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Convolutional neural networks (CNNs) can be applied to graph similaritymatching, in which case they are called graph CNNs. Graph CNNs are attractingincreasing attention due to their effectiveness and efficiency. However, theexisting convolution approaches focus only on regular data forms and requirethe transfer of the graph or key node neighborhoods of the graph into the samefixed form. During this transfer process, structural information of the graphcan be lost, and some redundant information can be incorporated. To overcomethis problem, we propose the disordered graph convolutional neural network(DGCNN) based on the mixed Gaussian model, which extends the CNN by adding apreprocessing layer called the disordered graph convolutional layer (DGCL). TheDGCL uses a mixed Gaussian function to realize the mapping between theconvolution kernel and the nodes in the neighborhood of the graph. The outputof the DGCL is the input of the CNN. We further implement abackward-propagation optimization process of the convolutional layer by whichwe incorporate the feature-learning model of the irregular node neighborhoodstructure into the network. Thereafter, the optimization of the convolutionkernel becomes part of the neural network learning process. The DGCNN canaccept arbitrary scaled and disordered neighborhood graph structures as thereceptive fields of CNNs, which reduces information loss during graphtransformation. Finally, we perform experiments on multiple standard graphdatasets. The results show that the proposed method outperforms thestate-of-the-art methods in graph classification and retrieval.

DGCNN: Disordered Graph Convolutional Neural Network Based on the Gaussian Mixture Model