Tensor and Subspace Learning Methods with Applications to Medical Imaging

张量和子空间学习方法及其在医学成像中的应用

• 批准号: 2053697
• 负责人: Xin Zhang
• 金额: $ 18万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2053697&HistoricalAwards=false
• 关键词: Tensor; Subspace; Learning; Methods; Applications

Medical imaging techniques have become increasingly important for both clinical and research studies. For example, cone beam computed tomography has a major role in diagnosis and treatment planning in dentistry, and functional magnetic resonance imaging is routinely used to help researchers characterize brain activity. More efficient and powerful statistical techniques are needed to analyze medical imaging for diagnosis and prediction of diseases and other disorders. Through this project, new statistical theory, methods, and algorithms will be developed for the analysis of large complex data such as medical imaging data sets. The research is expected to provide new theoretical insights and practical methodologies that advance multivariate statistics while simultaneously responding to the growing needs and challenges of medical imaging data analysis. Results of the research in this project will be disseminated through collaborations with neuroscientists and biomedical engineers, as well as substantial graduate student training and outreach activities. Open source and user-friendly software will also be produced.Ultra-high dimensionality, tensor structure, and high correlations are embedded in modern scientific and engineering data. Estimation and inferential techniques become inefficient or even inconsistent if they ignore high correlations among variables, heterogeneity caused by additional covariates, or intrinsic structural information. To address these challenges, statistically rigorous and computationally efficient learning methods will be developed. A key idea is to construct and estimate targeted subspaces that exclude the noise and irrelevant information in the data set. The research project is expected to make significant contributions on two fronts: computational and theoretical foundations for envelope subspace estimation in high dimensions, and efficient tensorial parameter estimation in regression and classification models.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.

医学成像技术对于临床和研究变得越来越重要。例如，锥形束计算机断层扫描在牙科诊断和治疗计划中发挥着重要作用，功能性磁共振成像通常用于帮助研究人员表征大脑活动。需要更有效和更强大的统计技术来分析医学成像以诊断和预测疾病和其他疾病。通过该项目，将开发新的统计理论、方法和算法，用于分析医学成像数据集等大型复杂数据。该研究预计将提供新的理论见解和实用方法，推动多元统计，同时应对医学成像数据分析日益增长的需求和挑战。该项目的研究结果将通过与神经科学家和生物医学工程师的合作以及大量的研究生培训和外展活动来传播。还将生产开源且用户友好的软件。超高维度、张量结构和高相关性嵌入现代科学和工程数据中。如果忽略变量之间的高度相关性、额外协变量引起的异质性或内在结构信息，估计和推理技术就会变得低效甚至不一致。为了应对这些挑战，将开发统计严格且计算高效的学习方法。一个关键思想是构建和估计排除数据集中的噪声和不相关信息的目标子空间。该研究项目预计将在两个方面做出重大贡献：高维包络子空间估计的计算和理论基础，以及回归和分类模型中的有效张量参数估计。该奖项反映了 NSF 的法定使命，并被认为值得支持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。

项目成果

An Efficient Convex Formulation for Reduced-Rank Linear Discriminant Analysis in High Dimensions

高维降阶线性判别分析的高效凸公式

• DOI: 10.5705/ss.202021.0047
• 发表时间: 2023
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Zeng, Jing;Zhang, Xin;Mai, Qing
• 通讯作者: Mai, Qing

Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction

• DOI: 10.1111/biom.13486
• 发表时间: 2021-05
• 期刊: Biometrics
• 影响因子: 1.9
• 作者: Kai Deng;Xin Zhang

Envelopes and principal component regression

• DOI: 10.1214/23-ejs2154
• 发表时间: 2022-07
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Xin Zhang;Kai Deng;Qing Mai

Likelihood-Based Dimension Folding on Tensor Data

张量数据上基于似然的维度折叠

• DOI: 10.5705/ss.202020.0040
• 发表时间: 2023
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Wang, Ning;Zhang, Xin;Li, Bing
• 通讯作者: Li, Bing

Generalized Liquid Association Analysis for Multimodal Data Integration

• DOI: 10.1080/01621459.2021.2024437
• 发表时间: 2020-08
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Lexin Li;Jing Zeng;Xin Zhang