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.
