中文摘要：

目前的监督多流形学习算法大多数都根据数据的类别标记对彼此间的距离进行调整，能较好实现多流形的分类，但难以成功展现各流形的内在几何结构，泛化能力也较差，因此文中提出一种基于等距映射的监督多流形学习算法。该算法采用适合于多流形的最短路径算法，得到在多流形下依然能正确逼近相应测地距离的最短路径距离，并采用Sammon映射以更好地保持短距离，最终可成功展现各流形的内在几何结构。此外，该算法根据邻近局部切空间的相似性可准确判定新数据点所在的流形，从而具有较强的泛化能力。该算法的有效性可通过实验结果得以证实。

英文摘要：

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.