iPool -- Information-based Pooling in Hierarchical Graph Neural Networks
This addresses the need for effective hierarchical representations in graph neural networks, particularly for tasks like bioinformatics and social network analysis, though it is incremental as it focuses on an overlooked aspect (pooling) rather than a new paradigm.
The paper tackles the problem of graph classification by introducing a parameter-free pooling operator, iPool, which selects the most informative nodes to construct hierarchical graph representations, achieving state-of-the-art performance on most public datasets.
With the advent of data science, the analysis of network or graph data has become a very timely research problem. A variety of recent works have been proposed to generalize neural networks to graphs, either from a spectral graph theory or a spatial perspective. The majority of these works however focus on adapting the convolution operator to graph representation. At the same time, the pooling operator also plays an important role in distilling multiscale and hierarchical representations but it has been mostly overlooked so far. In this paper, we propose a parameter-free pooling operator, called iPool, that permits to retain the most informative features in arbitrary graphs. With the argument that informative nodes dominantly characterize graph signals, we propose a criterion to evaluate the amount of information of each node given its neighbors, and theoretically demonstrate its relationship to neighborhood conditional entropy. This new criterion determines how nodes are selected and coarsened graphs are constructed in the pooling layer. The resulting hierarchical structure yields an effective isomorphism-invariant representation of networked data in arbitrary topologies. The proposed strategy is evaluated in terms of graph classification on a collection of public graph datasets, including bioinformatics and social networks, and achieves state-of-the-art performance on most of the datasets.