# Geometry-V-Sub: An Efficient Graph Attention Network Struct Based Model for Node Classification
## 1 Introduction  
With the implementation and practice of machine learning in other fields, more and more data research has been extended to the field of graph structure data representation and learning. Because of its natural logic and relational representation, graph structure has increasingly appeared in various interdisciplinary fields. Datasets with graph structure data, such as Cora [1, 2], citeseer [3], PubMed [4]; Datasets PPI in biomedical field [5]; Data sets of social relations and community discovery spamme [6], Reddit [5], etc. Therefore, a large number of models and algorithms applied to graph learning have been developed. In the current models, most of the models used for graph classification tasks originate from graph convolution network (GCN) or its improved version. For example, spectral-based graph convolution neural networks (such as Spectral CNN [7], ChebNet [8], 1 st ChebNet [9]) and spatial based graph convolution neural networks (such as message passing neural networks (MPNN) [10], GraphSage [5], diffusion revolution neural networks (DCNN) [11]) and graph attention networks (such as Graph Attention Network(GAT) [12] Gated Attention Network (GAAN) [13], etc.). Graph convolution network based on spectrum is an earlier network structure, which has more research results and theoretical basis. Graph convolution based on spectrum [7] treats graph structure data as signals, and maps graph data in spatial domain to frequency domain for convolution. In the initial research results, the process of Fourier transform convolution inverse Fourier transform is used for calculation [8]. The disadvantage is that it requires many computing resources and needs to calculate the whole map, so it is not suitable for large-scale map inference and directed graph calculation. In the follow-up work, Chebyshev polynomial and 1 st ChebNet are used to reduce the need of computing power [9]. Because the features decomposition of the Laplace matrix used inthe derivation process needs to meet the condition that the Laplace matrix is a symmetric matrix, this improvement still cannot be inferred directly on the directed graph. If the directed graph inference is carried out by this method, it needs to convert the directed graph into an undirected graph to reason, and thus the direction information will be lost. If the inference is carried out by cutting the sub-graph, the slight change of the graph structure data will lead to a huge difference in the generation of Laplace matrix. However, in the follow-up work [14], the author improved the graph convolution network to a certain extent, so that it can deal with directed graphs, and also took a step in the scientific research results of spectrum-based graphs. In addition, the improved spectrum-based graph convolution network includes adaptive graph convolution network (AGCN) [15] and dual graph convolution network (DGCN) [16]. In order to solve the limitations faced by the spectrum-based graph convolution network, the space-based graph convolution network Neural Network for Graphs (NN4G) [17] was first proposed. It realizes graph convolution by directly accumulating the features of adjacent nodes. Due to the use of non-standardized adjacency matrix, the value may be unstable. In order to make this GCN interpretable, a probabilistic model based on NN4G, Contextual Graph Markov Model(CGMM) [18], was proposed; the contribution of this article is that CGMM not only maintains spatial locality, but also has probabilistic interpretability. Diffusion Convolutional Neural Network (DCNN) [11] and Graph Diffusion Convolution (GDC) [19] are both propagated by using the power series of probability transfer matrix. The final propagation features are related to the distance (the distance between node A and node B is a few nodes), which can reflect the dependence of a node on the importance of remote nodes; the difference is that DCNN splices the final results, while DGC sums the final results.