A New Paradigm in Joint Registration, Analysis and Modeling of Function Data

函数数据联合配准、分析和建模的新范式

• 批准号: 1208959
• 负责人: Anuj Srivastava
• 金额: $ 25万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1208959&HistoricalAwards=false
• 关键词: New; Paradigm; Joint; Registration; Analysis

The dual problems of registration and analysis of functional data are very important in statistical analysis. They play important roles in applications involving phase-amplitude separation of real-valued functions, shape analysis of curves and surfaces, registration of 2D and 3D images, and analysis of longitudinal data with values on nonlinear manifolds. The PIs develop a novel framework that will lead to statistically consistent functional analysis and will substantially improve algorithmic performances over the current methods. The key novelty is to use Riemannian methods and distance-based objective functions that are: (1) designed for measuring registration levels of functions explicitly, (2) studied in the quotient spaces of functions modulo the registration groups, and (3) formulated for ensuing statistical analysis/modeling. Here one represents registration variability by actions of the domain-warping groups on function spaces, chooses an appropriate Riemannian metric (such that the group actions are by isometries) and studies novel mathematical representations that enable statistical analysis under such metrics. The main advantage is that both registration and analysis, e.g, computation of mean, covariance, PCA, are performed jointly under the same metric rather than the current practice of using sequential and disjoint steps. Preliminary results on some subproblems including real-valued function registration and shape analysis of curves are shown to be superior, both empirically and theoretically, to the current approaches. The goal is to broaden this research to a larger class of registration problems with similar fundamental solutions. High-dimensional functional data is becoming omnipresent in today's society and one needs to nonlinearly align such observations in time and space, in order to improve data analysis, statistical modeling, and inferences. This project represents a multi-disciplinary effort that will develop both basic statistical science and computational tools for registration of functional data. This, in turn, will impact such data-rich applications as development of accurate growth charts for children, gene expression analysis, face recognition using images and videos, detection and evaluation of brain disorders (e.g. Alzheimer) using medical images, and human activity recognition using surveillance video data. The novelty and potential high returns of this project come from the variety of tools utilized---from differential geometry and statistics to imaging science.

功能数据的配准和分析是统计分析中的重要问题。 它们在实值函数的相位-振幅分离、曲线和曲面的形状分析、2D和3D图像的配准以及非线性流形上的纵向数据分析等应用中发挥着重要作用。PI开发了一个新的框架，这将导致统计上一致的功能分析，并将大大提高算法性能超过目前的方法。关键的新奇是使用黎曼方法和基于距离的目标函数：（1）设计用于显式测量功能的配准水平，（2）在功能模配准组的商空间中进行研究，以及（3）制定用于随后的统计分析/建模。在这里，一个代表注册的功能空间上的域扭曲组的行动的变化，选择一个适当的黎曼度量（这样的组的行动是由等距）和研究新的数学表示，使统计分析下这样的度量。其主要优点是，注册和分析，例如，计算的平均值，协方差，PCA，共同执行下相同的度量，而不是目前的做法，使用顺序和不相交的步骤。一些子问题，包括实值函数注册和形状分析曲线的初步结果被证明是上级，无论是经验和理论，目前的方法。我们的目标是扩大这项研究，以更大的一类注册问题，类似的基本解决方案。高维函数数据在当今社会中变得无处不在，人们需要在时间和空间上非线性地对齐这些观察，以改进数据分析，统计建模和推理。该项目是一个多学科的努力，将开发基础统计科学和计算工具，用于功能数据的登记。这反过来又会影响到数据丰富的应用，如儿童准确生长图表的开发，基因表达分析，使用图像和视频的面部识别，使用医学图像检测和评估大脑疾病（如阿尔茨海默病），以及使用监控视频数据识别人类活动。这个项目的新奇和潜在的高回报来自于所使用的各种工具-从微分几何和统计到成像科学。