CAREER: New Models, Representations, and Dimensionality Reduction Techniques for Structured Data Sets

职业：结构化数据集的新模型、表示和降维技术

• 批准号: 1149225
• 负责人: Michael Wakin
• 金额: $ 40万
• 依托单位: Colorado School of Mines
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-05-01 至 2018-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1149225&HistoricalAwards=false
• 关键词: CAREER; New; Models; Representations; Dimensionality

ABSTRACT:A significant byproduct of the modern Information Age has been an explosion in the sheer quantity of data demanded from sensing systems. This project focuses on developing effective new frameworks for data acquisition, processing, and understanding that will help meet the technological challenges posed by this ever growing demand for information. Possible areas of impact include, but are not limited to: social choice theory, recommendation engines, sensor networks, computer vision, LIDAR, machine learning, medical imaging, drug discovery, and neuroscience. Integrated with the research in this project are the educational goals to inspire and educate students by creating and disseminating new curricular and K-12 outreach materials that focus both on the challenges of high-dimensional data processing and on the principles behind the dimensionality reduction techniques for alleviating them.The research in this project draws from the concepts of sparsity and geometry in pursuing theoretically sound, integrated models and representations for broad classes of natural data. Of particular interest are (i) pairwise comparison matrices, which arise in a number of applications including recommendation engines, economic exchanges, elections, and psychology but are inadequately captured by low-rank models, and (ii) point clouds, which arise in signal and image databases and sensor networks but for which current models fail to properly capture intra- and inter-signal structures. In order to help mitigate the challenges in collecting and storing high-dimensional data sets (including those above), this project is developing principled techniques for recovering matrix-structured data sets from partial information that exploit far richer models than conventional low-rank recovery techniques.

摘要：现代信息时代的一个重要副产品是传感系统所需数据​​量的爆炸式增长。该项目的重点是开发有效的新数据采集、处理和理解框架，这将有助于应对不断增长的信息需求所带来的技术挑战。可能的影响领域包括但不限于：社会选择理论、推荐引擎、传感器网络、计算机视觉、激光雷达、机器学习、医学成像、药物发现和神经科学。与该项目研究相结合的教育目标是通过创建和传播新课程和 K-12 宣传材料来激励和教育学生，这些材料既关注高维数据处理的挑战，又关注高维数据处理背后的降维技术原理。该项目的研究借鉴了稀疏性和几何的概念，追求理论上合理的、集成的模型和广泛的自然数据的表示。特别令人感兴趣的是（i）成对比较矩阵，它出现在推荐引擎、经济交换、选举和心理学等许多应用中，但低秩模型无法充分捕获；（ii）点云，它出现在信号中以及图像数据库和传感器网络，但当前模型无法正确捕获信号内和信号间结构。为了帮助缓解收集和存储高维数据集（包括上述数据集）方面的挑战，该项目正在开发从部分信息中恢复矩阵结构数据集的原则性技术，这些技术利用比传统低秩恢复技术更丰富的模型。