Collaborative Research: New Directions in Multidimensional and Multivariate Functional Data Analysis

协作研究：多维多元函数数据分析的新方向

• 批准号: 1806063
• 负责人: Ka Wai Wong
• 金额: $ 9.68万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-16 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1806063&HistoricalAwards=false
• 关键词: Collaborative; Research; New; Directions; Multidimensional

Functional data analysis, which deals with a sample of functions or curves, plays an important role in modern data analysis. Nowadays in the era of "Big Data", multidimensional and multivariate functional data are becoming increasingly common, especially in biological, medical, and engineering applications. There are significant challenges posed by the very large dimension and complex structure of these data. The proposed research will substantially narrow the gap between the increasing demand for handling such data in practice, and the insufficient development of statistical methods and computational tools. This research has applications to neuroscience, climate science, and engineering. It will provide scientists, engineers, and doctors with tools to help understand problems in their area, and enhance interdisciplinary collaborations.This project offers a comprehensive research plan to advance the understanding and applicability of multidimensional and multivariate functional data. The research will focus on the following three sub-projects: (1) Develop data-adaptive and interpretable representation of the covariance function for multidimensional functional data, (2) Develop a novel model-free procedure to detect dependency between components of multivariate functional data, and (3) Address the modeling and prediction of multivariate functional time series. The resulting methods will be applied to neuroimaging and climate data. The integration of these three sub-projects will foster creative directions and strategies for multidimensional and multivariate functional data.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.

函数型数据分析是处理函数或曲线样本的一种方法，在现代数据分析中起着重要的作用。如今在“大数据”时代，多维和多元函数数据变得越来越普遍，特别是在生物，医学和工程应用中。 这些数据的维度非常大，结构复杂，这带来了重大挑战。 拟议的研究将大大缩小实际处理此类数据的需求日益增加与统计方法和计算工具发展不足之间的差距。 这项研究已应用于神经科学，气候科学和工程学。 它将为科学家、工程师和医生提供工具，帮助他们理解各自领域的问题，并加强跨学科合作。该项目提供了一个全面的研究计划，以促进多维和多元函数数据的理解和适用性。 本研究将集中在以下三个子项目：（1）开发多维函数数据的协方差函数的数据自适应和可解释的表示，（2）开发一种新的无模型程序来检测多元函数数据的组件之间的依赖关系，（3）解决多元函数时间序列的建模和预测。 由此产生的方法将应用于神经成像和气候数据。 这三个子项目的整合将促进多维和多元函数数据的创造性方向和策略。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Matrix Completion under Low-Rank Missing Mechanism

• DOI: 10.5705/ss.202019.0196
• 发表时间: 2018-12
• 期刊: ArXiv
• 作者: Xiaojun Mao;Raymond K. W. Wong;Songxi Chen

Low-Rank Covariance Function Estimation for Multidimensional Functional Data

多维函数数据的低秩协方差函数估计

• DOI: 10.1080/01621459.2020.1820344
• 发表时间: 2020
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Wang, Jiayi;Wong, Raymond K.;Zhang, Xiaoke
• 通讯作者: Zhang, Xiaoke

Statistical and machine learning methods applied to the prediction of different tropical rainfall types

统计和机器学习方法应用于不同热带降雨类型的预测

• DOI: 10.1088/2515-7620/ac371f
• 发表时间: 2021
• 期刊: Environmental Research Communications
• 影响因子: 2.9
• 作者: Wang, Jiayi;Wong, Raymond K. W.;Jun, Mikyoung;Schumacher, Courtney;Saravanan, R.;Sun, Chunmei
• 通讯作者: Sun, Chunmei

A Wavelet-Based Independence Test for Functional Data With an Application to MEG Functional Connectivity

• DOI: 10.1080/01621459.2021.2020126
• 发表时间: 2020-09
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Rui Miao;Xiaoke Zhang;Raymond K. W. Wong

Network Estimation via Graphon With Node Features

• DOI: 10.1109/tnse.2020.2973994
• 发表时间: 2018-09
• 期刊: IEEE Transactions on Network Science and Engineering
• 影响因子: 6.6
• 作者: Yi Su;Raymond K. W. Wong;Thomas C.M. Lee