A Domain Decomposition Method for Fast Manifold Learning

We propose a fast manifold learning algorithm based on the methodology ofdomain decomposition. Starting with the set of sample points partitioned into two subdomains, we develop the solution of the interface problemthat can glue the embeddings on the two subdomains into an embedding on the whole domain. We provide a detailed analysis to assess the errors produced by the gluing process using matrix perturbation theory.Numerical examples are given to illustrate the efficiency and effectiveness of the proposed methods.