Graph representation learning methods have attracted an increasing amount of attention in recent years. These methods focus on learning a numerical representation of the nodes in a graph. Learning these representations is a powerful instrument for tasks such as graph mining, visualization, and hashing. They are of particular interest because they facilitate the direct use of standard machine learning models on graphs. Graph representation learning methods can be divided into two main categories: methods preserving the connectivity information of the nodes and methods preserving nodes’ structural information. Connectivity-based methods focus on encoding relationships between nodes, with connected nodes being closer together in the resulting latent space. While methods preserving structure generate a latent space where nodes serving a similar structural function in the network are encoded close to each other, independently of them being connected or even close to each other in the graph. While there are a lot of works that focus on preserving node connectivity, only a few works focus on preserving nodes’ structure. Properly encoding nodes’ structural information is fundamental for many real-world applications as it has been demonstrated that this information can be leveraged to successfully solve many tasks where connectivity-based methods usually fail. A typical example is the task of node classification, i.e., the assignment or prediction of a particular label for a node. Current limitations of structural representation methods are their scalability, representation meaning, and no formal proof that guaranteed the preservation of structural properties. We propose a new graph representation learning method, called Structural Iterative Representation learning approach for Graph Nodes ( SIR-GN ). In this work, we propose two variations ( SIR-GN: GMM and SIR-GN: K-Means ) and show how our best variation SIR-GN: K-Means : (1) theoretically guarantees the preservation of graph structural similarities, (2) provides a clear meaning about its representation and a way to interpret it with a specifically designed attribution procedure, and (3) is scalable and fast to compute. In addition, from our experiment, we show that SIR-GN: K-Means is often better or, in the worst-case comparable than the existing structural graph representation learning methods present in the literature. Also, we empirically show its superior scalability and computational performance when compared to other existing approaches.

中文翻译：

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SIR-GN：一种用于图节点的快速结构迭代表示学习方法

近年来，图表示学习方法引起了越来越多的关注。这些方法专注于学习图中节点的数字表示。学习这些表示是图挖掘、可视化和散列等任务的强大工具。它们特别有趣，因为它们有助于在图形上直接使用标准机器学习模型。图表示学习方法可以分为两大类：保留节点连通性信息的方法和保留节点结构信息的方法。基于连接的方法专注于编码节点之间的关系，连接的节点在生成的潜在空间中更靠近。虽然保留结构的方法会生成一个潜在空间，其中在网络中提供类似结构功能的节点彼此靠近编码，而与它们在图中的连接甚至彼此靠近无关。虽然有很多作品专注于保留节点连接性，但只有少数作品专注于保留节点的结构。正确编码节点的结构信息是许多实际应用的基础，因为已经证明可以利用这些信息成功解决许多基于连接的方法通常失败的任务。一个典型的例子是节点分类任务，即为节点分配或预测特定标签。当前结构表示方法的局限性在于它们的可扩展性、表示意义、并且没有正式的证据可以保证结构特性的保存。我们提出了一种新的图表示学习方法，称为图节点的结构迭代表示学习方法（SIR-GN）。在这项工作中，我们提出了两种变体（SIR-GN: GMM和SIR-GN：K-均值) 并展示我们的最佳变化SIR-GN：K-均值：（1）理论上保证图结构相似性的保留，（2）提供关于其表示的明确含义以及使用专门设计的归因程序来解释它的方法，以及（3）可扩展且计算速度快。此外，从我们的实验中，我们表明SIR-GN：K-均值通常比文献中现有的结构图表示学习方法更好，或者在最坏的情况下可比。此外，与其他现有方法相比，我们凭经验展示了其卓越的可扩展性和计算性能。