Many classes of high-dimensional data are of interest to the Air Force. Social, computer, or command and control networks for cyberspace are some of the areas of interest, as are dynamic biological systems. As data sets get larger and more complex, the amount of data to display becomes an intractable problem as even the largest display cannot adequately show all information. However, a mathematically modeled system can be visualized and displayed on smaller scales or from differing perspectives. As an example, standard graphical practice shows only three dimensions at a time in a graph (e.g., x, y, and z). However, there are various methods to model higher-dimensional data such as those techniques found in computational geometry, computational statistics, and more. Visualization of network or system data needs to be taken to the next level, where visualization techniques are added to high-dimensional modeling or dimensional reduction to allow users to explore and understand the data. This is often referred to as visual analytics and the emphasis is on enhancing analytic reasoning by way of visualization techniques. However, we feel that the mathematics should be the backbone for the visualization, which would then be paired with an intuitive and interactive front-end, so a user would not need to understand higher order mathematics to utilize the visualization. We are interested in this cross road between optimal user interface, mathematics, and visualization of large, complex data sets.
Mathematical modeling; Statistical modeling; Complex systems; Information visualization; Visual analytics; Dimensional reduction; Computational geometry; Computational statistics;
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