论文标题
深图映射器：通过神经镜头查看图
Deep Graph Mapper: Seeing Graphs through the Neural Lens
论文作者
论文摘要
图表示学习中的最新进展导致了捕获图的主要属性的凝结编码的出现。但是，即使这些抽象表示对于下游任务也很强大，但它们并不适合可视化目的。在这项工作中，我们合并了映射器，这是一种拓扑数据分析（TDA）领域的算法，与图神经网络（GNNS）的表达能力合并，以产生图形的层次结构，拓扑结构的可视化。这些可视化不仅有助于辨别复杂图的结构，而且还提供了一种理解用于解决各种任务的模型的方法。我们进一步证明了映射器作为拓扑框架的适用性，可以通过数学上证明与最小切割和DIFF池的等效性来汇总。在此框架的基础上，我们引入了一种基于Pagerank的新型合并算法，该算法通过图形分类基准的最新方法获得了竞争结果。
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.
