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The Grand Tour in k-Dimensions

  • Edward J. Wegman

Abstract

The grand tour introduced by Asimov (1985) is based on the idea that one method of searching for structure in d-dimensional data is to “look at it from all possible angles,” more mathematically, to project the data sequentially in to all possible two-planes. The collection of two-planes in a d-dimensional space is called a Grassmannian manifold. A key feature of the grand tour is that the projection planes are chosen according to a dense, continuous path through the Grassmannian manifold which yields the visual impression of points moving continuously.

Of course, while the grand tour just described will reveal non-random two-dimensional structure, it may not be particularly helpful in isolating higher dimensional structure. We propose the k-dimensional grand tour in d-dimensions, where k ≤ d. We give basic algorithms for computing a continuous sequence through the Grassmannian manifold of k-flats. We use the k-dimensional parallel coordinate display to represent visually the projections of the data into k-flats.

Keywords

Basis Vector Grassmannian Manifold Generalize Rotation Dynamic Graphic Rotate Coordinate System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Edward J. Wegman
    • 1
  1. 1.Center for Computational StatisticsGeorge Mason UniversityFairfaxUSA

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