Riemannian Locally Linear Embedding with Application to Kendall Shape Spaces

Locally Linear Embedding is a dimensionality reduction method which relies on the conservation of barycentric alignments of neighbour points. It has been designed to learn the intrinsic structure of a set of points of a Euclidean space lying close to some submanifold. In this paper, we propose to generalise the method to manifold-valued data, that is a set of points lying close to some submanifold of a given manifold in which the points are modelled. We demonstrate our algorithm on some examples in Kendall shape spaces.