Abstract
Visualization provides insight through images [14], and can be considered as a collection of application specific mappings: problem domain → visual range. For the visualization of multivariate problems a multidimensional system of Parallel Coordinates is studied which provides a one-to-one mapping between subsets of N-space and subsets of 2-space. The result is a systematic and rigorous way of doing and seeing analytic and synthetic N-dimensional geometry. Lines in N-space are represented by N-1 indexed points. In fact all p-flats (planes of dimension p in N-space) are represented by indexed points where the number of indices depends on p and N. The representations are generalized to enable the visualization of polytopes and certain kinds of hypersurfaces as well as recognition of convexity. Several algorithms for constructing and displaying intersections, proximities and points interior/exterior/or on a hypersurface have been obtained. The methodology has been applied to visual data mining, process control, medicine, finance, retailing, collision avoidance algorithms for air traffic control, optimization and others.
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References
E.W. Bassett, Ibm’s ibm fix. Industrial Computing, 14 (41): 23–25, 1995.
A. Chatterjee, Visualizing Multidimensioal Polytopes and Topologies for Tolerances. Ph.D. Thesis USC, 1995.
A. Chatterjee, P. P. Das, and S. Bhattacharya, Visualization in linear programming using parallel coordinates. Pattern Recognition, 26–11: 1725–36, 1993.
J. Eickemeyer, Visualizing p-flats in N-space using Parallel Coordinates. Ph.D. Thesis UCLA, 1992.
C. Gennings, K. S. Dawson, W. H. Carter, and R. H. Myers, Interpreting plots of a multidimensional dose-response surface in a parallel coordinate systems. Biometrics, 46: 719–35, 1990.
C.K. Hung, A New Representation of Surfaces Using Parallel Coordinates. Submitted for Publication, 1996.
A. Inselberg, N-Dimensional Graphics, Part I - Lines and Hyperplanes, in IBM LASC Tech. Rep. G320–2711, 140 pages. IBM LA Scientific Center, 1981.
A. Inselberg, The plane with parallel coordinates. Visual Computer, 1: 69–97, 1985.
A. Inselberg, Parallel Coordinates: A Guide for the Perplexed, in Hot Topics Proc. of IEEE Conf. on Visualization, 35–38. IEEE Comp. Soc., Los Alamitos, CA, 1996.
A. Inselberg and B. Dimsdale, Parallel Coordinates: A Tool For Visualizing Multidimensional Geometry, in Proc. of IEEE Conf. on Vis. ‘80, 361–378. IEEE Comp. Soc., Los Alamitos, CA, 1990.
A. Inselberg and B. Dimsdale, Multidimensional lines i: Representation. SIAM J. of Applied Math., 54–2: 559–577, 1994.
A. Inselberg and B. Dimsdale, Multidimensional lines ii: Proximity and applications. SIAM J. of Applied Math., 54–2: 578–596, 1994.
A. Inselberg, M. Reif, and T. Chomut, Convexity algorithms in parallel coordinates. J. ACM, 34: 765–801, 1987.
B. H. Mccormick, T. A. Defanti, and M. D. Brown, Visualization in Scientific Computing. Computer Graphics 21–6, ACM SIGGRAPH, New York, 1987.
E. R. Tufte, The Visual Display of Quantitative Information. Graphic Press, Connecticut, 1983.
E. R. Tufte, Envisioning Information. Graphic Press, Connecticut, 1990.
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Inselberg, A. (1998). A Survey of Parallel Coordinates. In: Hege, HC., Polthier, K. (eds) Mathematical Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03567-2_13
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DOI: https://doi.org/10.1007/978-3-662-03567-2_13
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