Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings

TL;DR

The paper addresses signed graph representation learning by introducing SGAAE, a two-space, archetype-based autoencoder that uses a Skellam likelihood to model signed edges and a learned archetypal polytope to encode polarization. It equips separate GNN encoders for positive and negative interactions and enforces self-explainability through archetype memberships, enabling 2-level polarization to capture both intra- and inter-community dynamics. Empirical results on four real-world datasets show state-of-the-art performance in signed link prediction and reveal interpretable archetypes that distinguish positive and negative structures, with notable gains in challenging negative-link tasks. This approach offers a principled, explainable framework for analyzing polarization in social networks and could inform interventions addressing echo chambers and conflicting communities, while acknowledging optimization and parameter-count challenges.

Abstract

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.

Figures (5)

• Figure 1: Framework of the proposed Signed Graph Archetypal Autoencoder (SGAAE). Given a signed network as input, the model utilizes two GNN-based encoding components working on the positive and negative interactions, respectively. The archetypal membership matrices $\bm{z}_i,\bm{w}_i$ are procured which are later multiplied with the archetypal matrix $\bm{A}$ to get the final node embeddings for the positive and negative spaces $\Tilde{\bm{z}}_i,\Tilde{\bm{w}}_i$. Then the final embeddings are used to calculate the Skellam rates optimizing for the Skellam log-likelihood for reconstructing the original signed graph.
• Figure 2: Different levels of network polarization: Blue elements define positive ties whereas red define negative ties, displaying the total signed networks broken down into its two sign-specific components. (a) Showcases the traditional 1-level definition of network polarization focused on extracting structures with dense intra-community positive connections and negative inter-community ties. The adjacency matrices $\bm{Y}$, $\bm{Y}^+$, and $\bm{Y}^-$ and here are re-ordered based on the permutation matrix $\bm{\Pi}_{\bm{\sigma}^{(+)}}$ under the positive community memberships $\bm{\sigma}^{(+)}$. (b) Showcases two different permutations of the same signed network and its corresponding components that can be broken down under very dense positive communities and very dense negative communities. Importantly, the community memberships in the network for the negative and positive structures are not the same, yielding a 2-level polarization. The adjacency matrices in the left panel are re-ordered based on the permutation matrix $\bm{\Pi}_{\bm{\sigma}^{(+)}}$ under the positive community memberships $\bm{\sigma}^{(+)}$ while in the right panel we re-order $\bm{Y}$, $\bm{Y}^+$, and $\bm{Y}^-$ based on the permutation matrix $\bm{\Pi}_{\bm{\sigma}^{(-)}}$ under the negative community memberships $\bm{\sigma}^{(-)}$.
• Figure 3: Polarization Identity---Inner product proximity in Skellam rates.
• Figure 4: Inferred community memberships: (a)-(d) visualization of the re-ordered adjacency matrices based on the inferred community memberships of SGAAE, proving the expressive capabilities to provide characterization for both levels of polarization. (e)-(h) the same visualization for SLIM failing to explain or detect the structure over the negative ties and thus unable to account for the different polarization levels.
• Figure 5: Network Visualizations: for the WikiRfa where we show the re-ordered adjacency matrix based on the maximum positive/negative memberships to the archetypes---the positive/negative membership space where essentially we visualize the soft-memberships over the archetypes in a circular plot where each archetype is positioned every $\frac{2\pi}{K}$ rads.