Mutual Information and Multidimensional Scaling as Means to Reconstruct Network Topology

Complex networked systems, such as mobile telecommunication networks, may have disturbance modes in which a large number of network nodes interact coherently. We are developing an appropriate statistical model to analyse stochastic disturbances in such networked systems. We present studies on a simple statistical state model based on Ising model known from statistical physics. We discuss how the network topology can be reconstructed from data, a crucial step in analysis of coherent systems. In particular, we apply multidimensional scaling (MDS) with statistical significance of mutual information (SSMI) as similarity measure to reveal the logical topology. We apply our method both to synthetic and real data, and show that MDS provides useful information about the topology when both the interactions between network nodes and the direct loading of nodes are relevant for the node state; that is when the net work can neither be described as a single state system nor as a system consisting of independent elements