Convolutional neural networks (CNNs) can be applied to graph similarity matching, in which case they are called graph CNNs. Graph CNNs are attracting increasing attention due to their effectiveness and efficiency. However, the existing convolution approaches focus only on regular data forms and require the transfer of the graph or key node neighborhoods of the graph into the same fixed form. During this transfer process, structural information of the graph can be lost, and some redundant information can be incorporated. To overcome this problem, we propose the disordered graph convolutional neural network (DGCNN) based on the mixed Gaussian model, which extends the CNN by adding a preprocessing layer called the disordered graph convolutional layer (DGCL). The DGCL uses a mixed Gaussian function to realize the mapping between the convolution kernel and the nodes in the neighborhood of the graph. The output of the DGCL is the input of the CNN. We further implement a backward-propagation optimization process of the convolutional layer by which we incorporate the feature-learning model of the irregular node neighborhood structure into the network. Thereafter, the optimization of the convolution kernel becomes part of the neural network learning process. The DGCNN can accept arbitrary scaled and disordered neighborhood graph structures as the receptive fields of CNNs, which reduces information loss during graph transformation. Finally, we perform experiments on multiple standard graph datasets. The results show that the proposed method outperforms the state-of-the-art methods in graph classification and retrieval.

本文提出基于混合高斯模型的无序图卷积神经网络（DGCNN）解决现有卷积方法在处理不规则形状的图数据时可能丢失结构信息和引入冗余信息的问题，实现了卷积核与图结点之间的映射，结合前向处理层和反向传播算法提高了信息处理效率，该方法在多个标准图数据集上的分类和检索任务中表现优于现有方法。

DGCNN：基于高斯混合模型的无序图卷积神经网络