Modeling Complex Functional Data

复杂功能数据建模

• 批准号: 1407852
• 负责人: Hans-Georg Mueller
• 金额: $ 33.77万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1407852&HistoricalAwards=false
• 关键词: Modeling; Complex; Functional; Data

There is increasing need for adequate statistical analysis methods for samples of time-dynamic and longitudinal data that include high-dimensional and other complex objects that are recorded over time. Such data arise in many areas of critical concern where adequate methodology to quantify changes of complex patterns over time is relevant to come to the right conclusions. This includes studies of environmental and climate change and the evolution of social networks over time. It also includes biological networks that are thought to operate between "hubs" in the brain and that are changing as a person ages. Such data are objects with a structure that defies established linear modeling approaches that have been previously developed in the statistical field of functional data analysis. The investigator and his research group are therefore developing new methods aimed at the analysis of such complex time-dynamic and longitudinal data. These techniques will lead to a better understanding of the underlying dynamics and the changes in the inherent patterns and interactions of the objects over time. Better understanding of time-dynamic phenomena will lead to better informed societal and individual decision making. The research also involves the training of students in upfront methodology and the creation of suitable fast algorithms to implement these new methods. The established field of Functional Data Analysis has been focused on linear methods such as functional linear principal component analysis. However, the applicability of these established models for "next generation" functional data is quite limited. This is because such data are inherently nonlinear, i.e., they do not live in a linear space, and therefore are far more complex than linear data. Second generation functional data are generated across the sciences and e-commerce and by online and physical tracking devices that continuously record signals and trajectories, in on-line settings, monitoring and sensor systems. Important types of time-varying "object data" are covariance matrices, densities or networks, and new methods will be developed to properly quantify the dynamics of such complex objects. Besides the non-Euclidean nature of these objects, additional challenges arise from the sparsity of available data in many longitudinal studies, due to missing data or irregular sampling schemes. This research addresses these issues and challenges and will lead to techniques to quantify the variability of complex dynamics by developing principled and theoretically supported methodology for the analysis of these more complex data types. This research will benefit the analysis and understanding of the time dynamics of social and biological networks, and of other time-indexed objects, as well as the analysis of high-dimensional functional data. The research includes novel methods for the classification of functional data, which is an increasingly important problem in itself. It also includes methodology for the analysis of short snippets of time-dynamic observations, due to the need to come to quick conclusions under limited observation time, which is a feature of many current longitudinal studies in biomedical fields.

越来越需要对时间动态和纵向数据的样本进行适当的统计分析方法，这些数据包括随时间记录的高维物体和其他复杂物体。这些数据出现在许多关键关注领域，在这些领域中，适当的量化复杂模式随时间变化的方法与得出正确的结论有关。这包括对环境和气候变化以及社会网络随时间演变的研究。它还包括被认为在大脑“中枢”之间运作的生物网络，这些网络随着人的年龄而变化。这些数据的结构与先前在功能数据分析的统计领域中开发的已建立的线性建模方法相违背。因此，研究者和他的研究小组正在开发新的方法，旨在分析这种复杂的时间动态和纵向数据。这些技术将有助于更好地理解潜在的动态以及对象的固有模式和交互随时间的变化。更好地理解时间动态现象将导致更明智的社会和个人决策。该研究还包括对学生进行前期方法的培训，并创建合适的快速算法来实现这些新方法。功能数据分析已建立的领域集中在线性方法，如功能线性主成分分析。然而，这些已建立的模型对“下一代”功能数据的适用性非常有限。这是因为这些数据本质上是非线性的，即它们不存在于线性空间中，因此比线性数据复杂得多。第二代功能数据是通过科学和电子商务以及在线设置、监测和传感器系统中持续记录信号和轨迹的在线和物理跟踪设备产生的。时变“对象数据”的重要类型是协方差矩阵、密度或网络，并且将开发新的方法来适当地量化这些复杂对象的动态。除了这些对象的非欧几里得性质外，由于缺少数据或不规则采样方案，许多纵向研究中可用数据的稀疏性也带来了额外的挑战。本研究解决了这些问题和挑战，并将通过开发原则性和理论上支持的方法来分析这些更复杂的数据类型，从而导致量化复杂动态可变性的技术。该研究将有助于分析和理解社会和生物网络的时间动态，以及其他时间索引对象，以及高维功能数据的分析。该研究包括功能数据分类的新方法，这本身就是一个越来越重要的问题。由于需要在有限的观察时间内快速得出结论，这是当前生物医学领域许多纵向研究的一个特点，因此它还包括对时间动态观察的短片段进行分析的方法。