Abstract
Graph summarization has received much attention lately, with various works tackling the challenge of defining pooling operators on data regions with arbitrary structures. These contrast the grid-like ones encountered in image inputs, where techniques such as max-pooling have been enough to show empirical success. In this work, we merge the Mapper algorithm with the expressive power of graph neural networks to produce topologically grounded graph summaries. We demonstrate the suitability of Mapper as a topological framework for graph pooling by proving that Mapper is a generalization of pooling methods based on soft cluster assignments. Building upon this, we show how easy it is to design novel pooling algorithms that obtain competitive results with other state-of-the-art methods. Additionally, we use our method to produce GNN-aided visualisations of attributed complex networks.
Highlights
The abundance of relational information in the real world and the success of deep learning techniques have brought renowned interest in learning from graph-structured data
This result confirms that PageRank-based pooling exploits the power-law distributions in this domain
The performance of DMP is similar on social data and generally higher on molecular graphs. We attribute this to the fact that all nodes in molecular graphs tend to have a similar PageRank score—MPR is likely to assign all nodes to one cluster, effectively performing a readout
Summary
The abundance of relational information in the real world and the success of deep learning techniques have brought renowned interest in learning from graph-structured data Efforts in this direction have been primarily focused on replicating the hierarchy of convolutional filters and pooling operators, which have achieved previous success in computer vision Sperduti. We prove that SDGM is a generalization of pooling methods based on soft cluster assignments, which include state-of-the-art algorithms like minCUT (Bianchi et al, 2019) and DiffPool (Ying et al, 2018) Building upon this topological perspective of graph pooling, we propose two pooling algorithms leveraging fully differentiable and fixed PageRank-based “lens” functions, respectively. We investigate graph pooling as a tool for the visualization of attributed graphs
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