  A guided tour helps to visualise high-dimensional data by showing
low-dimensional projections along a projection pursuit optimisation path.
Projection pursuit is a generalisation of principal component analysis, in the
sense that different indexes are used to define the interestingness of the
projected data. While much work has been done in developing new indexes in the
literature, less has been done on understanding the optimisation. Index
functions can be noisy, might have multiple local maxima as well as an optimal
maximum, and are constrained to generate orthonormal projection frames, which
complicates the optimization. In addition, projection pursuit is primarily used
for exploratory data analysis, and finding the local maxima is also useful. The
guided tour is especially useful for exploration, because it conducts geodesic
interpolation connecting steps in the optimisation and shows how the projected
data changes as a maxima is approached. This work provides new visual
diagnostics for examining a choice of optimisation procedure, based on the
provision of a new data object which collects information throughout the
optimisation. It has helped to diagnose and fix several problems with
projection pursuit guided tour. This work might be useful more broadly for
diagnosing optimisers, and comparing their performance. The diagnostics are
implemented in the R package, ferrn.
