Graph Neural Networks (GNNs) and Variational Autoencoders (VAEs) have been widely used in modeling and generating graphs with latent factors. However, there is no clear explanation of what these latent factors are and why they perform well. In this work, we present Dirichlet Graph Variational Autoencoder (DGVAE) with graph cluster memberships as latent factors. Our study connects VAEs based graph generation and balanced graph cut, and provides a new way to understand and improve the internal mechanism of VAEs based graph generation. Specifically, we first interpret the reconstruction term of DGVAE as balanced graph cut in a principled way. Furthermore, motivated by the low pass characteristics in balanced graph cut, we propose a new variant of GNN named Heatts to encode the input graph into cluster memberships. Heatts utilizes the Taylor series for fast computation of heat kernels and has better low pass characteristics than Graph Convolutional Networks (GCN). Through experiments on graph generation and graph clustering, we demonstrate the effectiveness of our proposed framework.

本研究提出了基于Dirichlet Graph Variational Autoencoder (DGVAE)的图聚类成员资格作为潜在因素的方法，以连接基于VAEs的图生成和平衡图割，提供了一种理解和改进VAEs的图生成内部机制的新方法。

狄利克雷图变分自编码器