Incremental selection of the neighborhood size for ISOMAP

The success of ISOMAP depends greatly on selecting a suitable neighborhood size; however, itpsilas an open problem how to do this efficiently. When the neighborhood size becomes unsuitable, shortcut edges can be introduced into the neighborhood graph and destroy the approximation ability of the involved shortest-path distances to the corresponding geodesic distances greatly. Itpsilas obvious that shortcut edge links two endpoints lying close in Euclidean space but far away on the manifold, which can be measured approximately by its order presented in this paper. Based on the observation, this paper presented an efficient method to find a suitable neighborhood size incrementally, which doesn´t need to compute shortest-path distances or run the MDS algorithm as those methods based on residual variance do. Finally, the feasibility of this method can be verified by experimental results.