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A visibility graph transforms time series into graphs, facilitating signal processing by advanced graph data mining algorithms. In this paper, based on the classic limited penetrable visibility graph method, we propose a novel mapping method named circular limited penetrable visibility graph, which replaces the linear visibility line in limited penetrable visibility graph with nonlinear visibility arc for pursuing more flexible and reasonable mapping of time series. Tests on degree distribution and some common network features of the generated graphs from typical time series demonstrate that our circular limited penetrable visibility graph can effectively capture the important features of time series and show higher robust classification performance than the traditional limited penetrable visibility graph in the presence of noise. The experiments on real-world time-series datasets of radio and electroencephalogram signals also suggest that the structural features provided by a circular limited penetrable visibility graph, rather than a limited penetrable visibility graph, are more useful for time-series classification, leading to higher accuracy. This classification performance can be further enhanced through structural feature expansion by adopting subgraph networks. All of these results demonstrate the effectiveness of our circular limited penetrable visibility graph model.

Radio modulation classification is widely used in the field of wireless communication. In this paper, in order to realize radio modulation classification with the help of the existing ImageNet classification models, we propose a radio–image transformer which extracts the instantaneous amplitude, instantaneous phase and instantaneous frequency from the received radio complex baseband signals, then converts the signals into images by the proposed signal rearrangement method or convolution mapping method. We finally use the existing ImageNet classification network models to classify the modulation type of the signal. The experimental results show that the proposed signal rearrangement method and convolution mapping method are superior to the methods using constellation diagrams and time–frequency images, which shows their performance advantages. In addition, by comparing the results of the seven ImageNet classification network models, it can be seen that, except for the relatively poor performance of the architecture MNASNet1_0, the modulation classification performance obtained by the other six network architectures is similar, indicating that the proposed methods do not have high requirements for the architecture of the selected ImageNet classification network models. Moreover, the experimental results show that our method has good classification performance for signal datasets with different sampling rates, Orthogonal Frequency Division Multiplexing (OFDM) signals and real measured signals.

Our digital world is full of time series and graphs which capture the various aspects of many complex systems. Traditionally, there are respective methods in processing these two different types of data, e.g., Recurrent Neural Network (RNN) and Graph Neural Network (GNN), while in recent years, time series could be mapped to graphs by using the techniques such as Visibility Graph (VG), so that researchers can use graph algorithms to mine the knowledge in time series. Such mapping methods establish a bridge between time series and graphs, and have high potential to facilitate the analysis of various real-world time series. However, the VG method and its variants are just based on fixed rules and thus lack of flexibility, largely limiting their application in reality. In this paper, we propose an Adaptive Visibility Graph (AVG) algorithm that can adaptively map time series into graphs, based on which we further establish an end-to-end classification framework AVGNet, by utilizing GNN model DiffPool as the classifier. We then adopt AVGNet for radio signal modulation classification which is an important task in the field of wireless communication. The simulations validate that AVGNet outperforms a series of advanced deep learning methods, achieving the state-of-the-art performance in this task.