Abstract: 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.

Key words: Manifold learning, ISOMAP, Manifold with a gap