Populations of Complex Objects, Visualization and Smoothing

点击翻译按钮获取中文摘要

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.