The Grand Tour: A Tool for Viewing Multidimensional Data

Abstract

The grand tour is a method for viewing multivariate statistical data via orthogonal projections onto a sequence of two-dimensional subspaces. The sequence of subspaces is chosen so that it is dense in the set of all two-dimensional subspaces. Desirable properties of such sequences of subspaces are considered, and several specific types of sequences are tested for rapidity of becoming dense. Tabulations are provided of the minimum length of a grand tour sequence necessary to achieve various degrees of denseness in dimensions up to 20.