Deep Graph Mapper: Seeing Graphs through the Neural Lens
This work addresses the need for better visualization and understanding of graph structures and models, with incremental contributions to graph pooling methods.
The paper tackles the problem of visualizing complex graphs by merging Mapper from Topological Data Analysis with Graph Neural Networks to produce hierarchical, topologically-grounded visualizations, and introduces a novel pooling algorithm based on PageRank that achieves competitive results on graph classification benchmarks.
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. In this work, we merge Mapper, an algorithm from the field of Topological Data Analysis (TDA), with the expressive power of Graph Neural Networks (GNNs) to produce hierarchical, topologically-grounded visualisations of graphs. These visualisations do not only help discern the structure of complex graphs but also provide a means of understanding the models applied to them for solving various tasks. We further demonstrate the suitability of Mapper as a topological framework for graph pooling by mathematically proving an equivalence with Min-Cut and Diff Pool. 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.