A traditional approach for scientific discovery is to model a natural system mathematically then extrapolate new insights analytically. For models that are analytically intractable this is not possible. One approach to resolve this issue is called Parameter Space Exploration (PSE). The general idea is to perform mass simulations of a model over a uniform distribution of possible parameter inputs, then mine the resulting data to make inferences. Here I propose a methodology that combines PSE simulation with visualization and data mining to support interactive scientific discovery. Tools and techniques are described for supporting the analysis of very large, multidimensional databases. I evaluate and detail the applicability of pixelization, dimensional stacking, query based color maps, and a number of machine learning algorithms that accept human input for interactive analysis. These approaches have been used to investigate model neuron simulation data with the resulting images appearing in the Journal of Neurophysiology. They have also been implemented in a tool called NDVis (N-Dimensional Visualization Tool) which is now being used in graduate neuroscience classes at Emory University. Evaluation of the methods are based on two in-depth long term case studies in different data domains. This includes an attempt to generalize the approaches to non-simulation data sets.
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