Collaborative Research: Sparse Optimization in Large Scale Data Processing: A Multiscale Proximity Approach

协作研究：大规模数据处理中的稀疏优化：多尺度邻近方法

• 批准号: 1912958
• 负责人: Yuesheng Xu
• 金额: $ 12.5万
• 依托单位: Old Dominion University Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912958&HistoricalAwards=false
• 关键词: Collaborative; Research; Sparse; Optimization; Large

There is an emergent demand in areas of national strategic interest such as information technology, nanotechnology, biotechnology, civil infrastructure and environment for abstracting useful knowledge for decision making or uncovering truth from large-scale data acquired via various means such as sensors and internet. A core issue of these areas is to develop accurate mathematical models, which govern the abstraction process, and to design efficient algorithms that solve the underlying optimization problems for the models. A challenge of the tasks comes from the large-scale nature of given data. This nature requires determining a large number of model parameters and it is computationally expensive. To address this challenge, this project will take advantage of certain intrinsic multiscale structure of given data in modeling so that the resulting models have significantly fewer parameters to be determined. It is also crucial to introduce efficient algorithms for solving the resulting optimization problems for the models, which have intrinsic multiscale structures. The second goal of this proposed research is to provide rigorous training of young mathematicians and computational scientists so that they have the skill sets needed to face the challenges of the big data era through this proposed research and its associated educational components. Outcomes of the proposed research and its educational component will certainly contribute to the Federal strategic interest areas.This research project addresses several critical issues of processing large-scale data, such as high dimensionality and high noise, through properly choosing structured sparsity promoting non-convex functions in modeling and through synthesizing the multiscale representation of data and using fixed-point equations/inclusions involved the proximity operator in solving the resulting optimization problem. Structured non-convex sparsity promoting functions are proposed to overcome drawbacks of the existing modeling of large-scale data, leading to the design of efficient single-scale proximity algorithms. Multiscale analysis has been developed to efficiently represent data, while how multiscale representation of data is used to improve convergence of the fixed-point proximity algorithm remains unsolved. The proposed multiscale proximity method avoids iterations on the full large-scale of the fixed-point equation/inclusion. Instead, when data are represented in a multiscale analysis, iterations of the multiscale proximity algorithm are conducted only on a (small-scale) lower frequency component of the equation/inclusion (based on a single-scale algorithm), and only one functional evaluation on a (large-scale) high frequency component is required. The multiscale algorithm will preserve accuracy of the single-scale algorithm while accelerating its convergence significantly. This leads to a fast algorithm for solving the fixed-point equation/inclusion involved the proximity operator.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.

国家战略兴趣领域的需求很紧急，例如信息技术，纳米技术，生物技术，民用基础设施和环境将有用的知识抽象用于决策或从通过各种手段（例如传感器和互联网）获取的大规模数据中发现真相。这些领域的一个核心问题是开发准确的数学模型，该模型控制抽象过程，并设计有效的算法来解决模型的基本优化问题。任务的挑战来自给定数据的大规模性质。这种性质需要确定大量模型参数，并且在计算上很昂贵。为了应对这一挑战，该项目将利用建模中给定数据的某些固有的多尺度结构，以便确定所得模型要少得多。引入有效的算法来解决具有内在的多尺度结构的模型的优化问题，这也是至关重要的。这项拟议的研究的第二个目标是对年轻的数学家和计算科学家进行严格的培训，以便通过这项拟议的研究及其相关的教育组成部分，拥有面对大数据时代的挑战所需的技能。拟议的研究的结果及其教育组成部分肯定会为联邦战略兴趣领域做出贡献。该研究项目通过正确选择在建模和综合固定派对中的既定型组合方面促进非convex功能的结构性稀疏来解决处理大规模数据的几个关键问题，例如高维度和高噪音，从而解决了结构化的稀疏性，从而解决了非convex功能，从而解决了固定的稀疏功能。 问题。提出了结构化的非凸稀疏促进功能，以克服大规模数据现有建模的缺点，从而导致设计有效的单尺度接近算法。已经开发了多尺度分析以有效地表示数据，而数据的多尺度表示如何用于改善定点接近算法的收敛性。提出的多尺度接近方法避免了固定点方程/包含的整个大规模迭代。取而代之的是，当数据在多尺度分析中表示时，多尺度接近算法的迭代仅在方程/包含的（基于单个尺度算法）的（基于单个尺度算法）的（小规模的）较低频率分量上进行，并且只需一个功能评估（大频率）上的频率分量。多尺度算法将保持单尺度算法的准确性，同时显着加速其收敛性。这导致了一种快速的算法，用于解决涉及接近操作员的定点方程/包容性。该奖项反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的影响审查标准，认为值得通过评估来获得支持。

项目成果

Regularization in a functional reproducing kernel Hilbert space

• DOI: 10.1016/j.jco.2021.101567
• 发表时间: 2021-03
• 期刊: J. Complex.
• 作者: Rui Wang;Yuesheng Xu

Sparse Deep Neural Network for Nonlinear Partial Differential Equations

非线性偏微分方程的稀疏深度神经网络

• DOI: 10.4208/nmtma.oa-2022-0104
• 发表时间: 2022
• 期刊: Methods and Applications
• 作者: null, Yuesheng Xu;Zeng, Taishan
• 通讯作者: Zeng, Taishan

A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm

• DOI: 10.1088/1361-6420/ac490f
• 发表时间: 2022-03-01
• 期刊: INVERSE PROBLEMS
• 影响因子: 2.1
• 作者: Chen，Yun;Lu，Yao;Xu，Yuesheng
• 通讯作者: Xu，Yuesheng

Deeply learning deep inelastic scattering kinematics

深度学习深度非弹性散射运动学

• DOI: 10.1140/epjc/s10052-022-10964-z
• 发表时间: 2022
• 期刊: The European Physical Journal C
• 作者: Diefenthaler, Markus;Farhat, Abdullah;Verbytskyi, Andrii;Xu, Yuesheng
• 通讯作者: Xu, Yuesheng

Sparse regularization with the ℓ0 norm

使用 0 范数进行稀疏正则化

• DOI: 10.1142/s0219530522500105
• 发表时间: 2023
• 期刊: Analysis and Applications
• 影响因子: 2.2
• 作者: Xu, Yuesheng