How I Lost My Fear of Flying (Navigation with an Autopilot)

Abstract


This talk will begin by visualizing all US air traffic for a 24 hour period, a total of more than 40,000 aircraft. We will look globally in a traditional way, at first. Then we will look locally, a non-traditional approach. And finally we will view these data from the cockpit of one of the aircraft. Utilizing the metaphor of a pilot navigating an aircraft through the air, we will then visualize a flight through more arbitrary multivariate data. To overcome the weakness of projections for visualizing high-dimensional and/or nonlinear structures, we use a continuously changing sequence of projections of local regions. Such localizations may capture singularities in data as relatively simple substructures which can be seen in low-dimensional projections. We have developed an automatic procedure which pieces together local projections created from strategically chosen orientations. The procedure consists of two main steps: (1) estimating the best orientation at each location, and (2) sequentially rotating the orientations to create continuous projections (while retaining as much information from the first step as possible). We also have a manual procedure which can be used as a complement to the automatic procedure. While the manual procedure can explore only a 3-dimensional subspace at a time, it enables the viewer to incorporate global ideas about the data together with the local behavior of the automatic procedure. This is joint work with Shingo Oue of Hitosubashi University, Tokyo, Japan.

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