Deep learning models have achieved huge success in numerous fields, such as computer vision and natural language processing. However, unlike such fields, it is hard to apply traditional deep learning models on the graph data due to the `node-orderless' property. Normally, we use an adjacent matrix to represent a graph, but an artificial and random node-order will be cast on the graphs, which renders the performance of deep models extremely erratic and not robust. In order to eliminate the unnecessary node-order constraint, in this paper, we propose a novel model named Isomorphic Neural Network (IsoNN), which learns the graph representation by extracting its isomorphic features via the graph matching between input graph and templates. IsoNN has two main components: graph isomorphic feature extraction component and classification component. The graph isomorphic feature extraction component utilizes a set of subgraph templates as the kernel variables to learn the possible subgraph patterns existing in the input graph and then computes the isomorphic features. A set of permutation matrices is used in the component to break the node-order brought by the matrix representation. To further lower down the computational cost and identify the optimal subgraph patterns, IsoNN adopts two min-pooling layers to find the optimal matching. The first min-pooling layer aims at finding the best permutation matrix, whereas the second one is used to determine the best templates for the input graph data. Three fully-connected layers are used as the classification component in IsoNN. Extensive experiments are conducted on real-world datasets, and the experimental results demonstrate both the effectiveness and efficiency of IsoNN.

本文提出了一种名为同构神经网络（IsoNN）的新型模型，通过提取输入图与模板之间的图匹配同构特征来学习图表示，以消除节点顺序约束，并在广泛的基准数据集上进行了实验证明其在图分类任务中的有效性。

IsoNN: 图表示学习与分类的同构神经网络