Title: Graph Convolutional Normalizing Flows for Semi-Supervised Classification and Clustering. Abstract: Graph neural networks (GNNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective for prediction, as a representation learning approach, the node representations extracted from a GNN often miss useful information for effective clustering, because that is not necessary for a good classification. In this work, we replace a GNN layer by a combination of graph convolutions and normalizing flows under a Gaussian mixture representation space, which allows us to build a \emph{generative model} that models both the class conditional likelihood $p(\mathbf{x}|y)$ and the class prior $p(y)$. The resulting neural network, GC-Flow, enjoys two benefits: it not only maintains the predictive power because of the retention of graph convolutions, but also produces high-quality clusters in the representation space, due to the structuring of the representation as a mixture of Gaussians. We demonstrate these benefits on a variety of benchmark data sets. Moreover, we show that additional parameterization, such as that on the adjacency matrix used for graph convolutions, yields additional improvement in classification and clustering.
