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Introduction | Example Data Sets | References AbstractThis paper provides a suite of datasets from standard multivariate distributions and simple high-dimensional geomtric shapes that can be used to familiarize new users of grand tour visualizations. It contains Quicktime and Gif animations of 1-D, 2-D, 3-D, 4-D and 5-D grand tours, links to starting XGobi or XLispStat on the calibration data sets, and C code for generating a grand tour.The purpose of the paper is two-fold: providing code for the grand tour that others could pick up and modify (it is not easy to code this version which is why there are very few implementations currently available), and secondly, provide a variety of training datasets to help new users get a visual sense for high-dimensional data. IntroductionThe grand tour is a method for viewing multivariate data "from all sides". As originally proposed by Asimov (1985) it is a movie of data projections, where the viewer is shown a continuous sequence of d-dimensional projections of the p-dimensional data. The dimension of the projection can be 1, 2, 3, ... , p. Currently there are implementations of grand tours available in XGobi (Swayne, Cook and Buja, 1997), XLispStat (Tierney, 1991)and ExplorN (Carr, Wegman and Luo, 1996).Grand tour examples Here are some examples of a grand tour running on a small seven dimensional dataset. This is the primeval form of the grand tour, a la Asimov (1985). They are purely movies with fixed play speed and no user interaction. Gif animations of points at the corners of a nine dimensional cube are available through the links if you are viewing this on a platform that doesnt support quicktime.
A Note: The animated gifs run through the grand tour sequence once. They should show smooth changes to the image as the animation runs, but it may appear jerky and non-smooth over the net. To re-run it you need to reload. The quicktime movies used through out this paper allow better control of each animation. These examples illustrate tours implemented using the algorithm in Buja, Cook, Asimov, Hurley (1997). They are geodesic tours that contain no "within-projection-plane" spin, which is optimal for viewing tours where d is less than p . This is the type of tour implemented in XGobi , with the main difference being that XGobi is capable of 2-D projections only. Example Data SetsWays to view the data If you have your web browser set up to recognize quicktime movies then you can simply click the animation image to start downloading and viewing the moives. If you have your web browser set up to recognize files with a .xgobi extension then you can simply click the XGobi button beside the data explanations below. (You'll need the latest version of XGobi, at least the Oct 1997 beta release for this to work correctly.) If you have your web browser set up to recognize files with a .xli extension as XLispStat, then you can simply click the XLispStat button beside the data explanations below. This will start up a tour in XLispStat on the dataset. Compile C code to compute arbitrary dimension projection vectors for composing a grand tour and display results in S/S-Plus. Samples from Standard Multivariate Distributions
Note: Variables need to be scaled together (min/max over all measurements is used) in the viewing transformation so that variance difference are reflected. In XGobi, this is achieved by creating a file with the extension .vgroups with each row having a 1 in the the first place and nothing else on the line. The number of rows should match the number of variables. To maintain the scale differences in the latter two datasets we have used a trick: two points are added to the top of the data files which delimit the min/max values of the variables with the largest variances. These appear as two anomalous data points floating far from other points in the grand tour, visually distracting but they work to force XLispStat, and XGobi initiated from the web browser, to keep the variable scales relevant to each other.
Simple Geometric Shapes
Challenge Data SetsThese data sets can be viewed on line through an applet with the button, or downloaded to view using XGobi or XLispStat.
AcknowledgementsThis work began with the writing of code to run a grand tour with arbitrary dimensional projections for use in the C2 Virtual Reality Lab at Iowa State University. It is possible as a result of the work in Buja, Cook, Asimov and Hurley (1997) which describes the algorithm. The work here can be viewed as an adjunct to that paper.Thanks to Dr Sigbert Klinke for valuable feedback on the material in this paper. The author was supported by National Science Foundation grants DMS9632662 and DMS9214497. ReferencesAsimov, D. (1985) The Grand Tour: A Tool for Viewing Multidimensional Data, SIAM Journal of Scientific and Statistical Computing, 6(1):128-143. Buja, A., Cook, D., Asimov, D., Hurley, C. (1997) Dynamic Projections in High-Dimensional Visualization: Theory and Computational Methods, Journal of Computational and Graphical Statistics, submitted. Carr, D. B. and Wegman, E. J. and Luo, Q. (1996) ExplorN: Design Considerations Past and Present, Technical Report No. 129, Center for Computational Statistics, George Mason University . Swayne, D. F., Cook, D., Buja, A. (1998) XGobi: Interactive Dynamic Graphics in the X Window System, Journal of Computational and Graphical Statistics, 7(1):113-130. See also www.research.att.com/areas/stat/xgobi/. Tierney, L. (1991), LispStat: An Object-Orientated Environment for Statistical Computing and Dynamic Graphics, Wiley, New York, NY. |
