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，人类学家使用化石动物牙的形状分类来重建过去的环境，并根据石器形状的变化来评估不同的技术策略。其他应用包括根据植物叶片的形状对植物进行分类，以及识别肿瘤的形状。虽然有许多统计工具可以用于分类，但大多数方法都是基于完整的形状，对于部分观察到的或不完整的形状可用的方法相对较少。这个项目的重点是开发新的统计方法，基于多重填充的思想，用于部分观察到的形状的分析。该项目提出了一个起点，利用非参数的热板式多重填充的思想来定义由未标记的点和/或函数定义的形状，而不是由地标定义的形状，在那里可以应用传统的多重填充方法。所提出的方法包括将部分观察到的形状匹配到完全观察到的形状，从与该部分形状良好匹配的形状中随机选择完全观察到的施主形状，然后用该施主形状的不匹配部分来完成该部分形状。将进行仿真研究，比较不同部分匹配方法的相对优点。将使用牛科的牙齿来测试分配框架，这些牙齿的分类在生物人类学中扮演着重要的角色，用于识别标本的分类，进而用于重建古环境。这一奖项反映了NSF的法定使命，并通过使用基金会的智力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.