Topology identification of complex networks from noisy time series using ROC curve analysis

As it is known, there is various unknown information in most real world networks, such as uncertain topological structure and node dynamics. Thus how to identify network topology from dynamical behaviors is an important inverse problem for physics, biology, engineering, and other science disciplines. Recently, with the help of noise, a method to predict network topology has been proposed from the dynamical correlation matrix, which is based on a general, one-to-one correspondence between the correlation matrix and the connection matrix. However, the success rate of this prediction method depends on the threshold, which is related to the coupling strength and noise intensity. Different coupling strength and noise intensity result in different success rate of prediction. To deal with this problem, we select a desirable threshold to improve the success rate of prediction by using Receiver Operating Characteristic (ROC) curve analysis. By the technique of ROC curve analysis, we find that the accuracy and efficiency of topology identification is mainly determined by coupling strengths. The success rate of estimation will be reduced if the coupling is too weak or too strong. The presence of noise facilitates topology identification, but the noise intensity is not always crucial to the effectiveness of topology identification.