Many irregular domains such as social networks, financial transactions, neuron connections, and natural language structures are represented as graphs. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. However, in many of the applications, the underlying graph changes over time and existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs based on a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results that establish the connection between the proposed tensor approach and spectral convolution of tensors are developed. Numerical experiments on real datasets demonstrate the usefulness of the proposed method for an edge classification task on dynamic graphs.

翻译：许多非常规领域,如社交网络、金融交易、神经连接和自然语言结构等,都以图表形式出现。近年来,各种图形神经网络(GNNs)被成功地应用于这些图表上的演示学习和预测。然而,在许多应用中,长期的基本图形变化和现有的GNNs都不足以处理这些动态图表。在本文件中,我们提出了一种新技术,用于学习基于高代数框架的动态图形嵌入。我们的方法扩展了流行的图形共变网络(GCN),以便利用最近提出的高压M产品技术来学习动态图形的演示。建立了拟议的高压方法与高压光谱相联的理论结果正在形成。关于真实数据集的数值实验显示了拟议方法在动态图表上的边缘分类任务中的有用性。