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arXiv 2203.05919cs.LG
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基于图神经网络的图摘要

Graph Summarization with Graph Neural Networks

Ulm University(乌尔姆大学);University of Essex(埃塞克斯大学)

Maximilian Blasi, Manuel Freudenreich, Johannes Horvath, David Richerby, Ansgar Scherp

摘要:

图摘要的目标是以结构化和紧凑的方式表示大型图。基于等价类的图摘要保留了$k$跳邻域内图顶点的预定义特征,例如顶点标签和边标签。基于这些邻域特征,顶点被分配到一个等价类。所分配的等价类的计算必须是对预定义特征的置换不变操作。这通过对特征值e进行排序来实现。例如,在一个实施例中,边缘标记(这在计算上是昂贵的),并且随后对结果进行散列。图神经网络(GNN)满足排列不变性要求。我们制定了一个子图分类任务的根顶点上的$k$跳邻域的图形摘要的问题。我们采用不同的GNN架构,基于流行的消息传递协议和替代方法,来执行结构图摘要任务。我们将不同的GNN与标准的多层感知器(MLP)和Bloom过滤器作为非神经方法进行比较。在我们的实验中,我们考虑了一个大型网络图上的四个流行的图摘要模型。这类似于具有挑战性的多类顶点分类任务,类的数量从$576$到数十万不等。我们的结果表明,GNN的性能彼此接近。在四分之三的实验中,非消息传递GraphMLP模型优于其他GNN。标准MLP的性能非常好,特别是在存在许多类的情况下。最后,Bloom过滤器的性能远远优于所有神经架构,除了具有最少数量的$576$类的数据集。

英文摘要:

The goal of graph summarization is to represent large graphs in a structured and compact way. A graph summary based on equivalence classes preserves pre-defined features of a graph's vertex within a $k$-hop neighborhood such as the vertex labels and edge labels. Based on these neighborhood characteristics, the vertex is assigned to an equivalence class. The calculation of the assigned equivalence class must be a permutation invariant operation on the pre-defined features. This is achieved by sorting on the feature values, e. g., the edge labels, which is computationally expensive, and subsequently hashing the result. Graph Neural Networks (GNN) fulfill the permutation invariance requirement. We formulate the problem of graph summarization as a subgraph classification task on the root vertex of the $k$-hop neighborhood. We adapt different GNN architectures, both based on the popular message-passing protocol and alternative approaches, to perform the structural graph summarization task. We compare different GNNs with a standard multi-layer perceptron (MLP) and Bloom filter as non-neural method. For our experiments, we consider four popular graph summary models on a large web graph. This resembles challenging multi-class vertex classification tasks with the numbers of classes ranging from $576$ to multiple hundreds of thousands. Our results show that the performance of GNNs are close to each other. In three out of four experiments, the non-message-passing GraphMLP model outperforms the other GNNs. The performance of the standard MLP is extraordinary good, especially in the presence of many classes. Finally, the Bloom filter outperforms all neural architectures by a large margin, except for the dataset with the fewest number of $576$ classes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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