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.
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
the computational topology relevant to stratification learning.
In this talk, I will give an overview of such efforts, and
discuss challenges and opportunities.
In particular, I will focus on stratification learning using local
homology, persistent homology, sheaves, and discrete stratified Morse