发表机构
South China Normal University; Academy of Mathematics and Systems Science, Chinese Academy of Sciences（华南师范大学; 中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对现有图池化忽略邻居高阶连接的问题，提出基于Ollivier-Ricci曲率及其流的RicciPool方法，通过谱聚类学习分配矩阵，在蛋白质和社交网络数据集上验证了有效性。
AI 中文摘要
近年来，研究人员提出了一种图池化操作，类似于传统卷积神经网络（CNN）中的池化过程，旨在降低图卷积神经网络（GCNNs）的计算成本。虽然大多数基于GCNN的方法将图池化视为节点聚类问题，并提议学习一个聚类分配矩阵，但现有的基于聚类的池化方法往往仅关注图的粗略拓扑信息，忽视了邻居之间高阶相互连接的利用。在图上的消息传递方面，边上信息传递的难易程度反映了相邻节点之间的紧密程度，这显著依赖于邻居之间的互连性。在本研究中，我们通过考虑这种局部连接信息来解决这一空白，并提出了一种新颖的图池化方法，名为RicciPool。我们引入离散图曲率，特别是Ollivier-Ricci曲率，作为边周围高阶连通性的度量。随后，我们构建了一个Ollivier-Ricci流公式来重新加权边权重，利用Ricci曲率提供的关键信息，这对于提取图中的聚类尤为重要。在此基础上，我们利用谱聚类技术来学习一个新的聚类分配矩阵。在多个生物信息学蛋白质数据集和社交网络上的实验结果表明了我们提出方法的有效性。
英文摘要
Recently, researchers have proposed a graph pooling operation, akin to the pooling process in conventional convolutional neural networks (CNN), aimed at reducing the computation cost of Graph convolutional neural networks (GCNNs). While most GCNN-based methods treat graph pooling as a node clustering problem and propose learning a cluster assignment matrix, existing clustering-based pooling methods tend to focus solely on the rough topology information of graphs, neglecting the exploitation of higher-order mutual connections among neighbors. In terms of message passing on graph, the ease of information passing on edges reflects the closeness between neighboring nodes, which significantly relies on the interconnectivity among neighbors. In this study, we address this gap by considering such local connection information and introducing a novel graph pooling method named RicciPool. We introduce discrete graph curvature, particularly Ollivier-Ricci curvature, as a measure of higher-order connectivity around an edge. Subsequently, we construct an Ollivier-Ricci flow formula to reweigh edge weights, leveraging the crucial information provided by Ricci curvature, particularly vital for extracting clusters in graphs. Building upon this foundation, we utilize the spectral clustering technique to learn a new cluster assignment matrix. Experimental results on multiple bioinformatics protein datasets and social networks underscore the effectiveness of our proposed method.
