CAREER: Nonlinear Factor Analysis for Sensing and Learning

职业：传感和学习的非线性因子分析

基本信息

批准号：
2144889
负责人：
Xiao Fu
金额：
$ 50万
依托单位：
Oregon State University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-05-01 至 2027-04-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2144889&HistoricalAwards=false
关键词：
CAREER Nonlinear Factor Analysis Sensing

项目摘要

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 underrepresented students’ participation in STEM disciplines. These education activities will lead to a diversified and 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.

因子分析（FA）工具，例如非负矩阵分解（NMF）和独立组件分析（ICA）是许多传感器和学习应用的基石，例如文档分析，高光谱成像，大脑信号处理和表示学习。 FA工具旨在以无监督的方式从数据（例如，文档集合中的重要主题）中发现有意义的潜在信息。但是，经典的FA模型并未考虑在数据采集/生成中经常发生的未知非线性畸变，因此在关键情况下经常无法产生敏感的结果。该项目将开发一套非线性因子分析（NFA）工具，该工具将通过有效，正确处理未知的非线性来改变现有的FA范例。该项目的结果将显着提高对各种NFA模型的基本属性和计算方面的理解，包括模型可识别性，样本复杂性，噪声鲁棒性和算法收敛性---在很大程度上是未知的研究领域。这些产品将在科学和工程学中提高各种感觉和学习任务的性能，例如，未知的非线性畸变经常出现，例如，远程灵敏度，脑部计算机界面，视觉/图像/文本数据分析，生物信息信息，地球科学，生物学，生物学和生态学。制定视觉吸引力和基于NFA的课程模块和软件的综合教育计划将减轻K-12和College的“数学动画”。预科课程外展计划和本科研究计划将有效地提高对数学的早期兴趣，并增强了代表性不足的学生参与STEM学科。这些教育活动将导致信号和机器智能的多元化和数学竞争性的未来劳动力。该项目将开发一个统一的分析和计算框架，以学习各种挑战和现实的NFA模型。具体而言，推力我将开发一个基于统一的功能方程的框架，用于在各种NFA设置下可证明的无监督的非线性模型标识。推力II将在现实条件下（例如有限样本和噪声案例）在理解NFA方面取得重要的进步，并将提供具有性能保证的有效NFA优化算法。推力III将仔细评估所提出的方法，以及时，重要的感官和学习任务，包括高光谱成像，生物传感器信号处理以及无监督的机器学习。这些推力将在理论和算法中产生基本结果，以应对NFA的关键挑战。新的基于功能方程的分析框架为各种NFA模型识别问题提供了理论的基础，这些问题无法实现现有工具的影响。现实设置（例如，有限数据）下的新的NFA性能表征工具将从所有使用过度理想的假设（例如无限数据）的现有作品中取得重大飞跃。通过整合统计分析，神经网络学习和非线性编程的计算框架将为NFA问题提供可证明且灵活的算法，目前所有这些问题都缺乏保证的解决方案。该奖项反映了NSF的法定任务，并被认为是通过使用基金会的知识分子和更广泛影响的评估来评估的支持，并被视为珍贵的支持。