The Grand Tour in k-Dimensions

Edward J. Wegman
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Edward J. Wegman: George Mason University, Center for Computational Statistics

A chapter in Computing Science and Statistics, 1992, pp 127-136 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2856-1_16

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DOI: 10.1007/978-1-4612-2856-1_16

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