ABSTRACT
Data are often represented as vectors in a Euclidean space Rp. But frequently they possess more structure and treating them as Euclidean vectors may be inappropriate. A simple example of this instance is when data are normalized to have unit norm, and thereby put on the surface of the unit sphere Sp−1. Such data are better viewed as objects on a manifold, and when building mathematical models for them, it is often advantageous to exploit the geometry of the manifold (here Sp−1).
