Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. To this end, during the encoding process, we commence by utilizing the hard node assignment to decompose a sample graph into a family of separated subgraphs. We compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. On the other hand, during the decoding process, we adopt the soft node assignment to reconstruct the original graph structure by expanding the coarsened nodes. By hierarchically performing the above compressing procedure during the decoding process as well as the expanding procedure during the decoding process, the proposed HC-GAE can effectively extract bidirectionally hierarchical structural features of the original sample graph. Furthermore, we re-design the loss function that can integrate the information from either the encoder or the decoder. Since the associated graph convolution operation of the proposed HC-GAE is restricted in each individual separated subgraph and cannot propagate the node information between different subgraphs, the proposed HC-GAE can significantly reduce the over-smoothing problem arising in the classical convolution-based GAEs. The proposed HC-GAE can generate effective representations for either node classification or graph classification, and the experiments demonstrate the effectiveness on real-world datasets.

翻译：图自编码器（GAEs）是图表示学习的强大工具。本文提出了一种新颖的基于层次聚类的图自编码器（HC-GAE），能够学习用于图数据分析的有效结构特征。为此，在编码过程中，我们首先利用硬节点分配将样本图分解为一组分离的子图。我们将每个子图压缩为一个粗化节点，从而将原始图转化为粗化图。另一方面，在解码过程中，我们采用软节点分配通过扩展粗化节点来重建原始图结构。通过在编码过程中层次化执行上述压缩过程以及在解码过程中层次化执行扩展过程，所提出的HC-GAE能够有效提取原始样本图的双向层次结构特征。此外，我们重新设计了损失函数，使其能够整合来自编码器或解码器的信息。由于所提HC-GAE的图卷积操作被限制在每个独立的子图内，且无法在不同子图间传播节点信息，因此该模型能显著缓解传统基于卷积的GAEs中出现的过度平滑问题。所提出的HC-GAE能够为节点分类或图分类任务生成有效表示，实验在真实数据集上验证了其有效性。