Abstract：In manifold learning algorithms, the data are assumed to be aligned on a single manifold. The application of algorithms is limited due to the general distribution of practical datasets on multiple manifolds. In this paper, multi-manifold learning based on boundary detection(MBD) is proposed. By the proposed method, data of distribution on several manifolds are efficiently learned through boundary detection and intra and inter manifolds geodesic distances can be kept faithfully. Firstly the boundary of data manifolds is detected and then the dimensionality of the manifolds is reduced separately. Finally, low dimensional coordinates are relocated into a global coordinate system. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated through experiments on both synthetic and real datasets.
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