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: 1832046
• 负责人: Xiaoke Zhang
• 金额: $ 7.69万
• 依托单位: George Washington 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: 2017-08-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1832046&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.

涉及功能或曲线样本的功能数据分析在现代数据分析中起着重要作用。如今，在“大数据”时代，多维和多元功能数据变得越来越普遍，尤其是在生物，医学和工程应用中。 这些数据的非常大的维度和复杂结构带来了重大挑战。 拟议的研究将大大缩小在实践中处理此类数据的需求与统计方法和计算工具不足的发展之间的差异。 这项研究在神经科学，气候科学和工程上有应用。 它将为科学家，工程师和医生提供工具，以帮助了解其地区的问题，并增强跨学科的合作。该项目提供了一项全面的研究计划，以提高多维和多元功能数据的理解和适用性。 该研究将重点放在以下三个子项目上：（1）为多维功能数据的协方差函数开发数据自适应和可解释的表示，（（2）开发了一种新型的无模型程序，以检测多元功能数据的组件之间的依赖性，以及（3）解决多个函数函数函数时间序列的模型和预测。 所得的方法将应用于神经影像学和气候数据。 这三个子项目的集成将促进多维和多元功能数据的创造性方向和策略。