In order to perform network analysis tasks, representations that capture the most relevant information in the graph structure are needed. However, existing methods learn representations that cannot be interpreted in a straightforward way and that are relatively unstable to perturbations of the graph structure. We address these two limitations by proposing node2coords, a representation learning algorithm for graphs, which learns simultaneously a low-dimensional space and coordinates for the nodes in that space. The patterns that span the low dimensional space reveal the graph's most important structural information. The coordinates of the nodes reveal the proximity of their local structure to the graph structural patterns. We measure this proximity with Wasserstein distances that permit to take into account the properties of the underlying graph. Therefore, we introduce an autoencoder that employs a linear layer in the encoder and a novel Wasserstein barycentric layer at the decoder. Node connectivity descriptors, which capture the local structure of the nodes, are passed through the encoder to learn a small set of graph structural patterns. In the decoder, the node connectivity descriptors are reconstructed as Wasserstein barycenters of the graph structural patterns. The optimal weights for the barycenter representation of a node's connectivity descriptor correspond to the coordinates of that node in the low-dimensional space. Experimental results demonstrate that the representations learned with node2coords are interpretable, lead to node embeddings that are stable to perturbations of the graph structure and achieve competitive or superior results compared to state-of-the-art unsupervised methods in node classification.

中文翻译：

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node2coords：使用Wasserstein重心的图形表示学习

为了执行网络分析任务，需要在图形结构中捕获最相关信息的表示形式。但是，现有方法学习的表示形式无法直接解释，并且对于图结构的扰动相对不稳定。我们通过提出node2coords（图的表示学习算法）来解决这两个限制，该算法同时学习一个低维空间和该空间中节点的坐标。跨越低维空间的图案揭示了图形的最重要的结构信息。节点的坐标揭示了其局部结构与图结构模式的接近度。我们使用Wasserstein距离测量这种接近度，从而可以考虑基础图的属性。因此，我们介绍了一种自动编码器，该编码器在编码器中使用线性层，在解码器中使用新颖的Wasserstein重心层。捕获节点本地结构的节点连通性描述符通过编码器传递，以学习一小组图结构模式。在解码器中，将节点连接性描述符重构为图结构模式的Wasserstein重心。节点连接性描述符的重心表示的最佳权重对应于该节点在低维空间中的坐标。实验结果表明，使用node2coords学习的表示形式是可解释的，