Characterization Of Physiological Signals From The Perspective Of Complex Networks Based On Geometric Invariability

Time series and complex networks are two kinds of describe paradigms in complex systems. With the growing of achievements appeared in these two areas, people gradually put their eyes on mutual and representation between complex network and time series. We expect to achieve the evolution regular of dynamical systems based on different complex systems framework. Therefore, this paper discusses and studies nonlinear time series based on the theory of complex networks system and equivalent representation from time series to complex networks. We also investigate the dynamics evolution of time series in complex network. This research presents another important method, which is different from the existing linear theory and nonlinear phase-space reconstruction. Information equivalence transformation is critical in the representation process form time series to complex networks.Combined with the actual characteristics of physiological signals and complex networks, this paper mainly focuses on the equivalent representation from physiological signals to complex networks and then verifies the divisibility of physiological signals space and the impacts of complex network connectivity on divisibility of cyberspace. We derive the continuous mapping which preserves the geometric invariability. Then we prove the mapping condition required for topological equivalence and finally verify the geometric invariant representation from physiological signal to complex cyberspace within the allowable threshold range. We notice that it can achieve linear consistency through the geometry invariance for the simulated Lorenz system and practical ECG time series. In addition, by comparison of correlation dimension of the time series and network representation generated by Lorenz system, it further validates the consistency of correlation dimension from both perspectives. This paper correspondingly employs the distance of linear and correlation dimension to determine the optimal range of threshold.Based on geometric invariant transformation from physiological signals to complex network, we transform the ECG data from the open ECG database to its network domain. Then we move a time window to partition ECG data and transform the segmented data to complex network. We analyze the distribution, clustering coefficient, edge density and other statistical indicators of complex network transformed from the ECG data. By using equivalent representation, we apply the nonlinear fitting of the network statistical characteristics to these series of windows. It can indicate the different ECG signal regions corresponding to their pathological features, thereby capturing the evolution of the dynamics hidden in the ECG system. Thus, we propose a discrimination index and conversion process parameters to characterize human ECG dynamic from the perspective of networks. Such analysis and observation of complex network is able to identify clinical pathological diagnosis hidden in human physiological data.At the same time, the paper analyzes and verifies another representation from time series to complex network--visibility graph, which is not based on the geometric invariant and correspondingly cannot guarantee equivalence of the conversion. Experimental results show that the same statistics shows low sensitivity and poor robustness for data with disease symptom. Slight fluctuation in sampling points will cause significant changes of the network index. We, therefore, conclude that visible graph is relatively unreliable for identification of physiological data, in comparison with the previous conversion method.