Robust and Scalable Volume Minimization-based Matrix Factorization for Sensing and Clustering

用于传感和聚类的鲁棒且可扩展的基于体积最小化的矩阵分解

基本信息

批准号：
1852831
负责人：
Nikolaos Sidiropoulos
金额：
$ 24.93万
依托单位：
University of Virginia Main Campus
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-09-01 至 2021-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1852831&HistoricalAwards=false
关键词：
Robust Scalable Volume Minimization based

项目摘要

This project focuses on matrix factorization using a simplicial cone model, which has a wide variety of applications in remote sensing (particularly hyperspectral imaging), radio frequency sensing for dynamic spectrum access, clustering and topic modeling, and social network analysis, to name a few. The project focuses on robust and scalable computational tools for this model, using a convex hull volume minimization criterion. The motivation partially comes from a result that was recently obtained by the principal investigators, showing that unique factorization is possible under mild conditions if one adopts the volume minimization criterion. These conditions are far more realistic than those required by existing approaches, suggesting that more challenging scenarios and even new application domains are within reach if only related optimization, robustness, and scalability challenges can be effectively addressed. This research will provide the computational underpinnings of these exciting developments. High-performance volume minimization software will be publicly released to enable researchers and practitioners to tackle new problems, handle much larger datasets, and boost performance in existing applications like hyperspectral imaging. On the education front, the project will help train a graduate student in cutting-edge computational engineering research, and will also help engage talented undergraduates through senior honors projects, introducing them to research and publication opportunities. In terms of theory and methods, key aspects of volume minimization-based matrix factorization are still poorly understood. The research will provide a set of high-performance computational tools rooted in deep understanding of the strengths and weaknesses of the original volume minimization criterion which promises exciting discoveries. The research will evolve along the following synergistic thrusts: i) robust optimization algorithms for volume minimization; ii) scalable and adaptive algorithms towards online volume minimization; iii) validation, using existing (e.g., hyperspectral imaging) as well as promising new (e.g., document clustering) applications; and iv) theoretical aspects of the volume minimization formulation, focusing on fundamentals such as identifiability and performance bounds. Devising scalable volume minimization algorithms makes a lot of sense for modern sensing and clustering problems which involve rapidly increasing amounts of data. From an applications point of view, volume minimization for spectrum sensing, channel identification, and document clustering are completely new and challenging.

该项目的重点是使用Simplicial圆锥模型进行矩阵分解，该模型在遥感（尤其是高光谱成像）中具有多种应用，用于动态频谱访问，聚类和主题建模的射频传感以及社交网络分析，以命名。。该项目使用凸面船体体积最小化标准专注于该模型的可靠和可扩展的计算工具。动机部分来自主要研究人员最近获得的结果，表明如果人们采用体积最小化标准，则可能在轻度条件下进行分解。这些条件比现有方法所要求的要现实得多，这表明只有可以有效解决相关优化，鲁棒性和可伸缩性挑战，更具挑战性的场景甚至是新的应用程序领域就可以触及。这项研究将为这些令人兴奋的发展提供计算基础。高性能量最小化软件将公开发布，以使研究人员和从业人员能够解决新的问题，处理更大的数据集并在高光谱成像等现有应用中提高性能。在教育方面，该项目将帮助培训一名研究生进行尖端的计算工程研究，还将通过高级荣誉项目来帮助有才华的本科生，从而将其介绍给研究和出版机会。就理论和方法而言，基于体积最小化的基质分解的关键方面仍然很少了解。该研究将提供一组高性能计算工具，这些工具植根于对原始体积最小化标准的优势和劣势的深入了解，这有望令人兴奋。该研究将沿以下协同推力发展：i）稳定的优化算法，以最小化量； ii）可扩展和适应性算法，以最小化在线量； iii）验证，使用现有的（例如高光谱成像）以及有希望的新（例如文档群集）应用程序； iv）体积最小化公式的理论方面，重点是诸如可识别性和性能界限之类的基本面。设计可扩展的体积最小化算法对于现代感测和聚类问题，涉及快速增加数据的数量很有意义。从应用的角度来看，频谱传感，通道标识和文档聚类的音量最小化是全新的，而且具有挑战性。