Weighted Complex Network Based on Visibility Angle Measurement

Visibility graph (VG) is a widely applicable tool for studying complex time series due to its advantages of few parameters and easy implement. However, the topological links of VG based methods are roughly represented as binary states. In order to better inherit the advantages of visibility graph and more accurately dig out the internal characteristics of time series, a novel method of constructing an weighted complex network based on visibility angle measurement, i.e., visibility angle based weighted visibility graph (VA-WVG), is proposed. Firstly, the data points of the original time series are represented as the nodes of the complex network. Secondly, after judging that the two data points satisfying the visibility criterion, visibility angle between the two data points is measured, which is used as the weight of the network connection. Mapping logistic signals under different parameter settings into VA-WVG, and extracting the network feature of strength distribution entropy, we find that the VA-WVG can not only accurately discriminate periodic signals from the chaotic signals, but also can precisely reflect the number of periodic state solutions and complexity of chaotic state, while the traditional VG can only roughly distinguish between periodic states and chaotic states. Next, the proposed method is applied to classify different types of EEG signals. Combining the extracted features and support vector machine, we identify epileptic EEG signals from healthy EEG signals with classification accuracy of 100%, while the accuracy of the VG method is only 83.84%.