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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) 和独立分量分析 (ICA)，是许多传感和学习应用的基石，例如文档分析、高光谱成像、大脑信号处理和表示学习。 FA 工具旨在以无人监督的方式从数据中发现有意义的潜在信息（例如，文档集合中的突出主题）。然而，经典的 FA 模型没有考虑数据采集/生成中经常发生的未知非线性失真，因此在关键场景中经常无法产生合理的结果。该项目将开发一套非线性因子分析 (NFA) 工具，通过有效且可证明地处理未知非线性来改变现有的 FA 范式。该项目的结果将显着促进对各种 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——这些在很大程度上是未知的研究领域。这些产品将提高科学和工程中经常出现未知非线性失真的广泛传感和学习任务的性能，例如遥感、脑机接口、视觉/图像/文本数据分析、生物信息学、地球科学、生物学和生态学。开发具有视觉吸引力的基于 FA 和 NFA 的课程模块和软件的综合教育计划将缓解 K-12 和大学的“数学焦虑”。大学预科推广项目和本科生研究计划将有效培养早期对数学的兴趣，并提高代表性不足的学生对 STEM 学科的参与。这些教育活动将为信号和机器智能领域培养多元化且具有数学竞争力的未来劳动力。该项目将开发一个统一的分析和计算框架，用于学习各种具有挑战性和现实的 NFA 模型。具体来说，Thrust I 将开发一个基于统一函数方程的框架，用于在各种 NFA 设置下进行可证明的无监督非线性模型识别。 Thrust II 将在现实条件下（例如有限样本和噪声情况）理解 NFA 方面取得重要进展，并将提供具有性能保证的有效 NFA 优化算法。 Thrust III 将针对及时且重要的传感和学习任务（包括高光谱成像、生物传感器信号处理和无监督机器学习）仔细评估所提出的方法。这些推动力将在理论和算法方面产生根本性成果，解决 NFA 的关键挑战。新的基于函数方程的分析框架为现有工具无法解决的各种 NFA 模型识别问题提供了理论基础。现实环境（例如，有限数据）下的新 NFA 性能表征工具将比所有使用过于理想的假设（例如，无限数据）的现有工作实现重大飞跃。通过集成统计分析、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，这些问题目前都缺乏有保证的解决方案。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。