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Graph convolutional networks (GCNs) are \emph{discriminative models} thatdirectly model the class posterior $p(y|\mathbf{x})$ for semi-supervisedclassification of graph data. While being effective, as a representationlearning approach, the node representations extracted from a GCN often missuseful information for effective clustering, because the objectives aredifferent. In this work, we design normalizing flows that replace GCN layers,leading to a \emph{generative model} that models both the class conditionallikelihood $p(\mathbf{x}|y)$ and the class prior $p(y)$. The resulting neuralnetwork, GC-Flow, retains the graph convolution operations while being equippedwith a Gaussian mixture representation space. It enjoys two benefits: it notonly maintains the predictive power of GCN, but also produces well-separatedclusters, due to the structuring of the representation space. We demonstratethese benefits on a variety of benchmark data sets. Moreover, we show thatadditional parameterization, such as that on the adjacency matrix used forgraph convolutions, yields additional improvement in clustering.

GC-Flow: A Graph-Based Flow Network for Effective Clustering