Prosection Views: Dimensional Inference through Sections and Projections

We present some basic properties of two general graphical techniques for constructing views of high-dimensional objects, projection and section. Projections can easily display aspects of structure that are only of low dimension, while sections, i.e., intersections of subspaces with a highdimensional object, can easily display structure of only low codimension (and hence often high dimension). However, compositions of sections and projections, here called prosections, can display aspects of structure of any intermediate dimension. These statements are relevant for data analysis: projections of data can be easily generated with x-yscatterplots, 3-D data rotations, and grand tours, while sections can be approximated in existing systems by scatterplot brushing and painting. Thus this paper is in part an investigation into the principles underlying these techniques. hhhhhhhhhhhhhhhhhh Authors’ Address: Bellcore, 445 South Street, P.O. Box 1910, Morristown, New Jersey, 07962-1910, USA We would like to thank Diane Duffy, Michael Littman, Adolfo Quiroz, John Schotland, Deborah Swayne, and Jeff Zacks for their comments on drafts of this paper. We owe special thanks to Deborah Swayne and Di Cook for their assistance with the XGobi software.