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

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。该项目的重点是为数据采集、处理和理解开发有效的新框架，以帮助应对日益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。与该项目的研究相结合的是教育目标，通过创建和传播新的课程和K-12扩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，也关注减轻这些挑战的降维技术背后的原则。该项目的研究借鉴了稀疏性和几何的概念，以追求理论上合理的、集成的模型和广泛类别的自然数据的表示。特别令人感兴趣的是(i)两两比较矩阵，它出现在许多应用中，包括推荐引擎、经济交流、选举和心理学，但不能被低秩模型充分捕获；（ii）点云，它出现在信号和图像数据库和传感器网络中，但目前的模型不能正确捕获信号内部和信号之间的结构。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技术，这些技术利用了比传统低秩恢复技术更丰富的模型。

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.