Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Our examples include graphs generated from 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data of real-world problems. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our method overcomes these issues by utilizing the pseudoinverse of the Laplacian. Another key ingredient is a low-rank approximation of the convolutional matrix, ensuring computational efficiency and increasing accuracy at the same time. We outline how the necessary eigeninformation can be computed efficiently in each applications and discuss the appropriate choice of the only metaparameter, the approximation rank. We finally showcase our method’s performance regarding runtime and accuracy in various experiments with real-world datasets.

图卷积网络（GCN）已被证明是对基于图的数据集进行半监督分类的成功工具。我们提出了一种新的GCN变体，其三部分过滤空间针对密集图。我们的示例包括从3D点云生成的图形，其中更多地关注非本地信息，以及基于现实问题分类数据的超图。这些图在其拉普拉斯图的光谱特性方面与普通的稀疏基准图不同。最值得注意的是，我们观察到大型eigengap，这对于现有的流行GCN体系结构而言是不利的。我们的方法通过利用拉普拉斯算子的伪逆来克服这些问题。另一个关键因素是卷积矩阵的低秩近似，同时确保计算效率和准确性。我们概述了如何必要eigeninformation能有效地在各个应用程序的计算和讨论的唯一metaparameter的适当选择，逼近排名。最后，我们在真实数据集的各种实验中展示了该方法在运行时间和准确性方面的性能。