Inferring a Drive-Response Network from Time Series of Topological Measures in Complex Networks with Transfer Entropy

Abstract

Topological measures are crucial to describe, classify and understand complex networks. Lots of measures are proposed to characterize specific features of specific networks, but the relationships among these measures remain unclear. Taking into account that pulling networks from different domains together for statistical analysis might provide incorrect conclusions, we conduct our investigation with data observed from the same network in the form of simultaneously measured time series. We synthesize a transfer entropy-based framework to quantify the relationships among topological measures, and then to provide a holistic scenario of these measures by inferring a drive-response network. Techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy are synthesized to deal with challenges such as time series being nonstationary, finite sample effects and indirect effects. We resort to kernel density estimation to assess significance of the results based on surrogate data. The framework is applied to study 20 measures across 2779 records in the Technology Exchange Network, and the results are consistent with some existing knowledge. With the drive-response network, we evaluate the influence of each measure by calculating its strength, and cluster them into three classes, i.e., driving measures, responding measures and standalone measures, according to the network communities.

Inferring Weighted Directed Association Networks from Multivariate Time Series with the Small-Shuffle Symbolic Transfer Entropy Spectrum Method

“…Of course, there are many more methods for association networks inference and we have not mentioned above, such as neural network [28], SparCC (Sparse Correlations for Compositional data) [29], S-estimator [30,31], Maximal Information Coefficient (MIC) [32], Local Similarity Analysis (LSA) [33,34], Transfer Entropy [35][36][37], and so on. They all showed some excellent performance through experiment and observation.…”

“…Because each strategy applies different assumptions, they each have different strengths and limitations and highlight complementary aspects of the network. Some of these popular tools are non-directional, e.g., correlation or partial correlation, mutual information measures and Bayesian Networks, thus these measures cannot satisfy one's directed association networks inference study [36]. Granger causality has acquired preeminent status in the study of interactions and is able to detect asymmetry in the interaction.…”

“…Symbolic transfer entropy uses a convenient rank transform to find an estimate of the transfer entropy on continuous data without the need for kernel density estimation. Since slow drifts do not have a direct effect on the ranks, it still works well for non-stationary time series [36]. Due to the fact the time delay is underdetermined, the symbolic transfer entropy is calculated n times for each pair of time series.…”

“…This characteristic is based on the theory of hypothesis testing which is often used in surrogate data methods [31,36,39,42]. Discriminating statistics are necessary for surrogate data hypothesis testing.…”

“…Discriminating statistics are necessary for surrogate data hypothesis testing. The cross correlation and average mutual information were selected as discriminating statistics in [41,42], and partial symbolic transfer entropy in [36]. In this paper, we consider transfer entropy as the discriminating statistics.…”