CIF: Medium: Collaborative Research: Advances in the Theory and Practice of Low-Rank Matrix Recovery and Modeling

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This project concerns one of the fundamental challenges facingcontemporary science and engineering today, namely, the efficientprocessing and analysis of massive amounts of high-dimensional data,such as images, videos, web pages, and bioinformatics data. In short,data now routinely lie in thousands or even billions of dimensions. Onthe one hand, massive data collection is motivated by 1) scientificdiscovery and 2) the need for better engineering systems. On the otherhand, the difficult task now is to conduct meaningful inference insuch high dimensions, and draw correct conclusions from limitedamounts of sample data and with limited computationalresources. Fortunately, scientific or engineering data often have verylow intrinsic complexity and dimensionality. This project addressesthe opportunities offered by this common situation, establishesconditions under which reliable inference is actually possible, anddevelops computational tools for extracting key information from hugedata sets.This interdisciplinary project is expected to have three outcomes: 1)the development of innovative mathematics needed to study the recoveryof data matrices from partial and corrupted information 2) thedevelopment of effective algorithms for recovering low-rank matricesand performing accurate dimensionality reduction with corrupted dataand 3) the development of novel applications in which these techniquesare expected to considerably advance the state-of-the-art. With thesenew tools, scientists and engineers will be able to efficientlyextract correct information from data, which was previouslyinaccessible or intractable by conventional techniques. This willenable the development of far better computer vision systems for facerecognition, better compression schemes of video sequences, a betterunderstanding of gene expression data, or better search engines forweb documents and images.