关键词: 数据可视化, ISOMAP, 邻域大小, 残差, 短路边, 序, 广度优先搜索, ,

Abstract: The success of the ISOMAP algorithm depends greatly on the suitable selection of its only one parameter，i.e.the neighborhood size；however，it’s an open problem how to do this efficiently.When the neighborhood size becomes unsuitable，shortcut edge can be introduced into the neighborhood graph and destroy the approximation ability of the involved shortest-path distances to the corresponding geodesic distances greatly.Unlike non-shortcut edge，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 presents an efficient method to find a suitable neighborhood size，which only requires running the breadth-first search algorithm incrementally，but doesn’t need to run the whole ISOMAP algorithm for every possible neighborhood size as those methods based on residual variance do.Finally，the feasibility of this method can be verified by experimental results.

Key words: data visualization, ISOMAP, neighborhood size, residual variance, shortcut edge, order, breadth-first search