It is largely agreed that social network links are formed due to either homophily or social influence. Inspired by this, we aim at understanding the generation of links via providing a novel embedding-based graph formation model. Different from existing graph representation learning, where link generation probabilities are defined as a simple function of the corresponding node embeddings, we model the link generation as a mixture model of the two factors. In addition, we model the homophily factor in spherical space and the influence factor in hyperbolic space to accommodate the fact that (1) homophily results in cycles and (2) influence results in hierarchies in networks. We also design a special projection to align these two spaces. We call this model Non-Euclidean Mixture Model, i.e., NMM. We further integrate NMM with our non-Euclidean graph variational autoencoder (VAE) framework, NMM-GNN. NMM-GNN learns embeddings through a unified framework which uses non-Euclidean GNN encoders, non-Euclidean Gaussian priors, a non-Euclidean decoder, and a novel space unification loss component to unify distinct non-Euclidean geometric spaces. Experiments on public datasets show NMM-GNN significantly outperforms state-of-the-art baselines on social network generation and classification tasks, demonstrating its ability to better explain how the social network is formed.

翻译：普遍认为，社交网络链接的形成源于同质性或社会影响。受此启发，我们旨在通过提出一种新颖的基于嵌入的图生成模型来理解链接的生成机制。与现有图表示学习方法（其中链接生成概率被定义为对应节点嵌入的简单函数）不同，我们将链接生成建模为这两个因素的混合模型。此外，我们将同质性因子建模于球面空间，将影响因子建模于双曲空间，以适应以下事实：(1) 同质性导致网络中出现循环结构，(2) 影响导致网络中出现层次结构。我们还设计了一种特殊的投影方法来对齐这两个空间。我们将该模型称为非欧几里得混合模型（NMM）。我们进一步将 NMM 与我们的非欧几里得图变分自编码器（VAE）框架 NMM-GNN 相结合。NMM-GNN 通过一个统一框架学习嵌入，该框架使用非欧几里得图神经网络编码器、非欧几里得高斯先验、非欧几里得解码器以及一种新颖的空间统一损失组件来统一不同的非欧几里得几何空间。在公开数据集上的实验表明，NMM-GNN 在社交网络生成和分类任务上显著优于现有最先进的基线模型，证明了其能更好地解释社交网络的形成机制。