A flow based approach for learning multiple manifolds

Abstract

In this paper, we investigate the problem of learning multiple overlapped manifolds from data samples with noise. Learning low dimensional nonlinear manifolds embedded in high dimensional Euclidean space has been an important issue in many data driven pattern analysis applications. The work in this paper extends manifold learning into the complex situations where an unknown number of manifolds may overlap. The approach proposed introduces the notion of flow consisting of multi-agents in a formation exploring a smooth curve on a manifold and thus separating different manifolds. A flow generates an ordered sequence of neighborhoods visited by the agents and can be used to simplify elastic mapping to discover the principal manifold structures. Simulations in various settings demonstrate the effectiveness of the proposed approach.