Collaborative Research: Statistical Analysis of Partially Observed Shapes in Two Dimensions

形状分类在许多领域都有重要的应用。例如，人类学家利用动物牙齿化石的形状分类来重建过去的环境，利用石器形状的变化来评估不同的技术策略。其他应用包括基于叶子形状的植物分类和肿瘤形状的识别。虽然有许多统计工具可用于分类，但大多数方法都是基于完整形状的，用于部分观察或不完整形状的方法相对较少。这个项目的重点是发展新的统计方法，基于多重输入的思想，用于分析部分观察到的形状。该项目建议作为一个起点，利用非参数的、热甲板式的对由未标记点和/或函数定义的形状进行多次插值的思想，而不是使用传统的多次插值方法的由地标定义的形状。该方法将部分观察到的形状与完全观察到的形状进行匹配，在与部分形状匹配良好的形状中随机选择一个完全观察到的供体形状，然后用供体形状不匹配的部分补全部分形状。将进行仿真研究，比较不同部分匹配方法的相对优点。该归算框架将使用来自牛科的牙齿进行测试，牛科的分类在生物人类学中对标本分类群的识别起着重要作用，而这反过来又用于重建古环境。该奖项反映了美国国家科学基金会的法定使命，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。

Classification of shapes has many important applications in a variety of fields. For example, anthropologists use shape classification on fossilized faunal teeth to reconstruct past environments and on variation in the shapes of stone tools to assess different technological strategies. Other applications include classification of plants based on the shape of their leaves and identification of shapes of tumors. While there are many statistical tools that can be used for classification, most methods are based on complete shapes with relatively few methods available for partially observed or incomplete shapes. This project focuses of the development of new statistical methodology, based on the ideas of multiple imputation, for the analysis of partially observed shapes.This project proposes as a starting point leveraging the ideas of nonparametric, hot-deck type multiple imputation to shapes that are defined by unlabeled points and/or functions, as opposed to shapes defined by landmarks where traditional methods of multiple imputation may be applied. The proposed method involves matching partially observed shapes to fully observed shapes, randomly choosing a fully observed donor shape among the shapes that are good matches for the partial shape, and then completing the partial shape with the unmatched part of the donor shape. A simulation study will be conducted to compare the relative merits of different partial matching methods. The imputation framework will be tested using teeth from the Family Bovidae, whose classification plays an important role in biological anthropology for identifying the taxa of specimens, which in turn is used to reconstruct paleoenvirnoments.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.