从全局到局部：基于粒度球的拓扑保持自适应图池化
Global to Local: Topology-Preserving Adaptive Graph Pooling via Granular-Ball
AI总结：
该研究提出TPAGP方法，通过粒度球划分生成多粒度图表示，结合多粒度图网络提升图分类性能，在基准数据集上优于现有池化方法，缓解了固定粒度策略的信息丢失问题。
AI中文摘要：
图池化旨在将图（包含节点嵌入及其底层拓扑模式）压缩为更紧凑的表示形式。现有研究主要关注节点过细粒度的表示，通过移除节点或将节点合并为簇逐步粗化图，从而忽略了图拓扑结构的全局到局部模式和自适应粒度。在实际场景中，图整体可视为最粗的粒度级别，封装了全局拓扑结构，从上到下呈现出逐步更细粒度的局部拓扑结构，该过程持续至每个子域达到自适应粒度为止。为此，我们提出一种新颖的拓扑保持自适应图池化（Topology-Preserving Adaptive Graph Pooling，TPAGP）方法，该方法通过整合节点特征与拓扑信息，将图动态划分为粒度球，从而生成多粒度表示，可有效捕获局部与全局结构模式。此外，我们设计了多粒度图网络模型，促进不同粒度间的特征交互与优化，显著提升图分类任务的性能。实验结果表明，TPAGP在各类基准数据集上均优于现有池化方法，有效缓解了固定粒度策略导致的信息丢失问题。
英文摘要：
Graph pooling aims to compress the graph, including both node embeddings and their underlying topological patterns, into a more compact representation. Previous works focus primarily on the overly fine-grained representation of nodes, progressively coarsening the graph by removing nodes or merging them into clusters, thus neglecting the global-to-local patterns and adaptive granularity of the graph's topological structure. In the real scenario, graphs as a whole can be considered the coarsest level of granularity, encapsulating the global topological structure, with progressively finer-grained local topological structures represented from top to bottom. This process continues until the adaptive granularity for each subdomain is reached. To this end, we propose a novel Topology-Preserving Adaptive Graph Pooling (TPAGP) method that dynamically partitions graphs into granular balls by integrating node features and topological information, enabling the generation of multi-granularity representations that effectively capture both local and global structural patterns. Additionally, we design a multi-granularity graph network model that facilitates feature interaction and optimization across different granularities, significantly enhancing performance in graph classification tasks. Experimental results demonstrate that TPAGP outperforms existing pooling methods across various benchmark datasets, effectively mitigating information loss caused by fixed-granularity strategies.
