Abstract: Since 2000,a series of nonlinear dimensionality reduction methods have been emerging,and Isomap in manifold learning is one of the representatives.The algorithm can reflect the global structure of the data set and is simple and efficient.But there are some shortcomings that low-dimensional manifold must be convex set and the computational complexity is large.L-Isomap successfully reduces the computational complexity,but majority of the landmarks is selected by random method,which makes the algorithm unstable.In this paper,according to the classical theoremes that bounded closed set is equivalent to compact set in finite-dimensional space and there is finite sub-coverage covering the compact set,we analyzed the topology of the area of the data set and selected a series of landmarks.This method has low computational complexity and is more stable than L-Isomap.In addition,this method weakens the condition that the data set is a convex set to a compact set (bounded closed set),which avoids enlarging “the hollow” error in the incomplete manifold.

Key words: Manifold learning,Isomap,Landmark points,Compact