Robust and Scalable Volume Minimization-based Matrix Factorization for Sensing and Clustering

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

This project focuses on matrix factorization using a simplicial cone model, which has a wide variety of applications in remote sensing (particularly hyperspectral imaging), radio frequency sensing for dynamic spectrum access, clustering and topic modeling, and social network analysis, to name a few. The project focuses on robust and scalable computational tools for this model, using a convex hull volume minimization criterion. The motivation partially comes from a result that was recently obtained by the principal investigators, showing that unique factorization is possible under mild conditions if one adopts the volume minimization criterion. These conditions are far more realistic than those required by existing approaches, suggesting that more challenging scenarios and even new application domains are within reach if only related optimization, robustness, and scalability challenges can be effectively addressed. This research will provide the computational underpinnings of these exciting developments. High-performance volume minimization software will be publicly released to enable researchers and practitioners to tackle new problems, handle much larger datasets, and boost performance in existing applications like hyperspectral imaging. On the education front, the project will help train a graduate student in cutting-edge computational engineering research, and will also help engage talented undergraduates through senior honors projects, introducing them to research and publication opportunities. In terms of theory and methods, key aspects of volume minimization-based matrix factorization are still poorly understood. The research will provide a set of high-performance computational tools rooted in deep understanding of the strengths and weaknesses of the original volume minimization criterion which promises exciting discoveries. The research will evolve along the following synergistic thrusts: i) robust optimization algorithms for volume minimization; ii) scalable and adaptive algorithms towards online volume minimization; iii) validation, using existing (e.g., hyperspectral imaging) as well as promising new (e.g., document clustering) applications; and iv) theoretical aspects of the volume minimization formulation, focusing on fundamentals such as identifiability and performance bounds. Devising scalable volume minimization algorithms makes a lot of sense for modern sensing and clustering problems which involve rapidly increasing amounts of data. From an applications point of view, volume minimization for spectrum sensing, channel identification, and document clustering are completely new and challenging.