Shape Statistics and Data Mining

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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.