Abstract

Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they are not equally suitable for visualisation purposes, which we believe to be an important part of the research process—-they do not only help discern the structure of complex graphs, but, perhaps most essentially, provide a means of understanding the models applied to them for solving various tasks.

In this talk, we will present our recent work that merges Mapper, an algorithm from the field of Topological Data Analysis, with the expressive power of graph neural networks to produce hierarchical, topologically-grounded visualisations of graphs. We further demonstrate the suitability of Mapper as a topological framework for graph pooling by showing an equivalence with the DiffPool and minCUT pooling operators. Building upon this framework, we introduce a novel pooling algorithm based on PageRank, which obtains competitive results with state-of-the-art methods on graph classification benchmarks.

The paper, currently under review for ICML ’20, and code are also available.