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：近年来，基于图神经网络（GNNs）的自编码器因其能够提取信息丰富的潜在表示、刻画复杂拓扑结构（如图）的能力而受到广泛关注。尽管图自编码器已得到普遍应用，但专门针对符号网络开发与评估可解释的神经图生成模型的研究仍较为有限。为填补这一空白，我们提出了符号图原型自编码器（SGAAE）框架。SGAAE通过将图投影到一个控制其极化的学习多胞形上，提取节点级别的表示，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。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，我们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。