Autoencoders based on Graph Neural Networks (GNNs) have garnered significant attention in recent years for their ability to extract informative latent representations, characterizing the structure of complex topologies, such as graphs. Despite the prevalence of Graph Autoencoders, there has been limited focus on developing and evaluating explainable neural-based graph generative models specifically designed for signed networks. To address this gap, we propose the Signed Graph Archetypal Autoencoder (SGAAE) framework. SGAAE extracts node-level representations that express node memberships over distinct extreme profiles, referred to as archetypes, within the network. This is achieved by projecting the graph onto a learned polytope, which governs its polarization. The framework employs a recently proposed likelihood for analyzing signed networks based on the Skellam distribution, combined with relational archetypal analysis and GNNs. Our experimental evaluation demonstrates the SGAAEs' capability to successfully infer node memberships over the different underlying latent structures while extracting competing communities formed through the participation of the opposing views in the network. Additionally, we introduce the 2-level network polarization problem and show how SGAAE is able to characterize such a setting. The proposed model achieves high performance in different tasks of signed link prediction across four real-world datasets, outperforming several baseline models.

翻译：基于图神经网络（GNN）的自编码器近年来因其提取信息丰富潜在表示的能力而备受关注，这些表示能够刻画复杂拓扑结构（如图）的特征。尽管图自编码器应用广泛，但专门针对符号网络开发与评估可解释的、基于神经网络的图生成模型的研究仍较为有限。为填补这一空白，本文提出符号图原型自编码器（SGAAE）框架。SGAAE提取节点级表示，这些表示反映了节点在网络中不同极端剖面（称为原型）上的隶属关系。这是通过将图投影到一个控制其极化的学习多面体上实现的。该框架结合了基于Skellam分布的符号网络分析似然函数、关系原型分析与图神经网络。实验评估表明，SGAAE能够成功推断节点在不同潜在结构上的隶属关系，同时提取网络中对立观点参与形成的竞争性社群。此外，本文提出了二级网络极化问题，并展示了SGAAE如何刻画此类场景。所提模型在四个真实世界数据集上的符号链接预测任务中均取得优异性能，超越了多个基线模型。