Graph and hypergraph representation learning has attracted increasing attention from various research fields. Despite the decent performance and fruitful applications of Graph Neural Networks (GNNs), Hypergraph Neural Networks (HGNNs), and their well-designed variants, on some commonly used benchmark graphs and hypergraphs, they are outperformed by even a simple Multi-Layer Perceptron. This observation motivates a reexamination of the design paradigm of the current GNNs and HGNNs and poses challenges of extracting graph features effectively. In this work, a universal feature encoder for both graph and hypergraph representation learning is designed, called UniG-Encoder. The architecture starts with a forward transformation of the topological relationships of connected nodes into edge or hyperedge features via a normalized projection matrix. The resulting edge/hyperedge features, together with the original node features, are fed into a neural network. The encoded node embeddings are then derived from the reversed transformation, described by the transpose of the projection matrix, of the network's output, which can be further used for tasks such as node classification. The proposed architecture, in contrast to the traditional spectral-based and/or message passing approaches, simultaneously and comprehensively exploits the node features and graph/hypergraph topologies in an efficient and unified manner, covering both heterophilic and homophilic graphs. The designed projection matrix, encoding the graph features, is intuitive and interpretable. Extensive experiments are conducted and demonstrate the superior performance of the proposed framework on twelve representative hypergraph datasets and six real-world graph datasets, compared to the state-of-the-art methods. Our implementation is available online at https://github.com/MinhZou/UniG-Encoder.

翻译：图和超图表示学习已引起各研究领域的广泛关注。尽管图神经网络（GNNs）、超图神经网络（HGNNs）及其精心设计的变体在常见基准图和超图上表现优异且应用丰富，但在某些情况下，即使是简单的多层感知器（MLP）也优于它们。这一观察促使我们重新审视当前GNN和HGNN的设计范式，并提出了有效提取图特征的挑战。本研究设计了一种用于图和超图表示学习的通用特征编码器，称为UniG-Encoder。该架构首先通过归一化投影矩阵将连接节点的拓扑关系正向变换为边或超边特征。生成的边/超边特征与原始节点特征一同输入神经网络。接着，通过投影矩阵转置描述的反向变换，从网络输出中导出编码后的节点嵌入，进而可用于节点分类等任务。与传统的基于谱域和/或消息传递的方法不同，所提架构以高效统一的方式同时全面利用节点特征和图/超图拓扑，覆盖同配图和异配图。设计的投影矩阵用于编码图特征，直观且可解释。大量实验表明，与最先进方法相比，所提框架在十二个代表性超图数据集和六个真实世界图数据集上具有优越性能。我们的实现已在https://github.com/MinhZou/UniG-Encoder上公开。