Deep Graph Mapper: Seeing Graphs Through the Neural Lens

Cristian Bodnar, Cătălina Cangea, Pietro Liò

Keywords: Graph Representation Learning, Mapper, Graph Neural Networks, Pooling, Graph Summarisation

TL;DR: We combine the Mapper TDA algorithm with graph neural networks to obtain a topologically-aware graph pooling framework, competitive with recent SOTA pooling methods.

Abstract: Graph summarisation 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 generalisation 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.

Previous Submission: No

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2002.03864/code)