Visualising high-dimensional spaces with application to particle physics models

Abstract

The grand tour, guided tour and manual tourare 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 Rp onto a viewing space Rd. 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 Rp. Defining it as G(d, p), ensures that within-plane rotation is removed from the sequence of views. This talk will discuss new work in adapting tour methods to examine multi-parameter models from particle physics. As experiments in physics get more sophisticated and precise, one is commonly confronted with the problem of interpreting the results in terms of models with multiple parameters. The difficulty of these comparisons between predictions and measurements increases enormously with the dimensionality of the parameter space. In response to these challenges, experimental collaborations have, for the most part, developed tools appropriate for their specific needs. The average theorist, on the other hand, still resorts to simply dropping all but one or two of the relevant parameters. Although this is a very useful way to guide analysis, it misses possible multivariate dependencies. Results obtained in this manner often produce many cluttered plots that are difficult to interpret or understand. Tours can help to examine the results in more than two dimensions. The new developments include ways to conduct guided tours to search for mismatches in distribution in high-dimensions, and new software for conducting tours in R.