Abstract The existing supervised multi-manifold learning algorithms adjust the distances between data points according to their class labels, and hence the multiple manifolds can be classified successfully. However,the poor generalization ability of these algorithms results in unfaithful display of the intrinsic geometric structure of some manifolds. A supervised multi-manifold learning algorithm based on Isometric mapping (ISOMAP) is proposed. The shortest path algorithm suitable for the multi-manifold structure is used to compute the shortest path distances which can effectively approximate the corresponding geodesic distances even in the multi-manifold structure. Then, Sammon mapping is used to further preserve shorter distances in the low-dimensional embedding space. Consequently, the intrinsic geometric structure of each manifold can be faithfully displayed. Moreover, the manifolds of new data points can be precisely judged based on the similarities between neighboring local tangent spaces according to the local Euclidean nature of the manifold, and thus the proposed algorithm obtains a good generalization ability. The effectiveness of the proposed algorithm is verified by experimental results.
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2014, Vol. 27 
