CAREER: Nonlinear Factor Analysis for Sensing and Learning

Oregon State University, Corvallis OR

Investigators

Abstract

Factor analysis (FA) tools, e.g., nonnegative matrix factorization (NMF) and independent component analysis (ICA), are the cornerstones of many sensing and learning applications, e.g., document analytics, hyperspectral imaging, brain signal processing, and representation learning. FA tools are designed to discover meaningful latent information from data (e.g., prominent topics in a collection of documents) in an unsupervised manner. However, classic FA models do not consider unknown nonlinear distortions that often happen in data acquisition/generation, and thus frequently fail to produce sensible results in critical scenarios. This project will develop a suite of nonlinear factor analysis (NFA) tools that will transform existing FA paradigms by effectively and provably handling unknown nonlinearities. Results from this project will significantly advance the understanding of fundamental properties and computational aspects of various NFA models, including model identifiability, sample complexity, noise robustness and algorithm convergence---which are largely uncharted research territories. The products will boost the performance of a broad spectrum of sensing and learning tasks in science and engineering where unknown nonlinear distortions often arise, e.g., remote sensing, brain-computer interface, vision/image/text data analytics, bioinformatics, geoscience, biology, and ecology. The integrated education plan of developing visually appealing FA and NFA-based course modules and software will alleviate “math anxiety” in K-12 and college. The precollege outreach programs and undergraduate research plans will effectively foster early interest in mathematics and enhance students’ participation in STEM disciplines. These education activities will lead to a mathematically competitive future workforce for signal and machine intelligence. This project will develop a unified analytical and computational framework for learning various challenging and realistic NFA models. Specifically, Thrust I will develop a unified functional equation-based framework for provable unsupervised nonlinear model identification under various NFA settings. Thrust II will make important advances towards understanding NFA under realistic conditions (e.g., finite sample and noisy cases), and will offer effective NFA optimization algorithms with performance guarantees. Thrust III will carefully evaluate the proposed approaches over timely and important sensing and learning tasks including hyperspectral imaging, biosensor signal processing, and unsupervised machine learning. These thrusts will produce fundamental results in both theory and algorithms addressing critical challenges in NFA. The new functional equation-based analytical framework offers a theoretical underpinning for various NFA model identification problems that are beyond the reach of existing tools. The new NFA performance characterization tools under realistic settings (e.g., finite data) will be a substantial leap forward from existing works that all use overly ideal assumptions (e.g., unlimited data). The computational framework through an integration of statistical analysis, neural network learning, and nonlinear programming will offer provable and flexible algorithms for NFA problems, which all currently lack guaranteed solutions. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.