A landmark selection method for L-Isomap based on greedy algorithm and its application

Isometric feature mapping (Isomap) is a widely-used nonlinear dimensionality reduction method, but it suffers from high computational complexity. L-Isomap is a variant of Isomap which is faster than Isomap. In this algorithm, a subset of points are chosen out of the total data points as landmark points so as to simplify the embedding computation. In this paper, we propose a novel landmark selection method for L-Isomap based on a greedy algorithm. Experiments performed on synthetic and physical data sets validate the effectiveness of the proposed method. Internet traffic matrix has been an effective model to analyzing the Internet. However, the Internet traffic matrix data usually possesses high dimensionality. In this paper, we apply the improved L-Isomap to the real Internet traffic matrix data to investigate its low-dimensional features. The experiment results show that the Internet traffic matrix has a small intrinsic dimension and there indeed exists a low-dimensional manifold structure.