Zhong Jianqi, Cao Wenming
Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University, Shenzhen, 518060, China.
State Key Laboratory of Radio Frequency Heterogeneous Integration, Shenzhen University, Shenzhen, 518060, China.
Sci Rep. 2025 Jan 2;15(1):170. doi: 10.1038/s41598-024-84483-0.
Graph neural networks (GNNs) have emerged as a prominent approach for capturing graph topology and modeling vertex-to-vertex relationships. They have been widely used in pattern recognition tasks including node and graph label prediction. However, when dealing with graphs from non-Euclidean domains, the relationships, and interdependencies between objects become more complex. Existing GNNs face limitations in handling a large number of model parameters in such complex graphs. To address this, we propose the integration of Geometric Algebra into graph neural networks, enabling the generalization of GNNs within the geometric space to learn geometric embeddings for nodes and graphs. Our proposed Graph Geometric Algebra Network (GGAN) enhances correlations among nodes by leveraging relations within the Geometric Algebra space. This approach reduces model complexity and improves the learning of graph representations. Through extensive experiments on various benchmark datasets, we demonstrate that our models, utilizing the properties of Geometric Algebra operations, outperform state-of-the-art methods in graph classification and semi-supervised node classification tasks. Our theoretical findings are empirically validated, confirming that our model achieves state-of-the-art performance.
图神经网络（GNNs）已成为一种用于捕捉图拓扑结构和建模顶点到顶点关系的重要方法。它们已被广泛应用于包括节点和图标签预测在内的模式识别任务中。然而，在处理来自非欧几里得域的图时，对象之间的关系和相互依赖性变得更加复杂。现有的GNNs在处理此类复杂图中的大量模型参数时面临局限性。为了解决这个问题，我们提出将几何代数集成到图神经网络中，使GNNs能够在几何空间内进行泛化，以学习节点和图的几何嵌入。我们提出的图几何代数网络（GGAN）通过利用几何代数空间内的关系来增强节点之间的相关性。这种方法降低了模型复杂性，并改善了图表示的学习。通过在各种基准数据集上进行的广泛实验，我们证明，我们的模型利用几何代数运算的特性，在图分类和半监督节点分类任务中优于现有方法。我们的理论发现得到了实证验证，证实我们的模型达到了现有方法的性能。
