GC-Flow: A Graph-Based Flow Network for Effective Clustering
This work addresses clustering in graph data, offering a novel generative approach that improves over discriminative GCNs, though it appears incremental as it builds on existing graph convolution and normalizing flow techniques.
The authors tackled the problem of graph data clustering by developing GC-Flow, a generative model that replaces GCN layers with normalizing flows to model class conditional likelihood and prior, resulting in well-separated clusters while maintaining predictive power on benchmark datasets.
Graph convolutional networks (GCNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective, as a representation learning approach, the node representations extracted from a GCN often miss useful information for effective clustering, because the objectives are different. In this work, we design normalizing flows that replace GCN layers, leading to 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, retains the graph convolution operations while being equipped with a Gaussian mixture representation space. It enjoys two benefits: it not only maintains the predictive power of GCN, but also produces well-separated clusters, due to the structuring of the representation space. 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 clustering.