The Grand Tour in k-Dimensions
- 429 Downloads
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
Unable to display preview. Download preview PDF.
- Buja, A. and Asimov, D. (1985), “Grand tour methods: an outline,” Computer Science and Statistics: Proceedings of the Seventeenth Symposium on the Interface, D. Allen, ed., Amsterdam: North Holland, 63–67Google Scholar
- Buja, A., Hurley, C. and McDonald, J. A. (1986), “A data viewer for multivariate data,” Computer Science and Statistics: Proceedings of the Eighteenth Symposium on the Interface, T. Boardman, ed., Alexandria, VA: American Statistical Association, 171–174Google Scholar
- Foley, J., van Dam, A., Feiner, S. and Hughes, J. (1990), Computer Graphics: Principles and Practice (2nd Edition), Reading, Mass.: Addison-WesleyGoogle Scholar
- Wegman, E. J. and Bolorforoush, M. (1990) Mason Hypergraphics, Fairfax Station, VA: Professional Statisticians Forum (MS-DOS software)Google Scholar