Analyses and applications of optimization methods for complex network reconstruction

Abstract

Inferring the topology of a network from observable dynamics is a key topic in the research of complex network. With the observation error considered, the topology inferring is formulated as a connectivity reconstruction problem that can be solved through optimization estimation. It is found that the different optimization methods should be selected to deal with the different degrees of noise, different scales of observable time series and such other situations when it comes to the problem of connectivity reconstruction, which has not been analyzed and discussed before yet. In this paper, four regression methods, namely least squares, ridge, lasso and elastic net, are used to solve the problem of network reconstruction in different situations. In particular, a further analysis is made of the effects of each regression method on the network reconstruction problem in detail. Through simulation of a variety of artificial and real networks, as it has turned out, the four regression methods are effective in respect to network reconstruction when certain conditions are respectively satisfied. Based on the experimental results, it is possible to reach some interesting conclusions that can guide our readers to know the internal mechanisms for network reconstruction and choose the appropriate regression method in accordance with the actual situation and existing knowledge.