DMS 9631351 Wegman This research focuses on the development of a synthetic environment to be used as a tool for exploring data. The synthetic environment will be constructed from and involve the integration of a number of exploratory data analysis tools some of which have already been created, some of which will be created under the scope of this research. Topic areas being explored include 1) a fractal-based grand tour, 2) 1-dimensional grand tour for images and random fields, 3) visualization using two- and three- dimensional wavelets, 4) exploratory signal analysis, and 5) visualization of huge data sets. Mathematical issues being addressed include a new method for constructing grand tours so that all the tour spends equal time in all regions of the multidimensional space and a new methodology for integrating multivariate (multispectral) image data into a single image. Computational issues being addressed include the establishment of a new metaphor for data exploration involving the creation of a data world and portals through regions of it. The research uses three-dimensional models extensively. %%% This research focuses on the exploitation of virtual reality techniques for the analysis of statistical and stochastic data. The thesis of this research is that virtual reality offers a better technology for human-computer interaction as it relates to exploratory analysis than does the desktop metaphor. Virtual reality technology not only offers a much more compelling visual focus than does a standard computer screen, but also a more complete engagement of the investigator with the data world. The major thrust of this research is to combine scientific visualization, exploratory data analysis and virtual reality into a new technology for exploring data. The plan is to create a data world made of analysis modules that can be accessed directly simply by moving from one domain within the data world to another domain via port als. As one moves seamlessly from one domain to the next through a portal, the current data set will be ported into the appropriate analysis or representation technique. The data explorer will be able to interact with the data in the current representation, either directly and/or by means of icons. The main task of this project will be to create a total synthetic environment for the exploratory analysis of data. The impact of this work should be wide ranging. The interactive focus on high-dimensional data analysis has immediate impact on settings where large amounts of multiattribute data are collected. Settings such as biotechnology (e.g. human genome), NASA's EOS-DIS and similar projects (e.g. monitoring global change), manufacturing settings in which many parameters are monitored in both the design and production processes, and materials science where optimization involving a large number of parameters of materials mixtures are examples of data amenable to the type of analyses being facilitated with this research. ***
