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数据采集，处理和理解的新框架，这将有助于满足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。结合本项目的研究，教育目标是通过创建和传播新的课程和K-12外展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，又关注降维技术背后的原理，以减轻这些挑战。本项目的研究借鉴了稀疏性和几何学的概念，为广泛的自然数据类别提供集成的模型和表示。特别令人感兴趣的是（i）成对比较矩阵，其出现在许多应用中，包括推荐引擎，经济交易，选举和心理学，但不能被低秩模型充分捕获，以及（ii）点云，其出现在信号和图像数据库以及传感器网络中，但当前模型无法正确捕获信号内和信号间结构。为了帮助减轻收集和存储高维数据集（包括上述数据集）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。