A novel landmark point selection method for L-ISOMAP

Isometric feature mapping (ISOMAP) presents remarkable performance for nonlinear dimensionality reduction in diversified research domains. Landmark-ISOMAP(L-ISOMAP) has been proposed to improve the scalability of ISOMAP by performing the most complicated computations on a subset of points referred as to landmarks. In this paper, we present a novel landmark point selection method for L-ISOMAP. The approach first attempts to find a minimum set cover of the neighbourhood sets and get the corresponding data points, referred as to landmark candidate points. After that, it removes the points which belong to neighbour sets of other points from the candidate point set and then the remaining candidate points are the landmarks. We run several experiments on synthetic and physical data sets and the experiment results validate the effectiveness of our proposed method.