Populations of Complex Objects, Visualization and Smoothing

复杂对象的群体、可视化和平滑

• 批准号: 9971649
• 负责人: James Marron
• 金额: $ 20.8万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2002-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971649&HistoricalAwards=false
• 关键词: Populations; Complex; Objects; Visualization; Smoothing

DMS-9971649The need for understanding the structure of populations of complex objects, including curves, images and surfaces, is becoming increasingly clear, especially as automatic data gathering capabilities are burgeoning in many fields. Research into functional data analytic methods is proposed to address this need. An important part of this thrust will be in the direction of robust methods, where few of the standard methods are applicable because of the very high dimensionality coupled with small sample sizes. New visualization methods are needed for functional data analysis, when the objects are images and surfaces. Creative visualization ideas are proposed in a different direction in the proposed work on smoothing. The central issue for real data applications of smoothing is which features in the smooth are really there? SiZer was one such methodology, and a variety of improvements are proposed. New visual paradigms will be developed for the challenging and important cases of dependent data and two dimensional smoothing. Work is also proposed on studying the mathematical statistical underpinnings of SiZer, and related methods.The proposed work is motivated by problems in opthalmology, computer science, software engineering, and geology. The work in ophthalmology and computer science is on finding statistical and visual methods for gaining insight into the structure of populations of complex objects. Possible types of objects are very diverse, with work under way on images representing corneal curvature and on shape representations of corpus collosa. The methods developed are expected to be useful in many other fields, but an immediate benefit will be improved diagnosis of kerataconus and schizophrenia. The work in software engineering and geology is a combination of visualization and smoothing methods to find, and verify, unexpected structure in data. For example one newly developed method, both establishes a link between perfective maintenance and decreased fault rate in software engineering, and also provides the first statistically significant connection between glaciation and volcanism. Another newly developed method shows how legacy software systems age, and also gives statistical proof of periods of extinction of mollusks, due to climatic changes.

DMS-9971649了解包括曲线、图像和曲面在内的复杂对象群体结构的需求变得越来越明显，特别是在许多领域的自动数据收集能力迅速发展的情况下。功能数据分析方法的研究正是为了满足这一需求而提出的。这一努力的一个重要部分将是稳健性方法的方向，其中很少有标准方法适用，因为维度很高，加上样本量很小。当对象是图像和表面时，需要新的可视化方法来进行功能数据分析。在提出的平滑工作中，从不同的方向提出了创造性的可视化思想。平滑在实际数据应用中的中心问题是，平滑中到底有哪些功能？Sizer就是这样一种方法，并提出了各种改进建议。对于相关数据和二维平滑的具有挑战性和重要的情况，将开发新的视觉范例。还建议研究SIZER的数理统计基础和相关方法。建议的工作是由眼科学、计算机科学、软件工程和地质学问题推动的。眼科学和计算机科学的工作是寻找统计和视觉方法，以洞察复杂物体的群体结构。可能的物体类型非常不同，正在研究代表角膜曲率的图像和代表舌体形状的图像。所开发的方法有望在许多其他领域有用，但立竿见影的好处将是改进对圆锥角膜和精神分裂症的诊断。软件工程和地质学的工作是可视化和平滑方法的结合，以发现和验证数据中的意外结构。例如，一种新开发的方法，既在软件工程中建立了完美的维护和降低故障率之间的联系，也提供了冰川作用和火山作用之间的第一个统计上显著的联系。另一种新开发的方法显示了遗留软件系统是如何老化的，并提供了由于气候变化而导致的软体动物灭绝周期的统计证据。