The Grand Tour in k-Dimensions
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.
KeywordsBasis Vector Grassmannian Manifold Generalize Rotation Dynamic Graphic Rotate Coordinate System
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