A Domain Decomposition Method for Fast Manifold Learning

Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)

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Zhenyue Zhang, Hongyuan Zha


We propose a fast manifold learning algorithm based on the methodology of domain decomposition. Starting with the set of sample points partitioned into two subdomains, we develop the solution of the interface problem that 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.