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.
Stratification learning can be considered as an unsupervised, exploratory, clustering process that infers a decomposition of data sampled from a stratified space into disjoint subsets that capture recognizable and meaningful structural information. In recent years, there have been significant efforts in computational topology that are relevant to stratification learning. In this talk, I will give an overview of such efforts. In particular, I will discuss stratification learning using persistent local homology, discrete Stratified Morse theory, and sheaves.