  Molecular structures of RNA molecules reconstructed from X-ray
crystallography frequently contain errors. Motivated by this problem we examine
clustering on a torus since RNA shapes can be described by dihedral angles. A
previously developed clustering method for torus data involves two tuning
parameters and we assess clustering results for different parameter values in
relation to the problem of so-called RNA clashes. This clustering problem is
part of the dynamically evolving field of statistics on manifolds. Statistical
problems on the torus highlight general challenges for statistics on manifolds.
Therefore, the torus PCA and clustering methods we propose make an important
contribution to directional statistics and statistics on manifolds in general.
