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 high- dimensional 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-y- scatterplots, 3-D data rotations, and grand tours, while sections can be approximated in existing sys- tems by scatterplot brushing and painting. Thus this paper is in part an investigation into the princi- ples underlying these techniques.