The (variational) graph auto-encoder is extensively employed for learning representations of graph-structured data. However, the formation of real-world graphs is a complex and heterogeneous process influenced by latent factors. Existing encoders are fundamentally holistic, neglecting the entanglement of latent factors. This not only makes graph analysis tasks less effective but also makes it harder to understand and explain the representations. Learning disentangled graph representations with (variational) graph auto-encoder poses significant challenges, and remains largely unexplored in the existing literature. In this article, we introduce the Disentangled Graph Auto-Encoder (DGA) and Disentangled Variational Graph Auto-Encoder (DVGA), approaches that leverage generative models to learn disentangled representations. Specifically, we first design a disentangled graph convolutional network with multi-channel message-passing layers, as the encoder aggregating information related to each disentangled latent factor. Subsequently, a component-wise flow is applied to each channel to enhance the expressive capabilities of disentangled variational graph auto-encoder. Additionally, we design a factor-wise decoder, considering the characteristics of disentangled representations. In order to further enhance the independence among representations, we introduce independence constraints on mapping channels for different latent factors. Empirical experiments on both synthetic and real-world datasets show the superiority of our proposed method compared to several state-of-the-art baselines.

翻译：（变分）图自编码器被广泛用于图结构数据的表示学习。然而，真实世界的图形成过程复杂且异质，受多种潜在因素影响。现有编码器本质上是整体性的，忽略了潜在因素的纠缠。这不仅降低了图分析任务的效果，也使得表示的理解和解释更加困难。利用（变分）图自编码器学习解耦图表示面临重大挑战，在现有文献中仍鲜有探索。本文提出了解耦图自编码器（DGA）和解耦变分图自编码器（DVGA），这两种方法利用生成模型学习解耦表示。具体而言，我们首先设计了一种具有多通道消息传递层的解耦图卷积网络作为编码器，聚合与每个解耦潜在因素相关的信息；随后，对每个通道应用分量级流以增强解耦变分图自编码器的表达能力；此外，针对解耦表示的特性，我们设计了一种因子级解码器。为进一步提升表示间的独立性，我们针对不同潜在因素的映射通道引入了独立性约束。在合成数据集与真实数据集上的实验表明，与多个最先进的基线方法相比，本文方法具有显著优势。