AvgNet: Adaptive Visibility Graph Neural Network and Its Application in Modulation Classification

“In the simulations, we use cross-entropy loss function and Adam [44] optimizer.”

“The former is used to describe the topological structure of many complex systems, where nodes represent subsystems and links capture the relationship between them, leading to the emergence of complex networks [1], [2]; while the latter is used to capture the temporal dynamics of these systems.”

“These graphs are drawn by Gephi [44], and the layout is OpenOrd [44].”

“It is worth noting that, due to the great success of GNN [34], [35], [36], [37] and effective graph mapping methods, it would be also an exciting direction to first map time series into graphs and then utilize powerful GNN to classify them.”

“Fortunately, by introducing graph data mining technologies, we can detect and filter the false information and purify the Internet environment to certain extent [8], [9].”

“What’s more, we use PyTorch Geometric [43], a geometric deep learning extension library for PyTorch, to build the neural network layers of DiffPool in our AVGNet model.”

“It is worth noting that, due to the great success of GNN [34], [35], [36], [37] and effective graph mapping methods, it would be also an exciting direction to first map time series into graphs and then utilize powerful GNN to classify them.”

“[38] proposed the natural Visibility Graph (VG) algorithm for mapping time series into graphs to analyze time series from a new point of view, whose process is shown in Fig.”

“Besides, O’Shea et al. [30] also used a residual neural network for modulation classification, namely CNN1D.”

“In the simulation, we mainly use GAF, MTF, CD, CNN2D and CNN1D mentioned in Sec.”

“• X. Yang is with the Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China, and also with the Science and Technology on Communication Information Security Control Laboratory, Jiaxing 314033, China (E-mail: yxn2117@126.com). the graph kernel methods, which are mainly based on rand…”

“[26] proposed a two-layer Long Short Term Memory (LSTM) model for automatic modulation classification, which has considerable accuracy but is relatively time-consuming.”

“• X. Yang is with the Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China, and also with the Science and Technology on Communication Information Security Control Laboratory, Jiaxing 314033, China (E-mail: yxn2117@126.com). the graph kernel methods, which are mainly based on rand…”

“…Security Control Laboratory, Jiaxing 314033, China (E-mail: yxn2117@126.com). the graph kernel methods, which are mainly based on random walk [10], path [11] and subtree [12]; The second one is graph embedding methods, such as subgraph2vec [13] and graph2vec [14]; And the last one is deep…”

“[39] proposed the improved mapping algorithm, Horizontal Visibility Graph (HVG), and Gao et al.”

“It is worth noting that, due to the great success of GNN [34], [35], [36], [37] and effective graph mapping methods, it would be also an exciting direction to first map time series into graphs and then utilize powerful GNN to classify them.”

“The representative methods of graph classification can be divided into three types, the first one is the graph kernel methods, which are mainly based on random walk [10], path [11] and subtree [12]; The second one is graph embedding methods, such as subgraph2vec [13] and graph2vec [14]; And the last one is deep learni…”

“In the simulation, we mainly use GAF, MTF [28], CD [27], CNN2D [29], CNN1D [30], MCLDNN [31] and SigNet [32] mentioned in Sec.”

“In the simulation, we mainly use GAF, MTF [28], CD [27], CNN2D [29], CNN1D [30], MCLDNN [31] and SigNet [32] mentioned in Sec.”

“At present, biology, social science, computer science and other disciplines have a wealth of graph data [3], [4], [5], so that researchers can make full use of network analysis technologies to solve related problems in the corresponding fields.”

“Fortunately, by introducing graph data mining technologies, we can detect and filter the false information and purify the Internet environment to certain extent [8], [9].”

“For example, in the field of life science, there are interactions between biological molecules, based on which the complex biological networks can be established and the molecular properties can thus be predicted [6], [7].”

“The first is to use the RNN model to classify the signals, specifically, we use GRU and LSTM mentioned in Sec.”

“[33] used the spectrogram in the frequency domain feature to help classify.”

“For time series, here we mainly focus on modulation classification of radio signals [18], [19], [20], [21].”

“The representative methods of graph classification can be divided into three types, the first one is the graph kernel methods, which are mainly based on random walk [10], path [11] and subtree [12]; The second one is graph embedding methods, such as subgraph2vec [13] and graph2vec [14]; And the last one is deep learni…”

“[40] further introduced Limited Penetrable Visibility Graph (LPVG).”

“In the simulation, we mainly use GAF, MTF [28], CD [27], CNN2D [29], CNN1D [30], MCLDNN [31] and SigNet [32] mentioned in Sec.”

“For example, in the field of life science, there are interactions between biological molecules, based on which the complex biological networks can be established and the molecular properties can thus be predicted [6], [7].”

“In recent years, with the rapid development of deep learning, a number of neural network models have been introduced into this area [22], [23], [24].”

“For time series, here we mainly focus on modulation classification of radio signals [18], [19], [20], [21].”

“the graph kernel methods, which are mainly based on random walk [10], path [11] and subtree [12]; The second one is graph embedding methods, such as subgraph2vec [13] and graph2vec [14]; And the last one is deep learning methods, i.”

“In the future work, we may try to combine other graph classification models with AVG, or combine the graph data enhancement methods such as subgraph networks [45] in the field of network science, to further improve the classification performance of AVGNet.”

“For time series, here we mainly focus on modulation classification of radio signals [18], [19], [20], [21].”

“In recent years, with the rapid development of deep learning, a number of neural network models have been introduced into this area [22], [23], [24].”

“[41] further introduced circle system for the first time in the construction of VG, proposed Circular Limited Penetrable Visibility Graph (CLPVG), and realized higher accuracy in radio modulation classification with graph embedding technology than LPVG.”

“The representative methods of graph classification can be divided into three types, the first one is the graph kernel methods, which are mainly based on random walk [10], path [11] and subtree [12]; The second one is graph embedding methods, such as subgraph2vec [13] and graph2vec [14]; And the last one is deep learni…”

“For time series, here we mainly focus on modulation classification of radio signals [18], [19], [20], [21].”

“…deep neural networks (e.g., convolutional neural networks (CNNs) [40–44], recurrent neural networks (RNNs) [45–49], graph neural networks (GNNs) [50–52], transformers [53–55], and hybrid neural networks [56–59]) to perform the end-to-end feature 2 International Journal of Intelligent Systems…”

“…of DL in AMC, particularly through models, such as convolutional neural network (CNN) [7], recurrent neural networks (RNNs) [14], and graph neural network (GNN) [15], has facilitated the automated extraction of salient features from extensive data sets, substantially boosting performance.”

“These models include AvgNet [70], MCLDNN [39], Resnet1d, VGG [28], CNN2d [27], GRU [29], LSTM [8], GAF [59], and ConsCNN [62].”

“II-B and AVG [50] mentioned in Sec.”

“Recently, with the development of deep learning (DL) technology, DL-based models have made significant progress in AMR task [6], [7], [8], [9], [10], [11].”