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

Stanford University, Stanford CA

Investigators

Abstract

This project concerns one of the fundamental challenges facing contemporary science and engineering today, namely, the efficient processing 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. On the one hand, massive data collection is motivated by 1) scientific discovery and 2) the need for better engineering systems. On the other hand, the difficult task now is to conduct meaningful inference in such high dimensions, and draw correct conclusions from limited amounts of sample data and with limited computational resources. Fortunately, scientific or engineering data often have very low intrinsic complexity and dimensionality. This project addresses the opportunities offered by this common situation, establishes conditions under which reliable inference is actually possible, and develops computational tools for extracting key information from huge data sets. This interdisciplinary project is expected to have three outcomes: 1) the development of innovative mathematics needed to study the recovery of data matrices from partial and corrupted information 2) the development of effective algorithms for recovering low-rank matrices and performing accurate dimensionality reduction with corrupted data and 3) the development of novel applications in which these techniques are expected to considerably advance the state-of-the-art. With these new tools, scientists and engineers will be able to efficiently extract correct information from data, which was previously inaccessible or intractable by conventional techniques. This will enable the development of far better computer vision systems for face recognition, better compression schemes of video sequences, a better understanding of gene expression data, or better search engines for web documents and images.