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

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