A fundamental question in the study of high-dimensional data is as
follows: Given high-dimensional point cloud samples, how can we infer
the structures of the underlying data?
In manifold learning, we assume the data is supported by a
low-dimensional space with a manifold structure.
However, such an assumption may be too restrictive in practice when we are given point cloud samples not of a manifold but of a stratified space, which contain singularities and mixed dimensionality.