We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density in point clouds.
This leads to learning stratifications, that is, mixture of manifolds representing different characteristics and complexities in the data set. The basic idea relies on modelling the sample points as a process of Poisson mixtures. This framework allows a natural way to include regularizing restrictions. Theoretical asymptotic results for the model are presented as well. The presentation of the framework is complemented with artificial and real examples showing the importance of extending manifold learning to stratification learning.