High-dimensional density ridges for hippocampus shape analysis
Skeletal representations (s-reps) have been successfully adopted to parsimoniously parametrize the shape of three-dimensional objects, and have been particularly employed in analyzing hippocampus shape variation. Within this context, we provide a fully-nonparametric dimension-reduction tool based on kernel smoothing for determining the main source of variability of hippocampus shapes parametrized by s-reps. The methodology introduces the so-called density ridges for data on the polysphere (a high-dimensional product of spheres) and involves addressing manifold computational challenges through closed formulae, efficient programming, and computational tricks.
Palabras clave: Density ridges Dimension reduction Directional data Nonparametric Statistics Skeletal representations.