Manifold structure analysis of Internet traffic matrix based on E-Isomap

With the advent of big data, the Internet data traffic has taken over people´s lives. How to analyze these mass data has become an imperative problem to be solved recently. Traffic matrix has been a useful traffic model for addressing a variety of problems from the whole-network perspective. The principal challenge presented by Origin-Destination (OD) traffic matrix is that OD traffic matrix usually forms a high dimensional multivariate structure. In this paper we introduce an improved Isomap algorithm, Efficient-Isomap (E-Isomap), which is a much more efficient nonlinear dimension reduction tool than the classic Isomap, then we apply E-Isomap to real OD traffic matrix taken from the backbone network (Abilene). The simulation results show that the high-dimensional OD traffic matrix has a small intrinsic dimension and there indeed exists a low-dimensional manifold structure. The computing analysis and residual variance analysis indicate that E-Isomap is capable of finding the manifold structure of the high-dimensional OD traffic matrix more efficiently in keeping accuracy constant.