Collaborative Research: New Methods, Theory and Applications for Nonsmooth Manifold-Based Learning

协作研究：非平滑流形学习的新方法、理论和应用

基本信息

批准号：
1953189
负责人：
Lingzhou Xue
金额：
$ 20万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-06-01 至 2024-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1953189&HistoricalAwards=false
关键词：
Collaborative Research New Methods Theory

项目摘要

Nowadays, the availability of massive data is continuously increasing, primarily due to the continued advancement of technology. As a consequence, massive high-dimensional data are ubiquitous in many scientific and engineering disciplines, such as bioinformatics, computer vision, neuroimaging, and signal processing. The nonsmooth manifold-based learning with high-dimensional and multidimensional data is in general complicated due to its intrinsic non-convexity and non-smoothness. This project will address both statistical and computational issues of nonsmooth manifold-based learning and explore its new applications. It is known that statistical modeling of high-dimensional data may include the non-smooth regularization in the objective function, and some may even involve non-convex manifold constraints such as orthogonality constraints. The manifold-based learning offers a powerful framework for dimension reduction and signal processing. The combination of non-smooth regularization and non-convex manifold constraints brings new opportunities and challenges for designing optimization algorithms with convergence guarantees and also for developing new statistical methods and theory. The research outcomes of this project will provide new powerful analytic tools in nonsmooth manifold-based learning with theoretical guarantees. Software packages will be developed to make the research outcomes readily available to other researchers and practitioners.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.

如今，海量数据的可用性不断增加，这主要归功于技术的不断进步。因此，海量高维数据在许多科学和工程学科中无处不在，例如生物信息学、计算机视觉、神经成像和信号处理。高维和多维数据的非光滑流形学习由于其固有的非凸性和非光滑性而通常很复杂。该项目将解决基于非平滑流形的学习的统计和计算问题，并探索其新应用。众所周知，高维数据的统计建模可能包括目标函数中的非光滑正则化，有的甚至可能涉及正交性约束等非凸流形约束。基于流形的学习为降维和信号处理提供了强大的框架。非光滑正则化和非凸流形约束的结合为设计具有收敛保证的优化算法以及开发新的统计方法和理论带来了新的机遇和挑战。该项目的研究成果将为基于非光滑流形的学习提供新的强大分析工具并提供理论保证。将开发软件包以使其他研究人员和从业者能够轻松获得研究成果。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。