Learning a Joint Manifold Representation from Multiple Data Sets

The problem we address in the paper is how to learn a joint representation from data lying on multiple manifolds. We are given multiple data sets and there is an underlying common manifold among the different data set. We propose a framework to learn an embedding of all the points on all the manifolds in a way that preserves the local structure on each manifold and, in the same time, collapses all the different manifolds into one manifold in the embedding space, while preserving the implicit correspondences between the points across different data sets. The proposed solution works as extensions to current state of the art spectral-embedding approaches to handle multiple manifolds.