One of the main challenges facing Astronomy today involves the organization and analysis of the vast volumes of data that has been provided by recent advances in computer and data-collecting technology. This project pools the efforts of researchers in computational geometry, machine learning, and astrophysics in order to develop and apply computational techniques to aid in the analysis and synthesis of astrophysical data. The goal of this project is to provide the astrophysical research community with computational techniques, embodied in a software system called AstroExplorer, for analyzing very large, complex, multi-parameter data sets. Specifically, this project will provide new paradigms for performing general kinds of data extraction, data synthesis across databases, and cluster analysis. All of the methods are based on the unifying framework of viewing data points and the operations that act upon them geometrically. This work extends the current database technology by providing methods for dealing with geometrical data. This approach should significantly improve the productivity of astronomers in their search through the oceans of data that have been produced by the revolution in data collection and storage, for it gives them a computational tool for extracting data that match specified geometric patterns or can be clustered by methods based on natural and intuitive geometric concepts.
