Abstract: Kernel ISOMAP algorithms have relatively good generalization ability, but cannot be used to classify multiple manifolds directly. Within the multi-manifold structure, to judge the manifolds of new data points precisely is the basis to obtain good generalization ability, so this paper proposes a kernel ISOMAP algorithm suitable to classify multiple manifolds. This algorithm can judge the manifolds of new data points precisely, based on the similarities between neighboring local tangent spaces on the same manifold；in addition, it also simplifies the computation of the low-dimensional representations of new data points in the current kernel ISOMAP algorithms. Consequently, this algorithm has good generalization ability. Finally, experimental results show that this algorithm has higher classification accuracy.

Key words: multi-manifold learning, kernel ISOMAP, minimal spanning tree, local tangent space, constant-shifting

摘要： 核等距映射（Kernel ISOMAP）算法具有较好的泛化性能，但不能直接用于多流形的分类。在多流形下，准确判定新数据点所在的流形是其获得良好泛化性能的基础，因此，提出了能够用于多流形分类的核等距映射算法。该算法根据同一流形上邻近局部切空间的相似性能够准确判定新数据点所在的流形，并对目前核等距映射算法中新数据点低维表示的计算过程进行了简化，从而具有良好的泛化性能。实验结果证实，该算法具有较高的分类准确率。

关键词: 多流形学习, 核等距映射, 最小生成树, 局部切空间, 常数平移