人员建议建立一个基于 NMF 的数据挖掘综合框架：（a）加深对 NMF 聚类能力的理解；（b）扩展 NMF 的数据挖掘能力，以解决各种数据挖掘和机器学习问题； (c) 开发快速数值算法，其中纳入各种矩阵分解模型数值优化的最先进成果； (d) 制定新颖且严格的证明策略，以证明数值算法的正确性和收敛性； (e) 在现实世界应用中应用和评估这些新算法。所提出的工作创建了一种新的范式，通过改变已建立的矩阵计算方法来分析大量数据并从数据中发现新知识。这项新技术可以自动将新闻文章分组为有意义的类别，发现蛋白质网络中的蛋白质模块，提取气候数据中的天气模式，将图片分割成不同的对象，检测网络上的社区，并实现许多其他科学发现和新技术的创造。从根本上讲，所提出的工作证明简单的矩阵分解实际上可以解决具有挑战性的数据挖掘问题。这项研究强调了数学在当今以数据为中心的世界中的重要性，并鼓励学生学习数学。