Visualisation of high-dimensional spaces with application to econometric data and models

Abstract

The grand tour, guided tour and manual tour are used to sample projections of high-dimensional space. These are excellent for understanding the overall shape of structures, and differences between groups, in the space. The grand tour algorithm consists of a sequence of projections of the object space R^p onto a viewing space R^d. Often d=2, i.e., the object is mapped onto planes, but technically d might be 1, 2, 3, or larger. To be precise, denote G(d, p) to be the Grassmann manifold of d-dimensional planes in R^p. Defining it as G(d, p), ensures that within-plane rotation is removed from the sequence of views. There is new software to conduct tours in R. This talk discusses using the tour to examine multivariate distributions, dimension reductions, and cognostics describing high-dimensional time series.