Grand Tour (data visualisation)

The Grand Tour is a technique developed by Daniel Asimov (1985) which is used to explore multivariate statistical data by means of an animation. The animation consists of a series of distinct views of the data as seen from different directions, displayed on a computer screen, that appear to change continuously and that get closer and closer to all possible views. This allows a human- or computer-based evaluation of these views, with the goal of detecting patterns that will convey useful information about the data.

Technical description

Each "view" (i.e., frame) of the animation is an orthogonal projection of the data set onto a 2-dimensional subspace of the Euclidean space R^p where the data resides. The subspaces are selected by taking small steps along a continuous curve, parametrized by time, in the space of all 2-dimensonal subspaces of R^p, known as the Grassmannian G(2,p). To display these views on a computer screen, it is necessary to pick one particular rotated position of each view (in the plane of the computer screen) for display. This causes the positions of the data points on the computer screen to appear to vary continuously. Asimov showed that these subspaces can be selected so as to make the set of them (up to time t) increasingly close to all points in G(2,p), so that if the animation were allowed to run indefinitely, the set of displayed subspaces would correspond to a dense subset of G(2,p).