一种改进的有间隔流形ISOMAP算法

ISOMAP算法成功应用的潜在条件是要求数据集均匀抽样于单个的内在流形。如果数据集均匀采样于某个内在流形，但内部出现了一个间隔，ISOMAP算法可能失效。提出了G-ISOMAP(ISOMAP with a Gap)算法，该算法充分利用了数据集中的间隔特性。首先检测被间隔的子流形间最短欧氏距离对应的数据点，然后将这些数据点互相设置为邻域点，最后用ISOMAP算法找到低维嵌入结果。对G-ISOMAP与ISOMAP算法的区别与联系进行了详细的理论说明，得出ISOMAP算法是G-ISOMAP算法的一个特例，G-ISOMAP算法是ISOMAP算法扩充的结论。实验结果验证了该算法比其他常用的流形学习算法在有间隔的数据集上更有效。

Improved ISOMAP for a Single Manifold with a Gap

ISOMAP algorithm could have been applied successfully on uniform-density dataset drawn from a single manifold. However,given a uniform-density dataset with a gap,ISO MAP fails possibly. In this paper,G-ISOMAP(ISOMAP with a Uap)algorithm was presented, which exploits characteristic of the gap in the dataset. The algorithm first finds pairs of data points, whose Euclidean distances arc shortest between the separated submanifolds, and then makes them neighbors each other. At last, ISOMAP algorithm is applied to find low dimensional embedding structure. The theoretical discussion on difference and relationship between G-ISOMAP and ISOMAP can be given and it is concluded that ISOMAP is a special case of G-ISOMAP algorithm and G-ISOMAP is an extension of ISO MAP algorithm. The experimental results show that the proposed algorithm is best among the frectuently used manifold learning algorithms on several datasets with a gap.