Shape Statistics and Data Mining

这个项目是处理统计方法的大型和复杂的数据集涉及形状方面。一个例子的方法相关的这个项目是PRIM（弗里德曼和费舍尔，1999年），一个流行的数据挖掘算法与广泛的可能的应用。PRIM已被应用于一些真实的世界问题，最近开发了两个修改（Becker和Fahrmeir（2001）和LeBlanc等人（2002））。然而，没有理论基础的算法存在，这可能会提供一个更深入的理解算法。提供PRIM及其修改的分析是拟议项目的一部分。事实上，初步分析显示，基于最小体积集的方法与更好理解的方法有密切联系。这个启示也显示了与“形状统计”的联系。在另一个子项目中，本课题将开发一种新的投影寻踪型降维方法，用于后续的分类或模式搜索.这项任务涉及算法和理论的挑战，并再次“形状”方面（模式，反模式等）。更一般地说，可以说，人们承认缺乏对大型和复杂数据集的许多统计方法的（理论）理解，加强这方面的知识被认为是统计学的一项重要任务（见Kettenring等人，2003年）。该项目旨在直接和间接地为这一任务做出贡献：（a）直接通过提供对现有数据挖掘程序的分析，（B）间接通过为大型复杂数据集开发新方法，包括支持统计理论。

This project is dealing with statistical methods for large and complex data setsinvolving shape aspects. One example for a method relevant to this projectis PRIM (Friedman and Fisher, 1999), a popular data mining algorithm witha wide range of possible applications. PRIM has been applied to serval real worldproblems and two modifications have recently been developed(Becker and Fahrmeir (2001) and LeBlanc et al. (2002)). Nevertheless,no theoretical foundation of the algorithm exists which might provide a deeperunderstanding of the algorithm. To provide such an analysis of PRIM and its modificationsis part of the proposed project. In fact, a preliminary analysis revealed a close connectionsto much better understood methods based on minimum volume sets. This revelationalso shows the connection to "shape statistics". In another subproject the investigatorwill develop a novel projection pursuit type method for dimension reduction which isaimed at subsequent classification or mode hunting. This task involves both algorithmicand theoretical challenges, and again "shape" aspects (modes, antimodes, etc.)come into play.In more general terms it can be said that there is an acknowledged lack of(theoretical) understanding of many statistical methods for large and complex datasets, and enhancing this knowledge is considered to be an important task of statistics(see Kettenring et al. 2003). This project is aimed at contributing tothis task both directly and indirectly: (a) directly by providing an analysis ofsome of the existing data mining procedures, and (b) indirectly by developingnovel methods for large and complex data sets including supportingstatistical theory.