Network structure detection using convergent cross mapping on multivariate time series

Abstract

The recent developments in measurement techniques have allowed us to observe multidimensional time series data in various fields. Thus, detecting causal relations between elements from multidimensional time series data is useful for prediction, model generation, and system control. In addition, causal relations between elements can be detected to estimate network connections. In other words, the network structure can be estimated from multidimensional time series data by using causality detection methods. Among the several methods for detecting causality, Granger causality is a well-known method that is widely used for causal estimation between time series. On the other hand, a method called convergent cross mapping (CCM) has been proposed, which can distinguish causality from pseudo-correlation. It is important to investigate whether CCM will be effective with increased number of elements, even though the evaluation of its performance with a few elements has been reported in the literature. Moreover, it is important to evaluate the performance with changing dynamics of the elements. In this study, to estimate the connectivity between elements in complex networks, we apply CCM to mathematical models of complex networks, or the Watts-Strogatz model. In particular, we investigate how complex network structures affect causal estimation, by applying CCM to multidimensional time series data produced from complex networks. According to the results, we find the connectivity estimation accuracies in the regular ring-lattice network to be slightly higher than those in random networks. Furthermore, we reveal that it is easier to perform connectivity estimation for a network with a community structure than a random structure.